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people:mckenzie:math_220_hw

The following lists weekly assignments, broken down into one or two days. You'll see Friday HW is often a little longer than other days.

There is significant use of 'flipped learning', wherein you view a video before I teach the material. These are SHORT and HELPFUL. They are never much different from my approach to a topic.

The boldface **day** indicates the assignment given date. You are expected to have done this HW by the next class meeting. Your preparation is essential to your progress. I will sometimes check HW at desks, so it's a great idea to keep it in a separate notebook or folder.

WEEK 1

**Wed**: Read Ch 1 in Course Notes for Math 220 (Geoghegan and Brewster)

Do p 5 exercises: #1, 2, 7, 8

View first five videos at SUPPLEMENTAL MATERIALS

Find further review at: Simplifying radicals with constants only, With variables and Many videos on negative exponents

**Fri (weekend)** Read Ch 2 in Course Notes for Math 220 (Geoghegan and Brewster)
on
View: Finding domain of a function

Do p 16 exercises: #9-15

View Graphing piecewise functions

Do rest of Ch 2 exercises, pp 15-16, #1-6

Although I have not done chapter 3 in lecture, please do read it over the weekend and watch the videos.

Read Ch 3; view Break even problem 1 and Break even problem 2

WEEK 2

**Monday** The first problems in Ch 3 cover the review of lines, whose *general* form is px + qy + r = 0.

Do Ch 3 p 26 exercises #1-5

At the VIDEOS link, view the first group of videos (Cost, Revenue, Profit)

**Wed** Do rest of Ch 3 exercises pp 27-28 #6-16

Read Ch 4 (Exponential and Logarithmic Functions) View Graphing exponential fcns (up to minute 7:30) and Graphing log fcns

Do pp 43-44 #1-5

Topics for Quiz 1, Friday, covering Ch 2-3: Sketches of essential functions; finding domain of a function, using interval notation, composition of functions, equations of a line, linear cost, revenue, profit functions

**Fri** Here are some straightforward solving log and exp equation videos, by three different teachers, all fine!

Video 1, Video 2, and finally Video 3

Do exercises pp 43-44, #8 b e f g, 10 a c e f, 11 e f h, 12, 18, 19, 20 a-e, 21 b d f

WEEK 3

**Mon** No classes, Labor Day!

Per webpage – stay caught up on reading. Always read ahead and watch these videos.

Solving exp eqns, Solving log eqns Ex 1 and Ex 2

There are plenty of videos for solving equations, but people tend to have the most trouble with radicals. Watch these:

Solving an equation with one radical, Solving an equation with two radicals Solving rational inequalities

**Tues** DO THIS Solving equations and inequalities worksheet

Read Ch 5; view Compound Interest videos in VIDEOS

**Wed** Do Ch 5 exercises first set #1-7, and second set #1-4, 6, 7, 9, 10, 12

Hand in worksheet Fri for grade.

**Fri** Do the Effective Interest Rates exercises if you skipped in Ch 5

Read Ch 6 Limits and view Finding limits from a graph

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)

YOU CAN DEFINITELY DO first exercise in Ch 6 p 67 #1-12

If you need more help understanding Limits, see “Section 6” (that is, Chapter 6) block of videos in SUPPLEMENTAL MATERIALS

I often choose problems from the Supplemental Materials Worksheets for quizzes and exams.

WEEK 4

**Mon** Finish Ch 6 p 67 Exercises (through #30). My complete solutions are posted here and on solutions page Ch 6 solutions IGNORE #22

Also, do Supplemental Limits Worksheet and see the complete Limit worksheet solutions

Read Ch 7 and view first two videos under **Derivatives** at VIDEOS

**Wed** Watch the rest of the videos under **Derivatives** at VIDEOS

Also, check out these:

Just slope at x = a using limit of DQ

and

Slope at x = x1 (same as x = a) AND equation of the tangent:

Do Ch 7 Exercises p 71 #1 c, d, e, #2 c and Ch 8 Exercises p 77 #1-4

Brief quiz on Friday on Ch 6, 7/8. A few limits as well as eqn of line tangent to curve using limit def of derivative for slope.

