Department of Mathematics and Statistics, Binghamton University people:mckenzie

Assignments given on day of the lecture and are to be done before the following lecture. The range of days when you should be working on them is in bold.

For your convenience the first few days, I have put assigned exercise numbers here. Eventually, you will see only to “Do the assigned exercises in Sec X”, and the numbers will be found on the pdf Assigned Exercises. Exercises will be taken from other texts and worksheets as well.

—-

WEEK 1 August 24-27

Wed Aug 25-Thurs Aug 26 Read Chapters 1&2, paying attention to what was emphasized in class.

in Math 220 text and do the assigned exercises:

Section 1 page 5 #1, 2, 8a–i

Section 2 page 15 #1, 2a-e, 3, 5, 8, 9, 12, 14a–d

If you have time tonight (but ok to wait for weekend):

View Solving quadratic equations by factoring and Solving radical equations

Then do some problems on Solving quadratics worksheet and on Solving radicals worksheet

Fri Aug 27-Sun Aug 29 The first reading is from the Bittinger textbook. The first few pages are a review of lines, which you may or may not need. The applications pages are essential, and have better detail than our book.

Read Linear Cost, Revenue, Profit Functions (Bittinger text)

Read Sec. 3 in our textbook

View Cost/revenue/profit 1, Cost/revenue/profit 2, Cost/revenue/profit 3

Do exercises in our text Sec 3 page 26 #1–4; try #6–14 (the Bittinger reading and our text have many examples of this type)

WEEK 2 Aug 30-Sept 3

Mon Aug 30-Wed Sept 1 Note that many textbook solutions can be found under the link on the main Math 220 page, and here Annotated solutions to exercises

Finish reading Sec 3, our book and Bittinger pdf, esp the cost/revenue/profit pages (see weekend posting)

Read Sec 4 in our book

Do Sec 3 exercises #6-14 in our book

Review solving log and exponential equations in these videos, as much as you need each one to understand Properties of logs, Solving log equations, Solving exponential eqns (same base), Solving exp eqns (different bases)

Wed Sept 1-Sun Sept 5 View Wednesday lecture videos (total length < 90 min) Wednesday Lecture part 1, Wednesday lecture part 2, Wednesday lecture part 3/4

Do Sec 4 pp 42-44 #1–7, 10a–d, 11a–e, 12, 14 [do also base e], 20a–e, 21a, b, f

Watch the video The meaning of e

No quiz in class, obviously, today, but I will collect a homework (to be posted) next Friday, after break, and we will have a quiz on class on cost/revenue/profit and of course the essential function graphs!

WEEK 3 Sept 6-10

View mini-videos and read Sec 6 on Limits

Finding limits from a graph (This is one of his rougher videos, but well explained.)

Evaluate limits using properties, Ex 1

Evaluate limits using properties, Ex 2

View my Lecture on Limits (the Friday lecture video) No need to watch it all in one sitting.

Do Assigned Exercises (Sec 6) on p 66 (pdf p 71)

NOTE: I'll check attendance for Wed and Fri by looking at the Panopto logs (who viewed and for how long). Wed lecture took four smaller recordings. Fri I did in one long recording, so take a break in the middle!

Do Take-home quiz (Quiz 1). SUBMIT IN PERSON FRIDAY.

Study for Friday's in-class Quiz 2: Essential fcn graphs, piecewise fcns, domain, solving a radical and an exponential equation.

See Math 220 page for folder with DCN notes. These are Instructor David Cervantes Nava's lecture notes, which he's sharing with all sections. Feel free to access them to supplement my own.

WEEKEND OF SEPT 10-12 View the rest of the limit videos finish the limit exercises (I haven't done an example of indeterminate form in class, but below Patrick does loads of them):

More techniques for evaluating limits, Ex 3

Ex 4 involving radicals

Ex 5 also with radicals

Ex 6 involving rational expressions

Infinite limits

Read Sec 5

View Where does e come from?

The History of e

Compound interest (n times/year)

Continuous interest (infinite times/year)

WEEK 4 Sept 13-Sept 17

Mon Sept 13-Tues Sept 14

Extra help videos on Finding domain 1 and Finding domain 2; here's the supplementary worksheet with Practice on domains

Do Sec 5 pp 56-57 (first set of exercises only): #1, 3, 2 (in this order), #4–7

Wed Sept 15-Thurs Sept 16

Read Sec 7 and Sec 8 and view Difference quotient (DQ) and the definition of derivative

Do Sec 7 Assigned Exercises #1b, d, a, c, e, f (in this order), 3a–g

Study for Friday quiz on exponential equation solving, limits and compound interest

Do Take home #1 (compound interest) and hand in Friday

Friday Sept 18-Sunday Sept 20

The videos will take the place of the reading of Sections 9 and 10:

Differentiation Techniques and the Power Rule

Power rule examples

Do Assigned Exercises in Sec 8: #1-5 using power rule, not the definition of derivative!!

Read Selection 1 and Selection 2 on marginal functions and derivatives

Do Exercises Sec 10 p. 91 #3, 4, 6

Finally, watch Continuity and limits made easy

WEEK 5 Sept 20-Sept 24

Mon Sept 20-Tues Sept 21

Exam 1 is moved to Monday Sept 27

View (for real):

Derivative exponential fcn with base a

Derivative log fcn with base a

Product rule examples

Quotient rule examples

Do Sec 10 Asssigned exercises #8–10, 13a, d, e, 15, 16a–g, j

Supplemntary reading (and a great learning aid) Bittinger derivative sections

Derivative shortcut quiz tomorrow. Be ready, no notes.

Wed Sept 22-Thurs Sept 23

View (and I'm serious):

Proof of chain rule

Chain rule explained by Patrickmjt

Ex of chain rule for radical function

Ex of chain rule for natural log function

Read Sec 11

Do Assigned Exercises Sec 11 #1, 2a–h, k, l, 3a–f, h–o, r, 4c, d, e, 6, 7, 9, 13 all, 15, 16a–g, j, m–o

See Prof DCN and Student MK for their lecture notes, which are also on the Math 220-03 and -04 Fall 2021 main page

REVISED DERIVATIVE RULES AND EXAMPLES

Sept 25-26 Weekend study for Exam 1

The topics to focus on include (the first was not mentioned on Friday):

Solving for intercepts and roots of a function (critical skill we looked at the first week)
Domain of functions (interval notation) and graphing piecewise f(x) made up of essential functions
Find equation of a line tangent to a curve f(x) at a point
Evaluate limits including the in the definition of the derivative for one function
Continuity–reading from a graph where a function is not continuous and why it fails according to the definition: f(x) is continuous at x = a if f(a) exists and is equal to lim f(x) as x –> a
Cost/revenue/profit functions, demand function, break even point, marginal analysis (ideas from handout)
Derivatives computation, see REVISED DERIVATIVE RULES AND EXAMPLES
NO COMPOUND INTEREST ON THIS EXAM

Here is a another professor's previous semester exam solutions with some notes on tomorrow's exam

WEEK 6 Sept 27-Oct 1

Wed Sept 29

Implicit differentiation method often lets us find rates of change of one variable with respect to another even if there is no explicit function present. For example, the circle isn't a function, but its tangents are of interest to us. Differentiating the equation without solving for either of its 'branches' (top and bottom semicircles) is easier using ID.

Implicit differentiation (ID)

Proof of derivative of natural log function and Proof of derivative of exponential function (base a) both use implicit differentiation.

More ID examples (at 3:30 the ex has a non-trig equation)

Read Sec 14 Related Rates and corresponding section in Bittinger, Section 2.7 (pp 288-292)

Do Assigned Exercises for Sec. 12 #1, 2a, b, 4, 7, 8, 9 and Sec. 13 #1, 2a–c, 3, 5, 6, 8 (for discussion tomorrow)

Hand in tomorrow: Sec 12, #7, 8, 9 and Sec 13, #2c, 3, 6

Friday Oct 1

Watch Using ln and implicit differentiation to replace product and quotient rule

Do Assigned Exercises in the textbook for Sec 14 Related rates #1–6, 8–10, 12, 13. These are not the ones to hand in, but have them handy to show me later in the week

Friday recording I made a division mistake toward the end. See if you can spot it.

Add to the HW to hand in:Bittinger related rates problems (see Sec 2.7 in that text)

Previous HW said there would be a quiz on Monday, but that was a mistake. The next quiz is Wednesday. Thanks JC for catching it.

WEEK 7 Oct 4-8

Mon Oct 4-Tues Oct 5

Critical numbers . A critical number x = c of a function f(x) is a number in the domain of f where EITHER f'(x) = 0 OR where f'(x) does not exist. The relative extrema of a function occur at critical numbers.

Finding the critical numbers of a function is the first step to examining the behavior that a function models. Where it increases, decreases, attains local extremes and so on.

Read Sec Sec 2.1 of Bittinger (roughly corresponds to Sec 15 of our book)

View:

Extremes of a function

Critical numbers 1

Critical numbers 2

Increasing and decreasing functions

Do in our text the assigned exercises in Sec 15 on pp 129-130 #2, 4 a-i

Let's move the mini-quiz to FRIDAY. It will be on implicit differentiation and related rates.

Wed Oct 6-Sun Oct 10 Read Bittinger Sec 2.2 (corresponds to our textbook Sec 17; we're skipping Sec 16 for now)

View More finding critical numbers of a fcn

First derivative test

Second derivative test and concavity

I will you make copies of McKenzie summary of Secs 15, 17, 18

Mini-quiz Friday: 1 related rates problem and 1 implicit differentiation, similar to Bittinger word problems.

Bittinger exercises ! Work on these throughout the rest of the week and the weekend. It's not as much as it looks. Some are short answer.

You'll do these instead of our text exercises, and be sure you read the Bittinger sections as well:

Read Sec 2.1 and do exercises #7, 13,19, 21, 23, 27, 29, 71, 83, 89

Read Sec 2.2 and do exercises #9, 13, 27, 35, 39, 45, 49, 51, 103, 109, 113

WEEK 8 Oct 11-15

Mon Oct 11-Tues Oct 12

Read Sec 2.3 in Bittinger

View the following videos on curve sketching using skills learned so far:

Examples first and second derivative test to graph functions

Graphing a polynomial

Graphing a rational function

Graphing another rational function

Wed Oct 13-Sun Oct 17 Do over Fall break and hand in on Monday: Practice curve sketching assignment

You may use your notes and videos, but work independently!

For #4, the rational function, I plan to cover it tomorrow. We will do it as an in-class exercise, before you hand it in!

Also, though not to hand in: Revisit the topic of Related rates with supplemental worksheet; the solutions are available at the Supplemental Materials link.

WEEK 9 The assignments are given in one list to work on up till Tues Oct 26, the day before Exam 2

Exam 2 Oct 27 covers Sections 13 through 22 in our textbook

NOTE: DCN's latest lecture available notes are now posted, though one section is missing; he will share it soon

Read in Bittinger Secs 2.2-2.4 – not every word, but look at the examples and the wonderful graphs

Do in Bittinger – refer to Steps to curve sketching for guidance (and we will do several in class)

Sec 2.2 #7, 11, 25, 35, 41, 43, word problem #106

Sec 2.3 #3, 7-21 odd, 29, 31, 35, 41 (hole), 49, word problems #63, 65, 67, 73

Sec 2.4 #5, 15, 21, 35, 37, 53, 61, 79, word problem #103

Short videos on the Sec 16 theorems; a light treatment of the concepts will be on Exam 2:

Intermediate value thm

Rolle's and mean value thms

Extreme value thm which relates to absolute extrema.

In applications, the domain is usually a closed interval, so we need to check not only local extreme values but also the function value at its endpoints. Problems in this will be posted soon

POP MINI QUIZ ON FRIDAY We will correct it in class. It will be on curve sketching!

WEEKEND STUDY FOR EXAM 2

First of all, I realize I never linked you to the Videos for related rates. Here they are!

Implicit differentiation and related rates

And finally, a video on related rates that applies to a business application:

Cost and profit with respect to time

WEEK 10 Oct 25-29

Exam 2 review exercises for Monday

In-class solutions of Exam 2 review exercises

Rest of solutions 1, 2, 3, 4, 5, and 6

For WEEKEND 11 Oct 29 - Nov 1

We begin Unit 3 – OPTIMIZATION (maximization/minimization of functions).

We use critical numbers and extrema to find where functions such as revenue, cost and profit reach their max or min. There is also more discussion of demand functions vis-à-vis elasticity of demand and how this plays into maximizing revenue. Price is looked at more closely now. We also look at multivariable functions, which are more typical of real life, since more than one variable type often figures in any of the functions we have studied.

The unit roughly covers Math 220 Course Notes (Geoghegan text) Sections 22-29 and Bittinger Sections 2.4 and 2.5 and Sections 6.1-6.3 and 6.5. We will be reading from both books.

Fri Oct 29 - Sun Oct 31 (boo)

Over the weekend, please do Assigned Exercises #3a–e, 4–8 in Sec 22 read in our text.

Read Sec 23 and do #1-7

View Minimize surface area of a cylinder and Optimal pricing to maximize computer software sales

WEEK 12 Nov 1 - Nov 5

Mon Nov 1 - Tues Nov 2

Watch all at least once; the content is seen in quizzes and tests for the next two units

Sec 23, p 192 do #9, 10, 12, 15, 16

View Hot dog problem and Optimizing revenue given two points of data

Read Sec 24

TAKE HOME OPTIMIZATION QUESTIONS DUE FRIDAY Show all work, neatly, no partial credit for partial work Work independently. It's open book and notes. The videos I've put up should be sufficient, but see me if you need guidance.

Wed Nov 3 - Thurs Nov 4

STUDY FOR FRIDAY OPTIMIZATION QUIZ (it will cover Sec 23 and Sec 24 homework problem content)

Do Sec 24 p 199 #1-9

Wednesday lecture videos are at 11:20 class and 1:10 class

Prof DCN Lecture Notes and Student MK Lecture Nots are up to date at these links.

WEEKEND Fri Nov 5 - Sun Nov 7

Take a break from optimization exercises till Sunday.

Elasticity of demand part 1 and part 2

Do Sec 26 exercises p 212 #1, 3-8 (we can do #3 in class on Monday)

View Super cool graphics explaining partial derivatives

and Partial derivative examples

Here is the Workshopped Quiz 5 to hand in for a grade on Monday (even if you were present, I would like to collect it)

WEEK 13 Nov 8 - Nov 12

Mon Nov 8

* Do Sec 27 partial derivatives, assigned exercises #1a, b, d, e, f, h, I, 2a–d, f, #3–5, 7

View Anil Kumar's example of the Lagrange multiplier method of solving optimization w/constraint

Read and see the many examples in Bittinger Sec 6.5, Lagrange multiplier method

Short quiz Wednesday on elasticity and partial derivatives

Wed Nov 10

VERY IMPORTANT VIDEOS:

1. Krista King's example of Lagrange multiplier method

2.Anil Kumar's 4 examples of the Lagrange multiplier method

3. Understanding the Cobb-Douglas production function (and its marginals) P(L,K), where L is units of labor and K is units of capital

4. Solving a Cobb-Douglas production function for L and K that result in maximum production

To study/work through for exam review:

As emailed: Practice problems Exam 3 (you won't have curve sketching) and Solutions

To practice Lagrange optimization: Our text, Sec 29 p 233 #1, 2a, b, c, 4–6, 8, 9

WEEK 14 Nov 15 - 19

Mon and Tues

We are in the final and most important unit. If you don't watch the videos before class as assigned you will not be able to grasp the content in lecture. Integration applications make up a major area of calculus in all the disciplines where it is used.

Read the first several pages of Bittinger Integration Part 1 (Antiderivatives)

Watch: Antiderivatives and indefinite integration

Examples of basic indefinite integration

Wed-Thurs

Do Exercises #1-70 every odd numbered exercise on PDF pp 9-11 in Bittinger Integration Part 1 (Antiderivatives)

Fri-Sun The previous videos included ones I didn't mean to post at at the start of the unit. I've reviewed and adjusted the videos:

View Overview of antiderivatives and initial condition problems

Read all of pp 1-9 of Bittinger Integration Part 1

Do #47-57 odd, Bittinger pdf p 10

View Applying integral to marginal cost to find total cost function

Do #61-66 all, Bittinger pdf p 10

THANKSGIVING WEEK(END) Nov 22 - 28

For Monday Nov 29, preview: u-substitution (up to minute 6:00 is indefinite integrals; after that he does definite, which you can watch as a preview of week ahead – super easy!)

Read all of Sec 4.5 (u-substitution) pp 436-442 in Calculus and Its Applications, 10th ed. Bittinger et al.

Do in Bittinger pp 443 and 444: #5-25 odd, #63, 67, 69 (two u-subs are needed, see Example 12 technique) and word problems #71-73

WEEK 15 Nov 29 - Dec 3

Monday Lecture video

Due Wednesday, Dec 1, really, no exceptions: Integration take-home 1

Mon-Tues Little change here: going back to our text, where we don't run into definite integrals just yet

Sec 30: Antiderivative word problems without u-sub, pp 242-244 #4-8

Sec 31: u-sub – read for many great examples; do pp 248-249 #1 all and #3–5

Sec 32: Integration by parts – view Integration by parts; read; do #1 b, d, e, g, h, i, #3

Sec 33: View this fantastic pre-lecture video (up to minute 7:10):

Finding a definite integral, fundamental theorem of calculus

Due to my illness, class will again be on zoom tomorrow. It will be the same link as usual, but you will get it in an email. I will send the invite to you 10 minutes before we meet so you have no trouble accessing it.

Wednesday Sec 03 lecture recording and Sec 04 lecture recording

Now watch ALL of Finding a definite integral, fundamental theorem of calculus

Do Sec 33 exercises #1b, c, e, h, I, j, k, o, p

Quiz on Friday, no notes allowed, u-sub, IBP, word problem, and evaluate a definite integral!

Weekend Dec 4/5

Watch the mini-videos for definite integrals in case you didn't check the link on your own :

Example 1 and Ex 2 and Ex 3 (log and IBP) and Exs. 4 and 5 (two more IBP)

Do Sec 34 exercise #1a–f, 4, 6a, c, e, g, 8, 9

Read Sec 35 first pp (Riemann sum and average value of a function)

FINAL WEEK !!

Mon-Tues

View this very short video on Average value of a function theory and formula and An example and Average value of a function and applications (word problems in second half)

As you just saw in the videos, the average value of a function on [a, b] is simply the definite integral of the function on the interval, all divided by the length of the interval.

Do assigned exercises Sec 35 #1 a, d, e, 2, 3, 7, 8, 10

Before you read the rest of the Sec 35, you should review Compound interest and future value and Present value

Then view Applying definite integrals to continuous income streams

Wednesday Finish Sec 35 exercises #11-16,18

I recorded the second lecture on Wed due to a reasonable student request. It's a better presentation than the first:

Wednesday zoom lecture, recorded

FINAL REVIEW WORKSHEETS (you will notice some duplication among these documents; along with supplementary worksheets as needed):

Unit 4 integration review exercises

More Unit 4 integration review exercises

A few more Unit 4 integration review exercises

Unit 4 previous semester comprehensive quiz

TUESDAY DEC 14

First set EXAM 4 REVIEW EXERCISES PART I AND SOLUTIONS

Second set EXAM 4 REVIEW EXERCISES PART II AND SOLUTIONS

Third set Unit 4 Find total function from various rate functions of economics and business (know how to set these up; the numbers on these are best done on a calculator, whereas the numbers on the test will be mental math friendly)

FINAL EXAM FRIDAY DEC 17 12:50-02:50 PM IN LH 014

people:mckenzie:kate_s_notes

2018-04-24T17:11:21-04:00

people:mckenzie:lecture_notes

2015-05-06T16:26:49-04:00

Domain, lines piecewise functions

Exponential and log functions

Compounding interest

Limits and continuity

Difference quotient and derivative of a function

Derivative formulas sec 10 and 11

Local max and min

Def of critical pt and example, higher order derivative example

More on min, max IVT, EVT, MVT, Rolle's, critical numbers

Test 2 review notes

Test 2 review notes continued

Class notes on intro to curve sketching with calculus

Summary of first and second derivative with examples

Sec 17 curve sketching with some hw

Sec 18 curve sketching with some hw

Sec 18 curve sketching with some hw continued

Sec 21, 22 abs extremes on closed interval

Sec 23 optimization notes

Sec 24 elasticity notes

Sec 30 initial notes on antiderivative

Sec 31 and 32 u substitution and integration by parts

Sec 33 Definite integrals, fundamental theorem of calculus

Sec 34 Area (net and actual)

Sec 35 Riemann sum average value and more area under a curve

Sec 35 Present and future value

Sec 36 Improper integrals

people:mckenzie:lecture_notes2

2016-11-19T19:56:45-04:00

Compound interest and present and future value

Limits

Difference quotient

Equation of tangent line to a curve

Overview of critical numbers and why f(x) = |x| where f'(0) DNE

More on critical numbers, local max and min with examples

First derivative test (sec 17 cost problem)

Sec 17/18 FDT SDT worked problem

people:mckenzie:lecture_notes_fall_2014

2014-11-25T10:40:42-04:00

Notes on one-one even odd fcns

Inverse function overview

Inverse of a function example with domain notes

Inverse function example

Solving a radical equation

Multiplicity of roots

Graphing functions and transformations

Lines and parabolas

Absolute value properties

Solving systems of equations

Sigma notation summary and examples

The unit circle

More on the unit circle with worked examples

Revised notes on graphing transformations of trig functions

people:mckenzie:lumen

2020-04-09T16:36:48-04:00

Math 220 uses Lumen and Online Homework Manager (OHM) for additional instructional videos, readings, and graded homework assignments:

Accessing our OHM course:

Navigate to Lumen OHM
Click on “Enroll in a New Course”
Enter the Course ID 41043 and Enrollment Key KM220
Confirm course details and click on “Enroll”
If you already have an OHM account, login; otherwise, sign up for a new account
Once inside, click on “Help Using Lumen OHM” in left-side navigation bar for instructions

people:mckenzie:math106

2022-12-08T19:48:45-04:00

WELCOME TO MATH 106

Refer to this page for daily announcements, assignments, and other resources and materials (including videos, pdfs, and even links for emergency remote meetings).

Syllabus

Revised schedule will be posted here soon.

NOTE: Each assignment is written on the day you are to do it, not the day it is due. So an assignment on Tuesday is to be done by Thursday. Tues assignments are usually a bit longer than other days.

I do not collect assignments unless I announce ahead of time that I will do so. It is up to you to work them through and to have questions for me when the class next meets.

WEEk 1 AUG 23-26

ALL CLASSES NOW MEET ALL DAYS IN SCIENCE II ROOM 255

Read Section 1.1 Real numbers in textbook Intermediate Algebra for College Students

Note, you can access a free e-book for about 12 more days at BVT press. Enter A2826662 in the Instant Access Code field and click on the “Go” button. Follow instructions to create an account.

Do Sec 1.1 exercises (pp 7-8), #1-40
For Thursday: Read Sec 1.2 Fraction operations, order of operations
For Friday: Do Sec 1.2 exercises (pp 19-20) #1-32 even, #34-60 even & #73-76

WEEKEND AUG 26-28

Lecture notes Week 1
Complete the 'For Friday' exercises (above)
Read Secs. 1.3 & 1.4 Signed numbers and Basic exponents

Do this quiz as practice, using your notes. Hand it in with your actual quiz tomorrow.

WEEK 2 AUG 29-SEPT 2

Monday

* Mini-videos to watch tonight: Rules of negative numbers

Fun number line with a bird

Evaluating algebraic expressions

Do Sec 1.3 exercises (pp 23-24) # 1-28 even and 40
Do Sec 1.4 exercises (pp 28-29) # 1-54 even and 57, 62, 64, 68

Tuesday

Catch up on Monday's posted items
Read Sec 1.5. Properties of reals
Do Sec 1.5 exercises (p 34) # 19 & 26-50 even

Thursday I was out this day, but you should have read this anyway.

Read Sec 1.6 Basic absolute value and absolute value inequality
View Basic absolute value equations and Basic absolute value inequalities
Do Sec 1.6 exercises (p 43) # 1-22 even & 31-68 even

Friday through Labor Day Though we will not have covered much into rational (“fractional”) exponents by the end of Friday's lecture, please read those sections and view the essential videos on them at the bottom of this homework section.

Read Secs 8.1 & 8.2 Integer exponents
View Exponents explained
Do Sec 8.1 (p 279) #16-68 every other even; Sec 8.2 (p 284) #1-71 every other odd
View:

Here are Lecture Notes Week 2

WEEK 3 SEPT 6-9

Tuesday Repeating the exercises from the weekend: do these, and be ready with questions for me!

Do Sec 8.1 (p 279) #15-67 every other odd Do Sec 8.2 (p 284) #1-71 every other odd

At the top of this page, under the syllabus, is the Schedule and Readings and Exercise List for the semester

Thursday

Read (if you have not yet done so) Sec 8.3
Do Sec 8.3 p 291 #1-63 odd – here are the videos again:

Lecture notes Week 3

Friday-Sunday

View simplifying a radical with variables; these are similar but each has helpful examples:

Do Sec 8.4 p 197 #1-67 odd

Start preparing for Exam 1, Monday Sept 19!

WEEK 4 SEPT 12-16

Mon and Tues Finish the Sec 8.4 homework – here's another video on Simplifying radicals

View Combining radicals with addition and subtraction and Rationalizing the denominator

Read Sec 8.5 and do the assigned p 301 #1-43 odd (as many as you can with the reading and the videos as a guide)

IMPORTANT: You will not need to rationalize a two term denominator on this exam!

Watch the Office hour Thursday video!

Watch for the review sheet soon! Work on it and bring your work to class to ask questions tomorrow ~

Friday Exam 1 has been moved to Monday, Sept 19.

There’s an excellent set of review exercises in your book!! See pp 45-49 for Ch 1 and pp 312-316 for Ch 8. Exclude imaginary numbers (anything with i) and rationalizing denominators if they entail sums or differences of radicals, which requires radicals.

WEEK 5 Sept 19-23

Monday

Read Sec 2.1 Linear equations
View these mini-videos on Solving Linear Equations:

Do Sec 2.1 (p 59) #11-45 odd, 53,57
Read 2.2 Word problems

Wednesday

Do Sec 2.2 (p 66) #1,3,5,15,17,23,25,41,43,45
Read Sec 2.3 Formulas
Do Sec 2.3 (p 71) #1-27 odd

FRIDAY WE WILL MEET REMOTELY AT THE ZOOM LINK

Friday 9/23 through Wednesday 9/28

Read Secs 2.4, 2.5 Linear inequalities, abs value equations
View these mini-videos on Solving Linear Inequalities :

Do Sec 2.4 (p 76) # 1-47 odd
Read 2.5 Abs value equations, inequalities
Do Sec 2.5 (p 81) # 1-47 even

Sunday posting Here's the weekend homework!

We are back to doing the quiz for homework! Watch the these mini-videos (repeating from above):

WEEK 6 Sept 28-30

Wednesday

Catch up on homework listed for over the weekend
If you hope to correct any errors of content from you first exam, I recommend you work through Exam 1 Sec 01 and Exam 1 Sec 02. I appreciate that some of you asked to see these in clean form again.

Thursday

I accidentally posted a shorter version of the quiz than what I handed out in class on Friday. As long as you handed in one of these papers, you will have your homework credit. Obviously, I prefer you be in class and get the handout in order to avoid this kind of situation.

For tonight, go back and read sections 2.4 and 2.5. No written homework tonight, as I worked on something different with you today. However, please watch these videos on absolute value equations and inequalities:

Solving absolute value equations

Solving absolute value inequalities example 1

Solving absolute value inequalities example 2

Solving absolute value inequalities example 3

WEEKEND HW A familiar topic that you’ll enjoy!

Read Sec 7.1 and 7.2 Slope of line, equations of lines

View:

Graphing lines from a point and slope

Find equation of line using point-slope form

Do exercises in Sec 7.1 (p 242) #2-20 even & Sec 7.2 (p 251) #2-30 even. (The videos will be very helpful.)

I’ll desk check these on Monday; show your work and be sure you show all your work!

WEEK 7 OCT 3-7

Monday There's a mini-quiz on absolute value equation and inequalities tomorrow (Tuesday)–no make-ups, don't miss it!

Practice question |5 - x| = 9 |5 - x| < 9 |5 - x| > 9

Solve each, expressing the answer algebraically, graphically, in interval notation.

Tuesday-Thursday By now you should be able to finish Sec 7.2 (p 251) #2-58 even

Read Sec 7.3 and view Graphing vertical and horizontal lines

Graphing parallel and perpendicular lines

Do Sec 7.3 (p 259) #1-16 all

In Sec 7.2, add word problems #69-72

I will update the schedule to reflect our pace and topics in class. No quiz tomorrow.

We will finish Ch 7 tomorrow and Monday, so please bring your Ch 7 pp (all of them) to class Friday.

WEEKEND OCT 7-9

Look over Lecture notes from the last 2 weeks. The first page of Friday's outlines the topics for Exam 2, which is Thursday. I'm adding percent word problems. See practice problems under Monday homework.

Friday-Sunday

Read Sec 7.4 Linear inequalities of two variables

View Graphing linear inequalities in one or two variables

Do Sec 7.4, p 266, #1-35 odd

Read Sec 12.1 Distance & midpoint

Exam 2 topics

WEEK 8

View Distance and midpoint formula

Do Sec 12.1, p 448, #1-25 odd

Practice exercises for Exam 2 will appear here

IMPORTANT: The first part of Exam 2 will be on Thursday and the second part on Monday. We will go over word problems Friday and they start the new material Tuesday.

Thanks to Amanda for asking for better detail on the percent problems!

Wednesday Since Exam 2 is moved to Friday/Monday, I will have extra office hours tomorrow (Thursday) from 2 to 4.

You can also, at any time on the following fliers, see an EOP tutor:

FALL BREAK WEEKEND HOMEWORK OCT 21-23

Friday-Sunday REQUIRED VIEWING ON POLYNOMIALS

The next section is a topic that you have done recently, either during summer workshop or in several high school mathematics classes.

We are several sections behind! You are responsible for watching these videos and doing the worksheets that form the basis of Unit 4.

The terrific internet teacher Professor Dave gives lectures that are very clear and enjoyable. Most of these videos have a 'Checking comprehension' section at the end. Do these sections. They will help you with the homework.

Intro to polynomials (5 minutes)

Adding and subtracting polynomials by combining like terms (about 5 minutes)

Multiplying polynomials by FOIL (about 6 minutes)

Factoring polynomials and solving quadratics (about 10 minutes

DO ODD NUMBERED PROBLEMS: I WILL DESKCHECK THE WORKSHEETS ON MONDAY

Polynomial wksht 1--Simplifying & evaluating; Multiplying general distributive & FOIL

Polynomial wksht 2--Multiplying special products

Polynomial wksht 3--Common factoring

WEEK 9

All the worksheets will come from the **Open access text**

Over the weekend you did work from Sections 5.1, 5.2 and 6.1. Worksheet answers are on the following pp of this pdf:

Polynomial wksht 1, pp 459-460 under 'Answers to Introduction to Polynomials' & Answers to Multiply Polynomials'
Polynomial wksht 2, p 460 under 'Answers to Special Products'
Polynomial wksht 3, pp 461-462 under 'Answers to Greatest Common Factor'

Monday

In the Open Access Text, read Ch 6, Secs 6.1-6.3 (pp 212-221). (Note that you did the Sec 6.1 worksheet already, so if you understood it fine, then you may skip this reading)

View Factoring by grouping

Do the fourth worksheet, p 220, Factor by Grouping (I will turn this into a worksheet from home computer, as it doesn't work in the math dept office computer)

Go back and watch carefully Factoring polynomials and solving quadratics (about 10 minutes

Tuesday-Wednesday

Remote lecture 8:30 class recording

Posting for the second time, read Sections 6.1-6.3 (pp 212-221) in Open Access Text and do the following worksheets:

Polynomial wksht 4--Factor by grouping

Polynomial wksht 5--Trinomial factoring, leading coeff = 1

Don't forget that all these times are available for tutoring:

"First Year math tutoring hours"

Dan McKinney "Math Master tutoring and review sessions"

Thursday

In Open Access Text do:

Poly wksht 6 -- factoring, leading coeff NOT = 1, do odd only

Poly wksht 7 -- Factoring special products, do all odd except #30-40

And if you like, Poly wksht 8 -- Factoring all kinds, your choice for practice

View:

Solving quadratic equations by factoring

Friday-Sunday

Do Poly wksht 9 -- Solving quadratic equations by factoring, odd only (first several are already factored)

View: Professor Dave shows how to complete the square to solve for the roots of a quadratic trinomial we can’t factor (this is a replacement of the previous one; Professor Dave uses the familiar formula)

Do 1-8 in Poly wksht 10 -- Complete the square, fill in the value that completes the square

Professor Dave derives the quadratic formula for finding the roots of a quadratic equation

Do Poly wksht 11 --Solving quadratic equations by quadratic formula , odd only

WEEK 10

Mon-Wed Finishing quadratic polynomials and study for Exam 3

Exam 3 topics

General form of a polynomial expression in x: be able to identify degree and coefficients; sometimes the coefficients are zero because a term is not seen.

Given a list of expressions in x, be able to eliminate those which are NOT polynomials.

Evaluate polynomial expressions for a given x.

Remember, the square root of 1 is 1 and the square root of 0 is 0.

FACTORING:

Factoring by GCF (both numerical and variable – know the exponent rule that dividing like bases requires subtracting the exponents); factoring by trinomial factoring, factoring by grouping; factoring special products (difference of squares.

There is no factoring for a sum of squares).

Reduce a rational expression (which is a polynomial divided by another polynomial) by factoring them.

(a - b)/(b - a) = -1

Completing a square: find the constant to add to the x terms so you create a square of a sum or a difference.

SOLVING

We use the zero product property on the factored polynomial to find the roots of the polynomial equation. It is this: if AB = 0 then either A = 0 or B = 0.

Be able find the roots (x-intercepts, zeros) of quadratic equations by factoring and/or by using the quadratic formula (which comes from completing the square).

YOU MUST MEMORIZE THE QUADRATIC FORMULA.

General form of the quadratic polynomial equation y = ax^2 + bx + c, whose graph is a parabola.

Know that the y-intercept of any polynomial is simply the constant coefficient ao. In the case of the quadratic (parabola), it is simply the c.

Reducing roots after using the quadratic formula. This entails radical simplification and regular fraction reducing.

Two-term quadratics don't need to be factored. Just use the fact that if x^2 - c = 0, then x = +/- square root of c; but if x^2 + c = 0, then no real number solution exists.

Be able to graph these simple two-term quadratics:

y = x^2, y = x^2 + c, and y = x^2 - c; know that the first has one root, (0, 0), which is also its y intercept. The second has no roots, only a y-intercept. The third has two roots, x = +/- c.

All parabolas have a y-intercept, but they may be lacking roots.

Go over the Lecture notes for Weeks 9 and 10 up through Tues review day. Look over the worksheets and any problems you had to do in the Kohlman text.

Practice exam 3 part 1

Practice exam 3 part 2

WEEKEND NOV 6-7

Solving systems of linear equations! You can do this without me. It's all algebra we have done. Have at it!

Read in Open Access Text pp 134-143

View: Solving systems of equations by graphing, and

Solving linear systems by substitution

Do #1-25 odd in each set of exercises Worksheet 12 -- Solving linear systems by graphing and substitution

WEEK 11

Mon-Tues I didn't put any hw up on Monday, my oversight!!

Wed

Study for a Thursday pop quiz on long division of polynomials tomorrow!!

View tonight, Nov 9 lecture

Worksheet 12 – To hand in for 20 points: Find the x- and y-intercepts for #16, 20, 22 in first set; and #13, 21 and 25 in second set of Worksheet 12. Sketch all six systems using their intercepts, and mark clearly the x and y intercepts, showing how you got these values!

Thursday

In the Kohlman text, read Ch 6, Sections 6.1 an 6.2, functions!

Do Sec 6.2 Exercises #11-39 odd

Friday to Sunday

In this Worksheet 13 -- Introduction to functions you will find several videos that precede the exercises. View and do for Monday. There will be a desk check!

WEEK 12

Monday-Wednesday

Function lecture notes so far

Watch again Domain of a function. Stop at around 13:00, the last example, which has a quadratic under a radical. We will do this in class before moving on to graphing parabolas.

So please view Prof Anil Kumar's explanation, which is given in clear, deliberative detail. He is one of my favorite internet teachers: Domain with a quadratic under a radical

On the Worksheet 14 -- Function domain, zeroes, and intercepts, from Algebra and Trigonometery, 3rd ed., by Zill & Dewar, do #1-5, #11-20, and #35-49, to be desk checked Thursday.

ANNOUNCEMENT REGARDING TUES/THURS CLASS TIMES:

Except for Tuesday, Nov 29, Unit 4 exam day, the 8:30 class will begin at 8:45 and end the usual time, and the 10:05 class will begin at the usual time and end at 11:15. It is imperative you arrive on time for these classes!

Monday and Friday classes are at the usual times.

On Thursday, we will go over Worksheets 13 and 14, so please be sure all these are done, or if you had trouble, you know which problems you want to see especially.

Friday-Sunday

Keep working on the Domain handout worksheet; the quiz Monday will be taken from this worksheet's “Mixed Practice” #19-26

View Writing a parabola in vertex form

In Worksheet 15--Graphing parabolas rewrite the standard quadratic forms in vertex form, as the instructor on the video does.

WEEK 13 THANKSGIVING WEEK

Monday-Tuesday

View the follow up of the weekend video, now Graphing a parabola from the vertex form

Again, in Worksheet 15--Graphing parabolas, from the vertex form you found before, graph the parabolas in the exercises

Kiara's notes from Friday and My lecture notes from last week and Monday

WEEK 14 Exam 4 and final topic

CHANGE OF EXAM DATE

Because I never posted the worksheet and video for function composition, I must move the exam to Thursday.

View Function composition

Read the examples and do all the problems on this Worksheet 16 -- Function composition

TOMORROW IS THE FULL 85 MINUTES, so be on time, 8:30, and second class you will stay till 11:30.

WEEKEND DEC 3-4

This will be desk checked – intro material was covered Friday; if you were absent, seek notes from classmates

View Inverse functions

Read the material and do all #1-10 on Worksheet 17 -- Inverse functions

WEEK 15

Monday Do 11-39 odd, finding the inverse function in Worksheet 17 -- Inverse functions (review the video therein)

Tuesday classes will meet remotely at the link I send a few minutes before your class (8:30 and 10:05)

Tuesday

View Solving exponential equations with same or related bases

Read and do #1-10 all (and try others!) in the worksheet in this pdf: Worksheet 18--Solving exponential equations

Thursday-Friday This is the last homework. If you ignore it before tomorrow you will be lost. Watch the videos, read the worksheets and do the problems.

Do #11-39 odd in Worksheet 18--Solving exponential equations

View Logarithms explained and Converting logarithmic expressions to exponential form

Read and do the odd exercises (as many as you can) in Worksheet 19--Evaluating logarithms and solving log equations

WELCOME TO MATH 220

2023-02-25T18:45:56-04:00

WELCOME TO MATH 220

CALCULUS FOR BUSINESS AND MANAGEMENT (FALL 2020 ED.)

ADDITIONAL TEXTBOOK READING SOURCES

SYLLABUS

DAILY HOMEWORK

LIST OF ASSIGNED EXERCISES

SOLUTIONS TO TEXTBOOK EXERCISES

INTERNET MINI-VIDEOS

Student MK lecture notes

people:mckenzie:math223

2022-12-09T18:46:58-04:00

WELCOME TO MATH 223/224 INTRODUCTION TO CALCULUS/DIFFERENTIAL CALCULUS

See Math 223/224 Director's page for syllabus with grade policy and distribution of points to tests, quizzes/take-home assignments, participation, and WebAssign.

To create your WebAssign account, go to Cengage log in and register. Our class key is BINGHAMTON07007209

The e-book for Stewart's Precalculus 7e and Calculus 9e are found on the main student page in Cengage. Readings from both will be assigned; most problem sets will come from Calculus.

Exercises in Precalculus, Stewart, 7th ed. are to do in addition to the WebAssign. If they are listed it's because they focus on the skills you should have. Ask in class about any you have difficulty with.

Each week I'll desk check and sometimes collect a selection of these exercises. I'll let you know in the preceding class when I do this.

WEEK 1 AUG 24-26

Summary of assignments for first week – if an exercise gives you trouble, rest assured we'll cover them in class. These early exercises give me a broad idea of how familiar you are with fundamentals.

Exercises are to be done in a separate part of your notes. It's up to you to do them, and to have questions ready to ask in class. I will tell you ahead of time when I plan to collect a set.

Wednesday

Watch Real numbers
Read Appendix A in Calculus
In Appendix A, do #1, 5, 8, 10, 11, 25, 31, 43, 45, 49, 51
Do WebAssign warmup (you have free access until Sept 7)

Friday to Sunday

View Dr Kazmierczak's required videos and read the corresponding sections in Precalulus e-book:

Inequalities Sec 1.8

Lines Sec 1.10 Coordinate plane; graphs of equations; circles Sec 1.9

Helpful internet mini-videos on solving inequalities:

Video 1 Video 2 Video 3 Video 4

In Precalculus e-book, do Exercises Sec 1.8 #16, 18, 22, 32, 38, 47, 52, 60, 65, 79, 81, 97, 99, 113, 119 (Monday desk check only)
Lecture Notes Week 1

Go to Cengage unlimited for info on purchasing and renting the book

WEEK 2 Aug 29-Sept 2

WA schedule with some extensions to help those just getting into WA:

By Tuesday night, Appendix A and Warm-up Appendix C
By Wednesday, class time, Appendix B and Warm-up Sec 1.1
By Friday, class time, Warm-up Sec 1.2
By Friday before midnight, App C

—-

Monday-Tuesday

Do in Precalulus: Sec 1.10 (lines): #3-8 (short answer), 25, 29, 35, 37, 47, 59, 67, 77
View Graphing a circle in standard form and Completing the square to find circle equation
Do in Precalulus: Sec 1.9 (coordinate plane, circles) #7, 15, 16, 25, 85, 89, 91, 95* (we can do it in class), 99, 103

View Dr Kaz's videos, read corresponding sections in Precalulus e-book:

Rational expressions & domain Sec 1.4

Graphs of functions Sec 2.2

Getting information from a graph Sec 2.3

Transformations of functions Sec 2.6

Wednesday-Thursday

Read in Calculus e-book, Secs 1.1 & 1.2
Kazmierczak videos Equations, Quadratic fcns & models & Polynomial fcns & their graphs
Do in Calculus: Sec 1.1 (Four ways to represent functions) #39, 41, 47, 51, 53, 56 (important piecewise function), 65, 70, 81, 83, 85
Read Sec 1.2 (Mathematical models/essential fcns) #1, 4, 17, 21, 27, 28
Study Table 3: Essential fcns & their graphs (know how to sketch from memory by midterm)
Here are my own Essential fcn sketches with domains & short video to accompany it: Domain & range of 9 basic fcns
Summary of Stewart exercises so far: Precalulus Secs 1.8, 1.0, 1.10, & Calculus Secs 1.1, 1.2

Without fail, on Friday I'll do a desk check of these

Lecture notes Week 2

LABOR DAY WEEKEND

Before Tues lecture

If you need more on domain, view Domain of rational and root functions
Everyone view Odd and even functions
Read in Calculus, Sec 1.3 On fcn transformations
View Kazmierczak videos Fcn transformations (shifts) & Fcn transformations (reflections, stretches, and compressions)

WEEK 3 SEPT 6-9

WebAssigns due this week:

Class warmup Sec 1.3, due Tuesday night 9/6
Sec 1.1, due Wednesday night 9/7
Class warmup Dividing polynomials and factoring, due Thursday morning 9/8
Sec 1.2, due Thursday night 9/8
Class warmup App D, due Friday 9/9 before class, Sec 1.3, due Friday night

Tuesday

The second half of lecture today kind of fell short, in that I didn't take the time to do more combined transformations. So … I'll be adding some notes to the lecture notes and inserting them as before. And I will embellish the intro to polynomials.

Polynomial hw has been moved to Thursday night. Catch up on WebAssign.

* On the last page of Lecture notes Week 2 I've described the domains of the four composite functions. Express these in interval notation and hand in tomorrow. It's not an involved exercise!

Kazmierczak videos Dividing polynomials & Real zeros of polynomials

Wednesday-Thursday

Do exercises in Precalculus Sec 2.6 #7-51 odd (mainly short answer), 59, 63, 65, 69, 83-89 odd
Do exercises in Precalculus Sec 3.3 (dividing polynomials): #4 (can't do it with synthetic in the form it's in) 13, 17, 23, 27, 31, 39, 57, 63
Kazmierczak videos for Friday: Trigonometry of right angles, Unit circle
Division algorithm office hour video

Friday First trigonometry lecture

WEEKEND SEPT 10-11

Read App D in Calculus and for greater detail see Precalulus Secs. 5.1-2, 6.1-3
Do Exercises in Precalculus Sec 3.4 (real zeros of polynomials): #1, 5, 9, 11, 17, 31, 55, 61
Kaz video Trig fcns of real numbers
Trig exercises to start: Sec 5.1: #1, 5, 13, 17, 19, 25, 29, 47, 51 and Sec 5.2: 5-21 odd, 27-35 odd

WebAssigns due next (I've been generous with extensions of older function material, get them done)

CLASS WARMUP: Section 1.1 due Saturday night
Dividing Polynomials and Factoring due Monday night
Section 1.3 (Part 2) due Monday night Appendix D (Trigonometry)
Math 223 Midterm Review (not graded) Definitely do it by Wed class time

Lecture notes Week 3

WEEK 4 Sept 12-16

Monday New trig and review for Friday's midterm

Watch Unit circle video
UNIT CIRCLE ART HW GRADE! Create a unit circle to bring to class on Wednesday. Use a jar lid or compass to make an accurate circle and use a straight edge to make the lines. Prefer blank or copy paper to lined.
Short trig quiz on Wednesday (using unit circle you create)
Finish up Sec 5.1 and 5.2 exercises

Trigonometry exercises for the rest of the week

Textbook exercises in Calculus App. D #1, 5-11 odd, 19, 23-33 odd, 65-71 odd, 83-87 odd
Nutley H.S. solving trig eqns worksheet #1-10 (focus on sine, cosine, tangent)

Graphs are not on the quiz tomorrow, but an ability to render a graph is needed to both understand inverse functions next week and to draw trig transformations on the final).

Some of the questions here on the Previous midterm Fall 2015 and Solutions are not in our list, some are. Do the WebAssign midterm review and of course see exercises I have listed.

Midterm topics: Absolute value inequalities, quadratic or rational inequalities; write parabola or circle in standard (h,k) form to determine features and be able to graph result; transformations of essential functions and intercepts; polynomial stuff; trigonometry part 1 (anything we have done, including solving a simple trig eqn (Nutley HS).

Watch the Office hour video!. You can see some of the more recent midterm questions here, the one I can't post but did cover many items from in class and a couple here.

Friday Midterm, no lecture

—- WEEKEND SEPT 17-18

View Arc length and area of a sector of a circle
In Precalculus do Sec 6.1 Exercises #53-69 odd with arc length s = theta x r; sector area = (r²)(theta/2)
In Precalculus read Sec 2.8 (inverse fcns), Sec 5.5 (graphs of inverse trigonometric functions), and Sec 6.4 (evaluating inverse trig fcns)
View Kaz videos:

WEEK 5 Sept 19-23

Monday

First go back and do the weekend viewing; then do the arc length and sector area problems – I will post my own short video on this, as I never got a chance to talk about it in class
In Calculus read Sec 6.1 up to p 415 (skip the end of this section on derivatives!)
Sec 6.1 #17-29 odd, #37, 39
In Calculus read Sec 6.6 to p 489 (skip limits!)
View Inverse trig fcns and triangles
Try these inverse trig evaluations in Sec 6.6 #1-9 odd

Here’s my Arc length and sector area video

Wednesday

View Kazmierczak mini-videos (total viewing time is under 9 minutes!):

To hand in by email by Friday 3 pm from Nutley High School worksheet, #13, 15, and 16; be sure to show your complete work!

FRIDAY WE WILL MEET REMOTELY AT THE ZOOM LINK

Friday's quiz moved to Wednesday when we return. 5 questions total, 3 topics:

1. Determine if a fcn is even, odd, or neither using definitions 2. Find inverse of non-trigonometric fcn and graph the two fcns on one plane 3. Do three inverse trig function calculations, including a composition

WEEKEND SEPT 25

Friday Sept 23 lecture

Office hour questions on inverse trig fcns with Rui

Do these Calculus textbook exercises for Wednesday:

Trigonometry: Sec 6.6, #1-13 odd Inverse fcns: Sec 6.1 #7-13 odd, 25-29 odd Log and exp fcns: Sec. 6.2 #7, 9, 17; Sec. 6.3 #3-7 odd, 15, 17, 21, 23

WEEK 6 SEPT 28-30

Wednesday

Do these Calculus textbook exercises for Friday: Sec 6.2* #1, 3, 7, 9; Sec 6.3* #3, 5 (leave in e or ln form), 17, 21, 23; Sec 6.4* #1, 3, 7, 9

Friday-Sunday

Read in Calculus Secs 1.5 and 1.6; for more detail see Precalculus Secs 13.1 and 13.2

View Finding limits numerically and graphically and Finding limits algebraically

—- WEEK 7 OCT 3-7

Monday-Thursday All readings and exercises are in the Calculus text:

Sec 1.5, p 60, in addition to #1-18 ALL, do #27-35 odd

Read again Sec 1.6

view these: Lots of limits part 1 (with overview of techniques)

and Lots of limits part 2 (skip over the limits at infinity for now; you'll see them in 24)

Sec 1.6, p 70, do #1-31 odd (do as many as you can using the reading and video help); for class discussion, #44

By next week, getting ready for final, in Sec 6.3, p 438 do #3-11 all; #21-31 odd; 43, 47, 49-53

WEEKEND OCT 7-9

Friday-Sunday

I meant to give you this definition of vertical asymptote, which formally ties VA limit:

x = a is a vertical asymptote of f(x) is the limit as x goes to a from either direction is + or - infinity

The below video gives the same definition with several examples similar to what we did in class:

Vertical asymptotes

Lecture Notes: I re-uploaded above any that disappeared; here are the latest:

Lecture notes week 5 Lecture notes week 7 part 1 and Lecture notes week 7 part 2

Complete the WebAssignments by tonight, please. Continue working out the limit exercises. If WA asks for limits at infinity, you may omit those, but let me know.

Start working on Math 223 Fall 2015 Final and Math 223 Fall 2016 Final for practice

Read Sec 1.8, continuity

WEEK 8

Wednesday class will be at this Zoom link

View Limits and continuity

In Sec 1.6, p 70, do these further limit exercises #33, 44*, 45, 51, 54*

In Sec 1.8, do continuity exercises #3, 7-27 odd, 39-48 all, #54-58 all

You may like a complete overview of limits, view Intro to limits, Properties of limits (kind of tedious, but some good examples), and Determinng limits

On Friday you’ll have a Math 223 skills quiz. Today, Wednesday, is the zoom class.

Wednesday Here is Today's zoom lecture recording

Besides studying for the final exam, prepare for the Math 223 skills quiz on Friday, which will be these topics:

Domain of function
Essential graphs, including graphing an absolute value transformation (like we did today)
Factoring, including special factors
Evaluating trig expressions
Evaluating log and exponential expressions
Finding intercepts of circles and parabolas
Basic limits

Practice quiz page 1

Practice quiz page 2

Key to practice skills quiz page 1

Key page 2

Key graphs

Lecture Notes (recent) from Rui

Sunday Oct 16

Solutions to Fall 2015 final

Solutions to Fall 2016 final

WEEK 9 HERE IS WHERE MATH 224 BEGINS

Monday Review limits and continuity homework, readings and videos. For the new folks, here was the WEEK 8 homework. For the continuing students, this is a good time to go back and do the text exercises you might have 'missed'

Read in Calculus Secs 1.5 and 1.6; for more detail see Precalculus Secs 13.1 and 13.2

View Finding limits numerically and graphically and Finding limits algebraically

Do Sec 1.5 p 60, #1-18 ALL, do #27-35 odd and Sec 1.6, p 70, do #1-31 odd, #33, 44*, 45, 51, 54*

View these: Lots of limits part 1 (with overview of techniques)

and Lots of limits part 2 (skip over the limits at infinity for now; you'll see them in 24)

Lecture Notes: I re-uploaded above any that disappeared; here are the latest:

Lecture notes week 5 Lecture notes week 7 part 1 and Lecture notes week 7 part 2

Read Sec 1.8, continuity

Do Sec 1.8 exercises #3, 7-27 odd, 39-48 all, #54-58 all

NEW Link to Warm-up and flip videos for Math 224 which I will explain in class tomorrow how to navigate.

Wednesday Reminder: All readings and exercises are in Stewart Calculus, 9th ed. e-book on the Cengage site

1. View rest of Limit of a function, started in class, and Detail of limit of sin(x)/x as x --> 0

2. If you are not on solid ground with inequalities and absolute values, read Appendix A in Calculus e-book

3. Read Sec 1.4 and view Tangent and velocity problem

4. Write up to hand in:

Find the instantaneous rate of change (IROC) of f(x) = sq rt x at x = 1. (This is the a value.) Do this by using the detailed formula for finding IROC at x = a and showing all the work that gets you to the numerical answer. It's a limit problem.

Draw an accurate sketch of this function, and indicate with two secant lines arbitrary through the curve at a = 1 and a + h = 1 + h

Write a sentence about the most interesting thing you learned or were reminded of today in class (about mathematics, I mean, though feel free to share other new things you'd like to share)

Friday

Do exercises in Sec 1.4 and do exercises #3, 5, 7 (video and reading in Wednesday homework)

View Derivatives as rates of change

Read Sec 2.1

Do exercises #15, 17, 19, 23, 27

View these important Kazmierczak videos. They are largely review of limits, but without this understanding, the development of derivative has no framework (the first and last I have posted before).

And finally, something we looked at on Friday, but take another look! It will help you soon: Trigonometric limits

First set of WebAssignments, due next week; please do before the due date so you don't miss 8 a.m. posted time:

CLASS WARM-UP: Section 1.4 Monday Oct 31, 8 a.m. (before class)

WEEK 10

CLASS WARM-UP for Section 2.1 Wednesday Nov 2, 8 a.m. (before class)

Monday-Tuesday

Read Sec 2.2 and view the videos therein as well as:

Sec 2.2 Differentiation formulas

Wednesday I moved WebAssign Warmup Sec.2.3 to Saturday night Nov 5; you have Sec 2.4 Warmup on Monday.

Here are Mon and Wed lecture notes from Rui

From p 125 of Sec 2.2, “How can a function fail to be differentiable?” We looked a bit at this. The graph of function fails to be differentiable at points where either we can't establish a tangent line (corners and cusps – think absolute value function at x = 0); at points of discontinuity (kind of obvious); and at a point where the tangent line is vertical, hence its derivative undefined (e.g. cube root function).

Friday: 2-question quiz: something like #15 and #17 (interpreting a graph); something like #27-30 (equation of line tangent to polynomial curve at a given x, use power rule to determine derivative)

To hand in Friday with the quiz: Sec 2.2, #26 use definition of derivative (NO SHORTCUTS–an LCD will be needed)

Continue reading in Calculus, Sec 2.2; do Exercises #3, 7, 11, 13, 15

View these: Position, velocity, acceleration--nice! and Sec 2.3 Power rule

WEEKEND NOV 5-6

See the SKILLS TEST NEWS from the Director, Professor Kazmiercak

Do Sec 2.3 Derivative rule exercises #1-49 every other odd (#1, 5, 9, 13, etc.) #59, 63, 67, 83, 87

* Read App D and Sec 2.4, trigonometry review and trigonometric function derivatives

View Derivatives of trigonometric functions

Next WebAssigns I gave you a bit more time for Sec 2.3 Warmup. Moved the Practice Skills Test 1 to where you can see it in the WA current list.

CLASS WARMUP Sec 2.3 due 11-6-22 Sunday night

CLASS WARMUP Sec 2.4 due 11-7-22 Monday morning

WEEK 11

Monday

WebAssignments: Sec 2.2 due Nov 8 Tuesday night

CLASS WARMUP Sec 2.5 due Nov 9 Wednesday morning

For practice: WebAssign Skills Test 1. We've covered all the material. Have questions to ask in class!

Do Sec 2.4 trig derivatives p 154 #3, 7, 8, 13, 16, 23, 25, 39, 35, 37, 41, 45 (try also #47, 51)

Wednesday

TWO ANNOUNCEMENTS:

NO LIVE LECTURE TODAY, WEDNESDAY. Lecture will be recorded and posted this evening for your required viewing.

Ms Debra Levy at Cengage asks me to have you write to her directly debra.levy@cengage.com, if you have enrollment problems or other technical issue. She fixes things efficiently.

ASSIGNMENT

Thursday

View my recorded lectures:

Nov 10 part 1

Nov 10 part 2

Read (already assigned Monday night) Sec 2.5 and view Chain rule

Do Sec 2.5 chain rule p 162 #1, 3, 5, 9, 16, 18, 21, 34, 37, 45, 53, 51, 67

Friday to Sunday

MIDTERM IS WEDNESDAY! Do the Fall 2016 midterm and have questions ready for Monday. Skip the question on intermediate value theorem. If you have no questions, I will proceed with the lecture on new material, except for…

… Rui's question on trig limits in class. She was referring to lim as x goes to 0 of sin(ax)/bx. Or, sin(ax)/sin(bx). Thanks, Rui, for asking! She does the exercises. Which translates into high test marks, as I draw from them for the exams I write. We'll discuss both these types of limits.

I did prove the chain rule on my video with f(u(x)) notation! WATCH MY 2 RECORDED VIDEOS (required for Wed attendance) and Prof Mosely on chain rule. The real world scenario is motivating!

On Sunday I'll check Panopto for your viewing time and ask a sneaky question to see if you didn't just leave it running and go to the kitchen.

We start implicit differentiation on Monday (not on midterm). Read Sec 2.6 and see Dr Kazmierczak explain Implicit differentiation

WEEK 12

Monday The old exam I posted is actually the Fall 2016. Here it is again as well as solutions. And below it, the Spring 2016 midterm and solutions.

Fall 2016 midterm and Solutions

Spring 2016 midterm and Solutions

Tuesday I reserved the big room down the hall from my office, WH Room 227, for office hours, 1:30-3:30. That was the window I could get, so be sure you come sometime in that window with questions.

Wednesday-Thursday View Implicit differentiation and read Sec 2.6

WebAssign CLASS WARMUP for Section 2.6 due by class time Friday

WebAssign CLASS WARMUP for Section 2.7 due by class time Monday

Weekend homework in text will be posted Friday

Friday-Sunday

Implicit differentiation (ID) lets us find dy/dx even when y cannot be expressed as an explicit function of x (or other relevant IROC, such as a related rate)

View helpful ID video 1 and ID video 2

* Do Sec 2.6 exercises #3, 4 7, 11, 17, 21, 25, 29, 31, 39, 41

In-class quiz on Monday (inspired by above exercises)

Read Sec 2.7 and view motion videos (rates of change in science, and with deeper focus on motion):

Do Sec 2.7 exercises #1, 3, 9, 17, 21

WEBASSIGN CLASS WARMUP Section 2.6 due Sunday night

WEEK 13 THANKSGIVING WEEK

Mon-Fri The following work is not to be ignored over the break!

Read Sec 2.8 Related Rates and view:

Do Exercises #9, 13 (these are practically the same as the sliding ladder problem) and #2 (circle, see last video)

WEBASSIGN CLASS WARMUPS have been extended. PLEASE do them before the time runs out.

Friday-Sunday

Recent lecture notes (mine)

Here 20221209172236112.pdfis a Brief lecture on rates of change in science, but at the start I do an exercise from Stewart on implicit diff'n as well.

The final sections we will cover are Secs. 3.1, 3.3, 3.4, 3.5 (Sec 3.2 is covered in Math 225)

View Finding critical numbers of a function and local max and min

Finding absolute max and min of a fcn on a closed interval

Read Sec 3.1 and try textbook exercises: Sec. 3.1 #1, 3, 9, 11, 17, 18, 31, 35, 41, 45, 51, 59

NOTE: Skills Test 2 begins Nov 28. It covers trigonometric derivatives, chain rule, and implicit differentiation. You have until Dec 9, to take all 3 attempts.

WEEK 14

Monday-Tuesday

Read 3.3

Continue Sec 3.1 exercises.

(I didn’t do absolute extremes today, only local, of which there is more to say about the first derivative test for local maxima and minima, as demonstrated in class today, but not named as such. Much more on this soon.)

Webassign 3.1 warmup due Wed morning

Webassign 3.3 warmup due Wed night

View First derivative add shape of a graph and Second derivative and shape of a graph

Wednesday-Friday

Webassign 3.4 warmup due Friday morning

Do Sec. 3.3 #1, 4, 11-14, 15, 17, 20, 21, 27, 43, 49, 62, 63

My handout summary (used in class today) of Curve sketching with calculus

Today's recorded remote class

Thursday note I was looking at the exercises I mentioned in lecture yesterday, and I meant to assign #18 in obht Sec 2.7 and 2.8. The first #18 is interesting because its derivative is linear, but it will be good to see how it relates to absolute max and min!

Hold off on Sec 3.3 till I decide on two good ones.

Weekend assignment

View How to sketch a curve

In place of Dr Kazmiercazk paper assignment, you are doing this one, to hand in Monday: HW Quiz 5*.

* I forgot to add identify any vertical and horizontal asymptotes. Please do so by using the limit definitions if they apply.

We will use Dr. Kazmaierczak’s for curve sketching review this week.

WEEK 15

Monday

I was looking at Stewart solutions manual, and I notice it has slightly different problems (actually, the same, but different numbering, some of them). They are from an earlier edition. So after my class tonight I will match them up and post pics of many I like including the ones you did.

For homework, be sure you have read through Sec 3.5 (but skip Sec 3.2)

On Wednesday I will go over the Kazmierczak problems (not to hand in) and we will do a selection of Stewart problems on limits at infinity, from Sec 3.4 (no hw on those tonight, but catch up if you need to on WebAssign).

Wednesday-Friday

Sec 3.4 exercises #7, 8, 13, 17/18 (limits at infinity)

Recent notes through Friday part 1 and part 2

Previous exam (2016) with solutions

people:mckenzie:math224

2021-12-14T12:42:59-04:00

CONTINUATION OF MATH 223/224 INTRODUCTION TO CALCULUS/DIFFERENTIAL CALCULUS

See Math 224 Director's page for syllabus, old exams, and so on.

Also there you will find Math 224 weekly schedule of topics

I will assign Exercises in Calculus, Stewart, 9th ed. in addition to WebAssignments.

Sometimes I will collect a few!

WEEK 9/10 Oct 22-29

Fri Oct 22-Sun Oct 24 Read Sections 1.8 (intermediate value theorem) and 1.4 in Stewart Calculus e-book

Mon Oct 25-Wed Oct 27

Continue readings in Sections 2.1 and 2.2 (derivatives; derivatives as a function)

WebAssign schedule

The WA schedule is here for you to see easily. I want to avoid requests for extensions throughout the week.

CLASS WARMUP: Sec 1.4 Tuesday Oct 26, 8 AM

CLASS WARMUP: Sec 2.1 Wednesday Oct 27, 8 AM

CLASS WARMUP: Sec 2.3 Friday Oct 29 8 AM

Sec 2.2: Saturday Oct 30 11:59 PM

In case you didn't see the home page or the email, Math 224 are T/Th 1-3 at Office hours zoom link

Wed Oct 27-Fri Oct 29

View Determining derivative of quadratic and Square root function
Sec 2.1 exercises #7, 10, 11, 19, 25; also, #3 entails using two versions of DQ to find slope of tangent
Sec 2.2 #1, 3, 7, 11, 13 (graphs of derivatives from function graphs)
View a no-frills Position, velocity, acceleration video
Read Sec 2.3
Finally, Finding f'(x) where f(x) = x^1/3. Prof Kumar is deliberate and his voice is calming. He covers a lot of territory that pertains to derivatives Please watch it!

Here is a collection of videos that show how to determine the equation of the line tangent to a function f(x) at a given point via the definition of derivative to get the slope and the point-slope form of the line to get the eqn. Watch as many as you need to:

Ex 1, Ex 2, Ex 3, Ex 4

Finally, the flip learning videos (mine, not Stewart's) to help with the Sec 2.3 WebAssign, watch The basic rules for derivatives and Power rule examples

HALLOWE'EN WEEKEND EXERCISES, READING AND VIDEOS

One last development of limit def of f'(x), in detail (recommended by a classmate!

