Problem of the Week
Hilton Memorial Lecture
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.
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
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
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
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!
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 6 involving rational expressions
Read Sec 5
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
Friday Sept 18-Sunday Sept 20
The videos will take the place of the reading of Sections 9 and 10:
WEEK 5 Sept 20-Sept 24
Mon Sept 20-Tues Sept 21
Derivative exponential fcn with base a
Derivative log fcn with base a
Wed Sept 22-Thurs Sept 23
Chain rule explained by Patrickmjt
Ex of chain rule for radical function
Ex of chain rule for natural log function
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):
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.
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.
Increasing and decreasing functions
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
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
Examples first and second derivative test to graph functions
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
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
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
Related rates 1: Area of circle and changing radius rate
Related rates 2: Area of triangle and changing side length rate
Related rates 3: Ladder sliding down the wall problem
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
Wed Nov 3 - Thurs Nov 4
WEEKEND Fri Nov 5 - Sun Nov 7
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
Wed Nov 10
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
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 :
FINAL WEEK !!
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