**Friday** Read Ch 10 a couple times. Watch the videos again on derivatives.

Here's Patrick doing Power rule shortcut examples. You can follow his link to other examples if you need to.

Do Exercises in Ch 10 #1-5 and #6 a-d

WEEK 5

**Mon**

1. Finish Ch 10: As assigned Friday, you'll have no trouble *finishing* Worksheet worksheet on //C//', //R//' and //P//'

View Product rule examples and Quotient rule examples

2. Do Ch 10 #8-13 and #16 d-n

3. Ch 11, watch Chain rule explained by Patrick mjt

Read Ch 11 and view these *short* example videos:

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)]

**Wed** Do Ch 11 p 96 #1, and in each of the multi-part #2, 3, 4, do every other one. Also #6, 7 and 13 (every other)

*Read* Ch 12 (we've done the Leibniz notation – since this chapter should go before chain rule, I taught most of it already. A second derivative entails taking the derivative of a derivative. Don't worry about higher than derivatives than second.

Quiz on Friday on derivative computation (no word problems). I will put the 'forms' I talked about today on the overhead as a guide.

Here are Worksheet solutions for C', R' and P'

**Thurs** Prof Dave explains implicit differentiation

**Friday**

1. Re-read Ch 13 Implicit differentiation (ID); read Ch 14 Related rates (RR)

2. View videos, twice if necessary:

RR 1: Area of circle and changing radius rate

RR 2: Ladder sliding down the wall problem

RR 3: Cost and profit with respect to time

3. Do this worksheet, best you can, and see the same plus full solutions under it:

Related Rates Worksheet Solutions to Related Rates Worksheet

WEEK 6

**Mon** Do Ch 14, #1, 2, 4, 9, 12, 13

Study for Exam 1, which will be on Friday.

See solutions to Ch 14 exercises here Ch 14 #1, 2, 4, 8, 9, 12, 5 and 13 and in HW Solutions

TOPICS FOR EXAM 1: Please prepare your questions for review day (Wednesday) accordingly. Come prepared by looking over HW exercises and supplemental worksheets on these items, so you may ask about any you are still unsure of.

BE ABLE TO:

- Sketch any essential functions, showing x and y intercepts

- Sketch a piecewise function

- Solve equations and inequalities, and answer in interval notation (see first take home for types, which includes from among abs value, root, rational)

- Solve log and exp eqns using log properties and definition (see Ch 4, also second set of exercises in Ch 5)

- Find limits (left and right and two-sided, supporting work for infinite limits)

- Find derivatives of all kinds (including implicit)

- Find equation of line tangent to a curve at a point

- Solve cost/revenue/profit/demand problems that entail
*non-linear*functions, and*interpret through marginal phenomena*, clearly explaining*with words*the meaning of marginal cost, revenue, profit, demand, with respect to units of sales or production (x or q) or price (p)

- Solve a related rates problem (application to business)

**Wed** A few things to help you study:

Marginal analysis extra practice problems from internet pdf (edited, may look a little dodgy),

Derivative extra practice and Solutions thereof

More implicit differentiation problems

View Extrema

Critical numbers of fcn and excellent example to illustrate

More about excellent example in previous video

Patrick mjt finds critical numbers of a fcn

Patrick mjt does a harder example

Do Ch 15 pp 129-130 #1, 2, 4 a-i

Supplemental worksheets:

Related rates worksheet and Related rates worksheet solutions

WEEK 6 to 7 (Rosh Hashana)

**Fri-Tues**

1. Read Ch 15, Critical Numbers of a Function

2. View Extrema

Critical numbers of fcn and excellent example to illustrate

More about excellent example in previous video

Patrick mjt finds critical numbers of a fcn

Patrick mjt does a harder example

3. **Enroll in Lumen OHM**

- Go to ohm.lumenlearning.com

- Click on “Enroll in a New Class”

- Enter Course ID 35852 and Enrollment Key KM220F19

- Confirm the course details and click on “Enroll”

- Check out the Student Tutorial for using Lumen OHM

- Wait for my further instructions

**Wed** You should be reading Ch 15 and Ch 17

Do Ch 15 pp 129-130 #4 a-i (if you have trouble, watch the videos again from Monday).

Do also Critical numbers worksheet

OHM: Do HW 2.5. Watch this for additional information tomorrow.

**Fri** Read Ch 17

Vew: Increasing and decreasing functions

First derivative test for local extremes

Do Ch 17 p 141 #1, 2 a-m. As in the video and reading:

1. Find all critical numbers of f(x)

2. Put them on a number line

3. Inspect sign of f' in each interval created: does f increase (f' > 0), decrease (f' < 0), or do neither?

Check your work against the posted solutions.

WEEK 8

**Mon and Wed** Read Ch 18

View Second derivative test for local extremes: concavity

Print and bring to class this Summary of Curve Sketching Polynomials and Root Functions

Do exercises Ch 18 (in this order) #1, 3 a-e, 2 a, b, e, f, h

Do OHM HW 2.6 after watching the videos there, too. There are only 7 problems, so I will count this as an actual mark and not just for effort (which is how I counted the last one).

You will have a short curve-sketching quiz on Friday!

**Fri** I have covered all the material in Chapters 19-21, so please read those and view the remaining videos.

View Limits at infinity (horizontal asymptotes--including "tricks" at 6:16)

Graphing a simple rational function

Graphing a harder rational function

Sketching a more involved rational fcn with FDT and SDT

Ch 19, do exercises #1 a-c, #2 a d i; Ch 20 pp 167-168 #1 a, #3, #4 a-g #5 c d e f; Ch 21 p 174 #1, 2, 3

WEEK 9

**Mon** Study for Exam 2, Chapters 15-22 (there's a simple concept in Ch 16 I will talk about tomorrow that is easy to understand for a concept question). Ch 22 is another simple concept, absolute extreme on a closed interval.

*Topics*: Concerning the way derivatives (first and second) affect a curve (increasing, decreasing, local and absolute max and min, concavity, inflection: T/F and short answer and sketch a curve that follows the description given; limits at infinity for all kinds of functions (poly, rational, root, exp and log); curve sketching in detail similar to HW and the quiz, following the Ch 21 instructions (same as we did on the quiz on Friday) – see p 171; finding local max and min and absolute max and min if they exist on a closed interval.

MORE CURVE SKETCHING VIDEOS:

End behavior, rational functions

End behavior, exponential and polynomial

Again, please watch:

Examples first and second derivative test to graph functions

Graphing a simple rational function

Graphing another rational function

Finally, Supplemental Worksheets with Solutions

**Tues** This last chapter is a great review of the entire unit.

Read Ch 22

View: https://www.youtube.com/watch?reload=9&v=w6bafnqHOgU

Do Ch 22 exercises p 185 #3 ONLY (solutions to #4-8 are posted)

Do Absolute extreme exercises from OHM text

WEEK 9-10

Unit 3 begins: Optimization!

We'll use OHM for this *entire unit*! Leave your Course Notes text at home.

Links to various components of OHM are given below, so there's no doubt as what is due when and how to find it. HW includes reading, videos, OHM textbook problems (to prepare for class, as usual) and finally the online OHM HW, *which you should look at earlier than the Oct 27 pm due date!*

**Fri**

*Review reading* Ch 2.7 Critical numbers & values

*Read* OHM Ch 2.9 Optimization Problems

*View* Fence problem 1

For Monday, do #1-3, 9, 10 in OHM Ch 2.9 Optimization

**Mon** Keep up the *reading* in Ch 2.9

*View* Max and Min Applications Part 1 and Part 2

For Wed, do #4-8, 13, 14 OHM Ch 2.9 Optimization

**Tuesday**

*View* Computer software sales and the videos in the OHM for optimization as well (2.9)

**Wed** Read Elasticity Online Text 2.10

Friday, do only #16, 17, 18 a & b OHM Ch 2.9 Optimization – these are difficult problems, as it turns out, so do your best. I'll explain them in class.

