**Problem of the Week**

**Math Club**

**BUGCAT 2020**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

people:grads:fang:hwassignments

**Wed Aug 23** Read Sec 1 and Sec 2; do problems Sec 1, pp 5: 1, 2, 7, 8;

**Fri Aug 25** Read Sec2; do problems Sec 2, pp 15-16: 1-13

View Break even problem 1, Break even problem 2 Use derivative to find eqn of tangent line Ex 1 and Ex 2

**Mon Aug 28** Quiz on Sec 1, 2 will be Tuesday.
Read Sec 3 and Sec 4; do problems Sec 3, pp 26-27

**Wed Aug 30** Read Sec 4 again. Some helpful videos.

Solving exponential equations without and with logs

3 examples of solving exponential equations

Example solving logarithmic equations

Another example solving logarithmic equations

Do Problems pp 43 #1-5, 8 b e f g, 10 a c e f, 11 e f h, 12, 14 b, 17 a, 20 d e, 21 b d f

**Tue Sep 05** Read Chapter 5 and view *comprehensive* video lecture on compound interest problems:

The value of a loan or investment over time can be given by *P*(*t*) or *A*(*t*). Both stress functionality with respect to time.

Do Chapter 5 p 56 #1-7

An interesting video is Understanding the number e (exponential growth).

**Wed Sep 06** Read Sec 6 Limits and go to math220_videos to view the video on limits.

After looking over Today's notes and rereading Chapter 6, do Problems Chapter 6 p 66 #1-12 all and #16-30 even. These videos are helpful.

Evaluate limits using properties, Ex 1 and Ex 2

More techniques for evaluating limits, Ex 1, Ex 2, Ex 3

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

** Mon Sep 11** Read Chapter 7 and Chapter 8. Go to math220_videos and *view all* for this section. Many examples fully worked. Do Sec 7 pp72 #1, 2, 3; and Chapter 8, pp78 #1, 2, 3, 4

** Fri Sep 15** Here is a very good reading material for understanding marginal analysis in business and economics.
marginal_analysis_from_alternate_text.pdf. Read this chapter from an alternate text.

Read Chapter 9. View all three math220_videos on continuity. Do Chapter 9 pp 84-85 #1 a-e, 2 a-d, 4, 5, 6

Read Sec 10. Do pp 92 #1-6, #8-10

** Mon Sep 25** Read Sec 11; do pp 97-98 #1, 2 b c f g l m, 3 a-d, f l m, n, #4 a, #6, pp 98-99 #7, 13 c e f g h j m
(This set of homework is due next Tuesday.)

** Mon Oct 02** Do problems in Sec 12 p 107 #2, 4, 5

Read Sec 13. Do Sec 13 #1, 2, 3, 4, 8

Read Sec 14 (related rates) and view the related rate videos (read my synopsis on the Video page).

￼Related rates 1: Area of circle and changing radius rate

Related rates 2: Area of triangle and changing side length rate

** Fri Oct 06** Exam 2 is scheduled on Oct 25th. Contains Chapter 12-22.

Related rates 3: Ladder sliding down the wall problem

Read Sec 14 again and videos again. Add Cost and profit with respect to time

Do pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14

Read Sec 15.

View:Finding critical numbers of a fcn

Do pp 129-130 #2, 4 a-i

** Tue Oct 10** Read Sec 16 and view short videos on these theorems (not included on test but need to start them to be on schedule, since we have an extra day before the test than two other sections).

Do p 136 #1, 2

Also, try this Implicit and critical number practice quiz.

** Oct 13-17 ** Read Sec 17 and 18, and Kathy's notes:

Do Sec 17, p 141 #1, #2a-m

Read over this Notes on First and Second Derivative Tests

Read Sec 18; get to work on Sec 18 pp 148-149 (Do #3 before #2) #1, 3 a-e, 2 a, b, e, f, h

Read Secs 19-21.

**Mon Oct 23**

View Sketching rational functions and Sketching another rational function

Read Sketching rational function notes

Read some of Kathy's older notes on Curve-sketching book examples

and More curve-sketching book examples (These contain some Sec 18 HW problems, so see the solutions link, too)

View Sketching a polynomial with FDT and SDT and Sketching a more involved rational function with FDT and SDT

Sec 19-22 HW cover the skills we have now discussed fully.