View Sec 2.3: derivative rules
Here is Proof of product rule and

Proof of quotient rule as welll as Product rule examples, Quotient rule examples

Sec 2.3 Exercises #1-49 every other odd (#1, 5, 9, 13, etc.), some of which you are not to use product or quotient rules, but instead to change the form as we did in Friday's class so the power rule is all that is needed) and #59, 63, 67, 83, 87 (I will go over these in class if you ask)

Read Sec 2.4 and view Sec 2.4 derivatives of trig fcns, which you will need to complete the Monday warm up in WebAssign

WebAssign Schedule:

Sec 2.2 Saturday Oct 30 11:59 PM (repeating reminder here)

CLASS WARMUP Sec 2.4 Monday Nov 1 08:00 AM

Quiz Wednesday, through Sec 2.4

WEEK 11 Nov 1-Nov 5

View Squeeze theorem

Today's lecture on zoom [Note, by yesterday I hadn't assigned Sec 2.4 exercises, so ignore my comment asking if you had any questions]

QUIZ 1 ON WEDNESDAY covers Sec 2.1 to 2.4: Determine derivative from the definition, properties and rule, power rule shortcut, product and quotient rules, derivatives of the sine, cosine and tangent fcns

Do a bunch of the odd numbered exercises in Stewart Sec 2.4. I'll be more specific later.

Do next scheduled WebAssigns

Friday Nov 5-Sunday Nov 7

Read Sec. 2.6 Implicit differentiation and view Video 2.6a

Read Sec. 2.7 Rates of change in science + related rates and view Videos 2.7a and 2.7b

Basic Skills Test begins on Nov 8

Essential exercises in Stewart so far to help prepare you for upcoming Exam 1 and Skills Test:

Sec 2.4 p 154 #3, 7, 8, 13, 16, 23, 25, 39, 35, 37, 41, 45 (try also #47, 51)

Sec 2.5 p 162 #1, 3, 5, 9, 16, 18, 21, 34, 37, 45, 53, 51, 67

Sec 2.6 p 169 #3, 4 7, 11, 17, 21, 25, 29, 31, 39 (try #41)

WEEK 12 Nov 8-Nov 12

See e-book exercises I posted over the weekend; have questions to go over in class

Implicit differentiation lets us find dy/dx even when y cannot be expressed as an explicit function of x (or other relevant IROC, such as a related rate)

Watch Video 2.6 Implicit Differentiation, and from my collection: Implicit differentiation (ID) and More ID examples

Now try the examples I posted on the weekend: Sec 2.6 p 169 #3, 4 7, 11, 17, 21, 25, 29, 31, 39 (try #41)

Watch the Video 2.7 Rates of change in science and Video 2.8a Related rates 1 and Video 2.8b Related rates 2

Next WebAssigns: Sec 2.8 Wed Nov 10 11:59 pm

Basic Skills Test 1 began today, Nov 8; you have till Tues Nov 23 to take your 2nd and 3rd attempts covering limits, continuity, and differentiation formulas

Implicit differentiation quiz

Do Webassign 'FOR PRACTICE ONLY' Secs. 1.4, 2.1, 2.3-2.8 – especially Secs. 2.7 AND 2.8, as I might not get Stewart exercises from these sections listed

wednesday notes implicit differentiation and related rates

Weekend before exam 1

WEEK 13 Nov 15-19

Mon-Tues Read Sec 2.9, linear approximation (the important corollary to genesis and meaning of derivative)

Watch the Videos 2.9a and 2.9b therein and whatever else I post

Do WA Warm-up Sec 2.9 (see WA site for date and time, which I extended)

Wed-Thurs Read Sec 3.1, max/min values and watch Videos 3.1a and 3.1b and any mini-videos I'll add

Fri-Sun View this: Best video for linear approximation and differentials

Do e-book exercises Sec. 2.9 #1-3, 7, 13, 17 and Sec. 3.1 #1, 3, 9, 11, 17, 18, 31, 35, 41, 45, 51, 59

Skipping Sec 3.2

Read Sec 3.3, videos therein

WebAssign as scheduled

Open notebook quiz – short (after we go over the Sec 3.1 assigned exercises) on Sec 3.1

Please have any questions for me to address in class on anything since exam

WEEK 14

Mon Nov 22 - Sun Nov 28 THANKSGIVING BREAK WEEK

If you are rusty in solving trig equations, here's the Nutley High School Trig Eqn Worksheet and Solutions

Finding the critical numbers of a function is the first step to finding the signs of the first and second on an interval, to determine where a fcn is increasing or decreasing, hence the nature of its local extremes (max, min, neither), intervals of concavity, and points of inflection. The videos explain and give many examples of how to use the FDT and SDT, showing relevant examples done neatly and clearly.

Finding critical numbers of a fcn

Finding absolute extrema of f(x) on a closed interval

Finding intervals where f(x) increases and decreases

Determine local extrema of f(x) using first derivative test (FDT)

Determine local extrema of f(x) using second derivative test (SDT)

The function we did in class today, f(x) = x + 1/x, examined for extrema using FDT and SDT

* Bulletin: Mean value theorem/Rolle's theorem are NOT on the final; they show up in Math 225; but finding c such that f' = 0, is the skill needed to find critical numbers so reviewing it in the guise of Rolle's thm is great practice. The algebra is probably most people's difficulty. Imm making up a worksheet that tackles the usual trouble spots in solving all kinds of equations for their zeros.

Weekend assignment

See my communication in WA about doing practice problems in sections covered but not assigned/graded. They provide practice and feedback without the weight of deadlines or scores.

Reminder of past and a new set of exercises:

Sec. 2.9 exercises #1-3, 7, 13, 17

Sec. 3.1 exercises #1, 3, 9, 11, 17, 18, 31, 35, 41, 45, 51, 59

Sec. 3.3 exercises #1, 4, 11-14, 15, 17, 20, 21, 27, 43, 49, 62, 63

WEEK 15 Nov 15-19

Mon Thank you all for being flexible with the zoom today. You're great for helping me out so I can recover.

Wednesday lecture will be on Zoom again. I will send the invite directly from zoom at 7:50 a.m.

(DUE WED) On paper, show all work, for quiz grade, no late papers: Sec 3.1 #41, 45; Sec 3.3 #43, 49

Monday's lecture recording and Monday lecture's last function, graphed– notice, as we saw, since there was no POI candidate, there is POI; f inceases on (0, 1/4), decreases on (1/4, inf); hence, f(1/4) is local max (and absolute) max; concave down on entire domain (0, inf). At the end of the lecture I mused 'maybe f(1/4) is a cusp,' which is ridiculous, since f'(1/4) = 0, hence exists! I edited that out : /

Read Sec 3.4 limits at infinity and videos therein

For Friday: Jot down in your notebook 1 exercise from each of Secs. 2.9, 3.1, 3.3, 3.4 for me to address the following week; I'll send around a 'sign up sheet' on which you will write the question exercise numbers down and I will do as my hw over the weekend

Wednesday Today's lecture video

Please keep reading Sec 3.4 carefully! And watch the videos therein. Also:

View Limits at infinity of rational functions and Graphing rational functions

View Limits at infinity for a root function

Sec 3.4 #1-31 odd

In-class brief quiz Friday on Sec 2.9, finding L(x) for f(x) near some value x = a; use it to approximate the function at x near a), 3.1-3.3 using critical numbers and POI to describe the graph of a polynomial, including all features (local extrema, POI, intervals of increase/decrease/concavity) and sketch it!

WEEKEND AND LAST WEEK OF COURSE, DEC 4-10

Read Sec 3.5 and watch the videos therein. I'll add one brief set of exercises, from Sec 3.5

Read the Calculus of Curve Sketching handout and do the unworked exercises at the end of it. Note, this study guide doesn't have the rational functions and asymptotes on it. I am writing a “Part 2” but will probably not have it soon. So see the videos I posted last week.

The following are from the director, Prof Kazmierczak:

NEW DUE DATE Due Dec 10, counts 3% of course grade Curve sketching assignment

Note regarding the above: The function for #1 has one x-intercept (root), and it's difficult to find its value. The root is approximately x = 3.1, so use this value for the x-intercept when doing #1.

The are many problems in WebAssign for Sec. 3.5, for practice only, and will not be graded for the course. You should do them! They are your best prep for the final exam.

TUES DEC 14

Solutions to curve sketching homework

Stewart Sec 2.9 linear approx solns

Stewart Sec 3.4 limits at infinity and HA solns

Stewart Sec 3.5 summary of curve sketching solns

FINAL EXAM TOMORROW Wed. Dec 15, 2021, 03:15-05:15 PM IN LH 001

people:mckenzie:math_108_quizzes

2015-09-22T12:24:12-04:00

Quiz 2 take home and solutions

people:mckenzie:math_108_sec_02_syllabus

2017-09-09T00:43:27-04:00

Math 108 Sec 02 syllabus

Math 108 Sec 04 syllabus

people:mckenzie:math_220_hw_solutions

2020-03-22T22:57:23-04:00

Homework solutions are posted a day or so after it is is assigned.

Ch 7 and Ch 8 solutions

Ch 10 solutions

Ch 13 solutions

Ch 14 solutions #1, 2, 4, 8, 9, 12, 5 and #13 and #13 continued

Ch 15 HW solutions

Ch 17 HW solutions

Ch 18 HW solutions

people:mckenzie:math_220_syllabus

2017-10-22T18:10:35-04:00

Syllabus Fall 2017

Please note: There will be four 1-hour exams in Fall 2017. The second will be Oct 27.

The third will be around the middle of November and the fourth early in December during the final week of classes.

people:mckenzie:math_224_225_old_exams

2019-08-21T13:40:55-04:00

Below are some old exams from previous semesters. These are provided to give you a sense of what types of problems have been asked in semesters past. The exams you take this semester may not bear much similarity to those below.

Solutions to 224 Exam 1 - Sept 19, 2016

Solutions to 224 Exam 1 - Spring 2016

Solutions to 224 Exam 1 - Fall 2015

Solutions to 224 Exam 2 - Fall 2015

224 Exam 2 with solutions - Spring 2016

Solutions to 225 Exam 1 - Spring 2016

Solutions to 225 Exam 1 - Fall 2015

225 Final - Fall 2015

Solutions to 225 Final - Fall 2015

225 Final with Solutions - March 2016

225 Final - May 2016

Solutions to 225 Final - May 2016

Old test for MATH 224 with solutions - Fall 2014 (covers Exam 1 & 2 topics for 224)

Old test for MATH 224 with solutions - Fall 2012 (covers Exam 1 & 2 topics for 224)

people:mckenzie:quiz_and_practice_test_solutions

2014-12-11T17:17:38-04:00

Quiz 3 key

Transformation graphing quiz solutions

Solutions to practice test 2

Quiz 7 key

Other Quiz 7 key

Quiz 8 key corrected

Trig practice quiz/key

Trig computation quiz/key

Trig quiz/key

Key to Practice Trig Test

people:mckenzie:quiz_keys

2015-04-29T16:42:26-04:00

Quiz 2 key Log and exponential functions

Quiz 3 key Limits

Quiz 4 key Derivatives 1

Quiz 5 key Derivatives 2

Quiz 6 key Curve sketching 1

Quiz 7 key Curve sketching 2

Quiz 8 key u substitution

Quiz 9 key Integration by Parts take-home

Kathy McKenzie

2026-04-08T05:10:34-04:00

Kathy McKenzie

Adjunct Lecturer
At Binghamton since 2013

E-mail:	mckenzie@math.binghamton.edu
Phone:	(607) 777-2147, 2148 dept secretaries
Fax:	(607) 777-2450

Office: Whitney Hall Room 224

Office hours: In WH 224, M/W 1:30-3:30 or at Zoom link when so announced

Fall 2022 Schedule

Math 223 Intro to Calculus	Sec 07	M/W/F	11:20-12:50	LH 04
Math 224 Differential Calculus	Sec 01	M/W/F	11:20-12:50	LH 04
Math 106 Intermediate Algebra	Sec 01	M/F	8:30-9:30	S2 255	T/Th	8:30-9:55	S2 255
Math 106 Intermediate Algebra	Sec 02	M/F	9:30-10:40	S2 255	T/Th	10:05-11:30	S2 255

Course Web Pages – find all daily assignments, announcements and other resources here

Math 106-01 and -02 Fall 2022

Math 224-07 Fall 2022

Extra Help

MATH 106: Every Wednesday at 2 pm, Mr McKinney holds a Math 106 review session at the EOP tutorial center. It will go no longer than 90 minutes, that is, it will end no later than 3:30.