Here are the two worksheets and solutions from the Supplemental Materials:

Opt Wksht 1 and Opt Wksht 2 and the Solns to Opt Wksht 1 and Solns to Opt Wksht 2

Second chance on the desk check Friday. Have some work to show. Supplemental sheets are good, too!

Also for Friday–Video HW:

First, view this excellent presentation of overall picture, NO CALCULUS, explained by an economics professor in a highly accessible way, Prof Tarrok's Elasticity of Demand

Second and third, view the OHM videos, linked here, which give the formulas explained and worked problems OHM Elasticity 1 and OHM Elasticity 2. Note the demand function is labeled D(x), but it means the same as q(p), which we use in class.

**Fri** Complete the OHM HW Ch 2.9 online. Due Sunday at 6 p.m.

Do Optimization problems to hand in

Read Elasticity Online Text 2.10 and Ch 24 in our book and also my summary Price Elasticity of Demand

WEEK 11

**Mon** Do Supp Mat'ls elasticity exercises on Elasticity worksheet

and OHM Homework 2.10 (note, I have deleted the first two problems; there are only 5 problems or so)

Quiz *Wed* in class on Optimization / Elasticity

**Tues** Due to my absence Monday, the quiz will be on Friday.

Optimization problems to hand in are due Wed (instead of Mon)

Please bring your work on Elasticity worksheet on Wednesday; refresh your memory by watching the videos again at OHM Elasticity 1 and OHM Elasticity 2

**Wed** Read Ch 4.1 Lumen OHM text Ch 4 pp 234-239

Do in same Exercises #1-6 on p 249 and #11, 13, 19, 21, 23 on p 250

STUDY FOR QUIZ FRIDAY:

1. Practice problems for quiz–Notice #5 is not constrained by volume, but simply by minimizing cost. If it had a volume it had to hold, it would be more like #6. I won't give you exactly these problems, as the numbers will be different.

Optimization practice problem solutions (first two are at end of scan)

Note, an error in solution #7. See

2. Ch 24, p 199 #1-9 in *Course Notes*

Elasticity solutions part 1 and Elasticity part 2

**Thurs** Watch this or *you will be lost tomorrow*, as I am not spending loads of time on computation of partials:

*View* Partial Derivatives and Patrick mjt

You might have missed this one on Lumen: Lumen video 1 Functions of 2 variables

The OHM for this is not due till Friday 10 pm, but you could do it sooner

**Fri through Wednesday** *Lagrange Multiplier Method–solving a constrained optimization problem*

1. HEADS UP–Last OHM online till next unit: **OHM Online HW**: **4.1 due Friday 10 pm** and **4.2 due Mon 10 pm**

2. Partial derivatives reading: *Course Notes* Ch 27, and OHM text p 255, Examples 3 and 4 on pp 258-259

3. Do *Course Notes * p 219 Exercises #1 a b c e f i, 2, 3, 4

4. Do 4.2 OHM Online (due Monday night)

5. Reading on Lagrange multiplier method: *Course Notes* Ch 29 and //Bittinger// pp 579-58

6. View Prof Bhatnagar on Lagrange Multiplier Method

WEEK 13

**Mon** Do Lagrange method exercises in Bittinger pp 587, #1-13 odd and #17-21 and #25

and in *Course Notes* Ch 29 exercises

Study for Exam 3–Optimization, including Supplemental worksheets on Lagrange method (these are mostly the same as in Course Notes)

Here are Optimization problems from alternate text

**Wed** Study for Exam 3, all types of optimization, including elasticity, maximizing revenue, etc, constraints using Lagrange multiplier method, derivatives and partial derivatives. Interpreting partial derivatices, for example, the Cobbs-Douglas function problem

Here are my Course Notes Ch 24 Elasticity solutions #1-7 and #8 and Course Notes Ch 29 Lagrange solutions I need to edit my 'explanations' as they are not great. But study the working!