For example: Limits at infinity, which relate to horizontal asymptotes (including "tricks" at 6:16) and Detailed examples of first and second derivative for graphing a function

Do Sec 19 #1 a, b, c, #2 a, b

Do Sec 20 pp 167-168 #1 a, b, c, #3, #4 a-g, #5 c, d, e, f

Read How to find absolute extrema of a function on a closed interval

** Tue Oct 24**
Here's a supplementary worksheet for the Thms in Chapter 16.MVT,EVT,IVT and Rolles Thm Extra Worksheet

** Wed Nov 1** Read Sec 23

View:

Optimization problem (instructive)

Do p 192 #2-5, 6, 9, 10, 12, 15, 16

Read Sec 24, Elasticity

Do p 199 #1-5. Read over Kathy's summary here. Summary of Elasticity

** Mon Nov 6** Do p 199 #6-9

Prepare questions on any of the topics in the covered chapters.

** Exam 3 is on Tues Nov 14. The test covers Sec 23-24, 27-29. **

Here is an old quiz Kathy gave on the D test, all worked out. Write the question and try it on your own, comparing your answers to the one on the quiz key.

Quiz and solution on extremes in 3-space

Here are some partial differentiation practice and elasticity practice from Kathy:Partial differentiation practice

Elasticity problems and Elasticity solutions

** Final Exam is scheduled on Monday, Dec 11, 8:00 - 10:00 in SW 331. Here is the link: **
http://bannertools.binghamton.edu/exams/index.php?view=2&dept=MATH

** Fri Nov 10 ** Read Sec 26 (Functions of Two Variables) and Sec 27 (Partial Derivatives)

View Partial derivatives

Do Sec 26 p 212 #1-4, #6-8

Do Sec 27 p 212 #1 a-c, e, f, i

View Second order partial derivatives

Read Sec 29. View Optimization via Lagrange multiplier

Do problems p 233 #2 a b c e, 4, 6, 7

Here's Kathy's Notes and Detailed Example Sec 28 in which she explains why the criteria of the SDT using D(x,y) makes sense.

View:

More examples local max, min and saddle point by analyzing D value

Local extremes and saddle points of multivariate function

Do p 226 #1 a-e,i #2

** Mon Nov 13 ** Here's an extra problem set on Lagrange Multiplier. http://www.math.ttu.edu/~drager/Classes/08Spring/lagrange.pdf.

Soln to Quiz 9 is here! Soln to Quiz 9

** Class Schedule for the rest 2 weeks is here! **

**Mon Nov 27** Read Sec 30 and view the first video under the Integration unit videos.

View Finding a particular F(x), given initial conditions (xo, yo)

*Integration catch-up:* Know rules of antidifferentiation, pp 237-238 (basically the same as video and handout/pdf above)

Helpful videos to watch again: Indefinite integrals (basic examples) Finding a particular F(x), given initial conditions (xo, yo)

Read Sec 31. View u-substitution and Another u-substitution Do p 242 #1 a-i

Do p 248 #1 a b c e f g i j k l

Read Sec 32 Integration by parts. View Integration by parts made easy

Do problems p 255 #1 a b c d e g h i k (see video and examples in text)

Read Sec 33, Finding a Definite Integral

**Tues Nov 28** This week we cover the Fundamental Theorem of Calculus.

There are two parts to this theorem. We generally use the second part, which is what we need to find the value of a definite integral. To that end, watch Fundamental theorem of calculus part II

(The theoretically deeper but fascinating Fundamental Theorem of Calculus Part I is at the video link)

View Patrick's definite integral examples:

Example 1 of finding a definite integral

Example 2 of finding a definite integral

Do p 260 #1 a-e i j k o p q

Finally, read Sec 34, Definite Integral and Area.

Then view this important video: Finding area between two curves

** Last set practices **

Read Sec 35. This is a DENSE section that covers far more than the title suggests.

The road map:

- Riemann sum (area of rectangles of ever-increasing number approaches the area under the curve, i.e., the definite integral;

- average value of a function, which is neat because it tells us what value the function attains on an interval via the definite integral divided by the width of the interval;

- total value of a function, which is basically the FTC applied to a marginal or other rate function, whose antiderivative is the sought after function, say cost fcn, value fcn, any quantity given a rate of change of that quantity;

- present and future value of an investment through a constant flow of money (“income stream”) at continuous compounding (this is the analogous case to the Sec 5 topic of present and future value of a one-time investment).

View Average value of a function

The average value of a function is actually the mean value theorem of integration.

Read the rest of Sec 35, on Present and Accumulate (Future) Value of an Investment.

The difference from the Sec 5 topic, as I've said, is now we consider a continuous flow of money (an income stream, like an investment or a business venture).

Do p 278, all. The ones I have solutions prepared for are #1 a, d, 2, 4 a, 6-9, 11, 12, 15.

Solution to Quiz 10 is here

Solution to the take home quiz is here

**Sunday Dec 10** There will be a review session in LH 012 on Sunday Dec 10 from 1:00 pm - 3:00 pm.

people/grads/fang/hwassignments.txt · Last modified: 2017/12/08 16:42 by fang

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