Math Help Room Schedules

Campus Tutoring Services

Archived course

Math 220 Fall 2021

—-

Sites of interest:

BU Food Pantry

people:mckenzie:student_mk_lecture_notes_fall_2021

2021-11-04T09:22:41-04:00

First set lecture notes by MK

Second set of lecture notes by MK

Third set of lecture notes by MK

Fourth set of lecture notes by MK

people:mckenzie:videos

2021-10-22T15:51:17-04:00

Cost, Revenue, Profit

Cost/revenue/profit 1, Cost/revenue/profit 2, Cost/revenue/profit 3

Demand function and cost function

For a little later in the unit: Marginal Revenue, Average Cost, Profit, Price & Demand Function

Economics summary of cost, revenue and profit

Logarithms, Exponential and e

Graphing 2^x and log base 2 of x

Explaining Euler's number e, the natural log base

Compound interest, present and future value

Doubling something (after 1 year, say) is what we call 100% growth. Interest is generally paid at a much smaller amount. This video begins first with 100% growth, so the growth of the ball is easy to draw. This way the lecturer can get you to “e”. He then goes on to show a more reasonable growth rate r. First, some background on e:

The History of e

Where does e come from?

Understanding the number e (exponential growth).

This last one is a good presentation of the several types of problems seen in finding present and future value when interest of an investment or loan is compounded. The lecturer uses the variable A for F for future value. For F I used P(t) to show the it is a function of time, and Po for present value.

Compound interest, present and future value problems

Limits

Finding limits from a graph (This is one of his rougher videos, but well explained.)

Evaluate limits using properties, Ex 1

Evaluate limits using properties, Ex 2

More techniques for evaluating limits, Ex 3 (gives a little jump on continuity)

Ex 4 involving radicals

Ex 5 also with radicals

IMPORTANT Infinite limits in which a function goes to positive infinity or negative infinity as x approaches a:

Ex 6 involving rational expressions

Optional, good insight, might actually help you better understand the actual limits we have done:

Precise definition of limit

Continuity

Main idea: A function f(x) is continuous at x = a if f(a) exists and if limit of f(x) as x approaches a is equal to f(a).

First, check these helpful videos on graphing piecewise functions by Patrick, if you need them:

Graph a piecewise fcn 1 and Graph a piecewise fcn 2

Patrick discusses limits and the relationship to continuity. Watch for the important ideas, as we will discuss at length.

Continuity and limits made easy

Discontinuities in a function (piecewise)

More inspecting for discontinuities of a piecewise function

Derivatives

Instantaneous rate of change of a function at point via the difference quotient (DQ)

The numerical slope of a tangent line at some point of a function is derived from the function itself by means of the difference quotient. The function that describes the behavior of the slope of the tangent line at any point along the graph of a function is called the “derivative function” (or simply, the “derivative”).

This function we will soon see is the marginal cost function.

We evaluate a derivative function at a given x (say, x = a), we find the instantaneous rate of change of the function at that point.

This is an essential video: Difference quotient (DQ) and the definition of derivative

Here is the process: Finding derivative with DQ, Ex 1

and Finding derivative with DQ, Ex 2

Here are examples for finding equation l of line tangent to f(x) at a given point:

Ex 1, Ex 2, Ex 3 and Ex 4

Longer example of finding equation of tangent line

A practical application from the laws of physics (motion): Relationship between displacement, velocity and acceleration

Derivative Rules, Properties and Examples

Power rule examples

Proof of product rule

Proof of quotient rule

Derivative of an exponential fcn with base a

Derivative of a log fcn with base a

Proof of chain rule The lecturer uses Leibniz notation dy/dx. There's a little fudging where on u(x) and g(x) being the same, but he says so.

Product rule examples

Quotient rule examples

Chain rule explained by Patrickmjt

Ex of chain rule for radical function

Ex of chain rule for natural log function

Many great examples of chain rule involving ln[u(x)]

A couple more

While you are not responsible for the proofs, only the rules, you ought to see where the formulas come from. They rely on d/dx notation, implicit methods, and log properties, as well as limit process. None of these are difficult. They are short and very clear.

Proof of derivative of exponential function (base e)

This proof requires a result from a proof that uses a trig graph (i.e., not in the 'scope' of this course, but not hard either.

Proof of derivative of natural log function

Proof of derivative of exponential function (base a)

Implicit differentiation

Implicit differentiation method often lets us find rates of change of one variable with respect to another even if there is no explicit function present. For example, the circle isn't a function, but its tangents are of interest to us, especially where they fail to exist. Differentiating the equation without solving for either of its branches (top or bottom semicircle) is handy using ID.

Implicit differentiation (ID)

More ID examples

(Go to 3:30 for example that involves non-trig equation)

Related rates

One dimension (x) changes with respect to time (t), causing a related dimension (y) also to change with respect to time.

For example, area A of a circle is a function of its radius r; if r changes with time, then area changes also with respect to radius and ultimately time. We note the basic equation for this: dA/dt = (dA/dr)(dr/dt). The videos demonstrate this.

[Note: Videos by Krista, like Patrick's, are clear and no frills. Both convey mathematics methods effectively!]

Implicit differentiation and related rates

And finally, a video on related rates that applies to a business application:

Cost and profit with respect to time

Critical numbers

A critical number f(x) is that value of x (call it 'c') in the domain of f where EITHER f'(x) = 0 OR where f'(x) does not exist.

Finding the critical numbers of a function is the first step to applying the first and second derivative tests, by which we examine where functions attain local extremes, the intervals where the function is increasing or decreasing, intervals of concavity and points of inflection. We use these skills to sketch the curves of functions and so examine what kind of behavior a function models.

Finding critical numbers of a fcn

There are many more videos on the HW page for this topic.

First and second derivative tests

First derivative test

Second derivative test and concavity

Curve sketching with calculus

Examples first and second derivative test to graph functions

Graphing a polynomial

Graphing a rational function

Graphing another rational function

Optimization

Optimization problems dealing with geometry:

Fence problem 1

Fence problem 2

Box problem

More optimization: Wherein n = number of price reductions or increases. Notice I prefer n to the book's x for this variable, as we are used to x being quantity of sales.

Computer software sales

There are two examples done on this video. The first should be enough, and I like that it gives a graph as I did for the lamp sales problem today. The whole idea of graphing the upside down parabola and asking what its max and its y-intercept indicate is very important. (By the way, on the video's first problem, the y-intercept shown is incorrect, as it is definitely not the case that n = 0 price reductions would mean $0 revenue; but more about that in class).

Here's a similar one.

The hot dog problem

Finally, one where we have to come up with the price function (called the “demand function” here), to create the revenue function:

Optimizing revenue given two points of data

Multivariate functions

Multivariable functions up to 9:45

Partial differentiation

Partial derivatives

Local max and min of a function of two variables f(x,y)

In three-space, we find critical points essentially same as we do in two-space, but to determine if they are max, min, or saddle points, we have no first derivative test. Rather, we go straight to a second derivative test after finding critical values.

As you watch this be aware of the following:

1. Calculation of partial derivatives

2. Solving for critical numbers, which generally entails solving a simply linear system, but sometimes a non-linear one, and even discarding some values (Theorem 28.1).

3. Employing the SDT for f(x,y) (Theorem 28.2).

Critical points and second derivative test for local max and min of multi-variable function f(x,y)

Lagrange multipliers for solving problems in optimization with a constraint:

Prof. Kumar shows Lagrange multiplier method of solving optimization w/constraint

Lagrange Method with Krista Ex 1 and Lagrange Method with Krista Ex 2

Elasticity

First, watch the excellent presentation that explains the overall picture, NO CALCULUS, explained by an economics professor in a very accessible way.

Prof Tarrok's Elasticity of Demand

Second, the formulas explained and worked problems OHM Elasticity 1 and OHM Elasticity 2, and note that the demand function is labeled D(x), but it means the same as q(p), which we use in class.

Antiderivatives (indefinite integrals)

Antiderivatives and indefinite integration

Examples of basic indefinite integration

Antiderivative with initial conditions (finding a particular F(x))

Displacement, velocity, acceleration example

u-substitution

Examples of simple substitution

Integration by parts

Fundamental Theorem of Calculus (FTC) and Definite Integrals

The area under the curve f(x) represents the accumulation of that function on a stated interval.

Prof Dave on Integration as Area under a Curve

Prof Dave on Fundamental Theorem of Calculus

And a more rigorous version:

FTC: rigorous version

Here are examples:

Example 0 of finding definite integral

Example 1 of finding a definite integral (polynomial and power rule)

Example 2 of finding a definite integral (log and IBP)

Examples 3 and 4 (two more IBP)

Riemann Sum and the Definite Integral

Further understanding of this construct of area under the curve and the definite integral is found in the notion of the Riemann sum:

Riemann sum to approximate the area under curve on interval [a, b]

Definition of definite integral via Riemann Sum

Improper integrals

Improper integrals basic idea

Improper integrals continues

Applications of the definite integral

Finding area between two curves

Average value of a function 1

Average value of a function 2

Position, velocity and acceleration

Finally, Present and future value of a continuous income stream

The easy way to remember which formula gets the multiplier is to note that, since, PV < FV, present value lacks the multiplier that future value has. No need to overthink that one.

What is the usefulness of Present Value? It's a tool for comparing what you would make if you were to hold on to your business vs if you sell it right now and invest the money you are given.

people:mckenzie:zoom_notes

2020-04-15T19:00:23-04:00

Integration unit Zoom session notes

people:mckenzie:zoom_office_hours

2020-05-03T21:18:59-04:00

Final classtimes–Monday May 4:

8:30-9:45 a.m. Eastern Time Join Zoom Meeting @ https://binghamton.zoom.us/j/733843011

10:00-11:15 a.m. Eastern Time Join Zoom Meeting @ https://binghamton.zoom.us/j/733843011

Final office hours: Monday May 4 and Tues May 5:

3:00-4:00 p.m. Eastern Time Join Zoom Meeting @ https://binghamton.zoom.us/j/733843011