**Studying for Exam 3** Any of the above materials are good. A good way to review theory is to read Ch 24, 26, 27 and 29. Also, the OHM readings and HW you submitted.

I will suggest some focus-type problems, but don't conclude these are the exam questions. THEY ARE NOT. They are merely a guide.

The topics are derivatives, partial derivatives (pure first and second partials only, no mixed), interpretation of partials in terms of multivariable functions. Geometric and non-geometric optimization (one to be done with Lagrange and taken form among Alternate text. A Cobbs-Douglas function, to calculate partials, evaluate, and interpret as in the video I showed in class Here's a similar one. An elasticity function similar to Ch 24 and supplemental worksheet problems and videos. A hot-dog-type optimization as well as a straightforward single variable business, where you will be expected to form the functions from givens. And, some kind of synthesis to show you have absorbed the material.

Helpful previous semester quiz on Lagrange, elasticity and Cobb-Douglas functions

**Fri** Read pp 372-376 of Ch 5 Integration in TEXT, Hoffman et al.

View Antiderivatives and indefinite integration and Examples of basic indefinite integration

WEEK 12

**Mon** Read again, pp 372-376 of Ch 5 Integration in TEXT, Hoffman et al.

View Antiderivatives and indefinite integration and Examples of basic indefinite integration

Do #1-25 on p 381 of TEXT, Hoffman and Bradley

**Wed** View Antiderivative with initial conditions (finding a particular F(x)) and Examples of basic indefinite integration

Do Ch 30 #3-8 all; note error in wording on #5, it should say MC is cost to produce (x + 1)th item (Solutions are posted)

View: u-substitution

Examples of simple u-substitution

Read Ch 31 u-substitution of *Course Notes* and OHM Ch 3.4; supplement with Ch 5 Integration in TEXT, Hoffman et al.

UPDATE: OHM HW 3.3 is due Thursday, but I removed definite integral problems

**Fri** OHM HW 3.4 is due Sunday night; Do Ch 31 #1 a b c f h k l, # 2-5 pp 248-249

WEEK 14

**Mon-Tues** TOPICS: u-Substitution; Area Under a Curve

**Do** u-substitution exercises in Hoffman et al. pp 394-395 #3-25 and #51-55 (you can read section before it if you still need to see examples of u-substitution)

**Read** OHM 3.1 and to supplement it, Hoffman et al. pp 397-406 on FTC

**View** the *complementary* videos, which are foundational to this unit. Plan to spend about 30 minutes watching them over the course of the two days. The function called the antiderivative needs more thought than what was needed to understand derivative. Watch these over the next two days.

B) Approximating area using rectangles: START THIS ONE AT 5:20

C) Definition of definite integral: WATCH FROM 0 TO 2:30, THEN 4:00 TO END

D) Interpret meaning of area under curve Example 2 finding a definite integral (polynomial and power rule)

**Start** OHM HW 3.1 (due Thursday)

**Wed** Do Hoffman et al. pp p 410 #1-21 and p 412 #49-55

Also, practice from Supplemental Materials: Definite integration including with u-sub, #1-7 only

Do Take-home quiz on definite integral

Helpful video: Interpreting meaning of area under f(x)

Tomorrow, there is an in-class quiz on u-substitution and definite integral, including word problem

**Fri** View: Average value of a function f(x) on an interval

Read Average value and area under a curve, skip "Finding the Volume of Revolution" Do Average value and #1, 2, 3, 6, 7

WEEK 15

**Mon** View Integration by parts

Read Ch 32 of*Course Notes* on Integration by Parts and OHM Text Ch 3.5 Integration by Parts

people/mckenzie/math_220_hw.txt · Last modified: 2019/11/21 16:39 by mckenzie

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