The day (Mon, Tues, etc.) refers to the day the assignment is given, not when it is “due.”
By “due” I mean you should have done it and have questions ready for me. If you don't, then I move on.
Making an honest effort daily to do HW is the only way to pass the course. Occasionally, I collect a set of problems. Often, a collected assignment is a hand out or take-home quiz.
WEEK 1 (AUG 22-24) Your progress should be, roughly, 3 lines a day.
Read Sec 1 and Sec 2; view first five videos at SUPPLEMENTAL MATERIALS
Further review: Simplifying radicals with constants only
Do exercises: p. 5 #1, 2, 7 (first two, and for enrichment the third an fourth), 8
Do pp 15-16, #1 (domain), 2 (domain and roots–set the fcn = 0 and solve), 8, 9, 11, 12, 13
WEEK 2 (AUG 27-31)
Mon Read Sec 3 and Sec 4
Do exercises Sec 3, pp 26-27
Quiz topics to study for Friday Quiz Sec 1-3 Accurate sketches of essential functions showing intercepts and asymptotes; finding natural domain of a function; function composition; accurate sketches of a piecewise function and expressing its stated domain in interval notation; solving an equation for x (reference Ex 2.5 and 2.6); multi-part problem on cost, revenue and profit, as done in class today; definition (what is meant by) marginal cost for any cost function.
Read Sec 6, Limits. Watch the videos by Patrick. He is among my favorite Internet teachers for his ability to simply and clearly convey the lesson.
Fri-Sun Do p. 67 #1-12, #16-30 even. Numerous examples are found in the reading and in the rest of the videos under LIMITS at Videos. Here they are, as well.
Finding limits from a graph (This is one of his rougher videos, but well explained.)
More techniques for evaluating limits, Ex 3 (gives a little jump on continuity)
IMPORTANT Infinite limits in which a function goes to positive infinity or negative infinity as x approaches a:
Read Sec 7 and Sec 8.
Go to Derivatives section of Videos, read my intro there and watch the videos under the first section, Instantaneous rate of change of a function at point via the difference quotient (DQ)
WEEK 3 (Sept 3-7)
Tues Finish Sec 6 Exercises #1-30, on p 66. See my posted solutions!
Re-read sec 7 & 8
View Derivative videos: Difference quotient (DQ) and the definition of derivative
Wed Do Sec 7 p 71 #1, 2, 3 a-d
HAND IN ON FRIDAY the worksheet we started in class. Here it is again, with typo fixed:
I opened up the spacing, so you can do a nice neat job on this.
Read again "The derivative function and marginal analysis (of cost, revenue and profit)". This pdf is from a text that has many applications. Its approach is methodical and clear. Especially note the approximation of exact cost to producing an additional unit to the marginal cost, C'(x). For our purposes, we use C'(x) as this cost to produce and additional unit.
Rosh Hashana break homework
View enough of these to attain the skill for finding equation of the line tangent to f(x) at a given point:
Do Sec 8 p 78 #1, 2, 3, 4, 7 using power rule rather than limit definition to get f'(x) WEEK 4 (Sept 12-14)
Wed Study for SHORT Friday quiz: limit computation, equation of line tangent to f(x) (using power rule), and derivative computation. NO finding derivative via limit of DQ as h –> 0.
Read Sec 10 (product, quotient, log and exponential rules of differentiation).
Do Sec 10 pp 91-92 #1-6, #8-13. See example videos for product, quotient rules under “Derivatives”
Fri-Sun Catch up on Sec 10 exercises (see previous line).
Read Sec 11 (chain rule). View Chain rule proof
This is a pretty good video. The lecturer uses the Leibniz notation dy/dx. There's a little fudging of u(x) as g(x), but he says so. Chain rule is an ESSENTIAL skill. Most problems involve chain rule.
We did the exp and log base e derivative rules, but not the ones for bases other than e. They are similar but have an extra multiplier term. Here are two simple short videos that show examples of just what the book and the handout have:
See Videos for examples of working chain rule.
Do pp 96-Sec 11 #1, 2 b c f g l m, 3 a-d, f l m n, #4 a d e #6, 7
Read Sec 12, Higher Order Derivatives and Leibniz notation (dy/dx)
WEEK 5 Sept 17-21
Mon Do Sec 12 problems on Leibniz' dy/dx notation: p 107 #1 only.
Do Chain rule worksheet. Exercise 2 says decompose the function into f(u) and u(x). Please take the derivative dy/dx = (dy/du)(du/dx), too!
See my synopsis and watch video of Implicit Differentiation (ID) in Videos
Read Sec 13.
Tues/Wed Check your answers from the Chain Rule worksheet on:
Catch up on differentiation HW
View related rates videos; read synopsis Video page
Thurs PRINT AND READ this PDF on Sec 13/14
Fri Do Sec 13 #1, 2 a-d, 5, 6, 8; do Sec 14 pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14
STUDY FOR QUIZ ON MONDAY for SEC 01 (8:00 a.m.) class, TUESDAY for Sec 02 class
Catch up on all HW and have questions ready to review before next week's exam.
WEEK 6 This week you have EXAM 1 on Friday, covering Secs. 1-4, 6-8, 10-14
Omitted for now are Sec 5 (compound interest) and Sec 9 (continuity)
Mon/Tues Review these focus topics for the exam: