The assignment is given on the day named.
You should have questions for me and be ready to answer mine on the previous day's assignment.
Quizzes will be announced for the most part, about one per week.
Making an honest effort daily to do HW is the only way to pass the course. Sometimes I collect a few problems. Maybe a hand-out or a take-home quiz. Sometimes, I do a desk check during the lecture break.
Wed to Thurs: Read Ch 1 and 2; view first five videos at SUPPLEMENTAL MATERIALS
Do p 5 exercises: #1, 2, 7, 8
Do p 16 exercises: #9-15
Fri-Sun View Graphing piecewise functions; do rest of Ch 2 exercises, pp 15-16, #1-6
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
Mon At the VIDEOS link, view the first group of videos (Cost, Revenue, Profit)
Do rest of Ch 3 exercises pp 27-28 #6-16.
Read Ch 4 (Exponential and Logarithmic Functions)
Do pp 43-44 #1-5, 8 b e f g, 10 a c e f, 11 e f h, 12, 14, 18, 19, 20 a-e, 21 b d f
Wed Read Ch 5
At the VIDEOS link, view the second group of videos (Compound Interest)
Study for Quiz 1 Friday, Ch 2-5; draw up 1 page of thumbnail sketches of essential functions covered in class, which you may use on the quiz.
Here is a scan of My essential function sketches
YOU MAY NOT USE MY PAGE. Copy it in your own hand.
Fri-Sun Do Ch 5 exercises #1-7 and continue if you need practice with the extra exponent practice.
View the last two Ch 5 videos at SUPPLEMENTAL MATERIALS, on continuous compounding and effective interest rate.
View all (yes, all) limit videos at VIDEOS
Read Ch 6. (Stay tuned here. One other post to come, which is practicing graphing piecewise functions.)
Mon Did you watch all the limit videos? Watch them again and use them and the examples in the book to do as many of the problems as you can so far.
Do Exercises p. 67 #1-12, #16-30 even.
The short of it is this: To find a limit, first plug in the x = a given. If you don't get a number, but get 0/0 or number/0, then you have to resort to algebra. The videos are your friend. I will be, too, but not till Wednesday.
Hint: I have posted the solutions already, so you could follow along.
Read Ch 9 Continuity
Find several more, including videos on graphing piecewise functions under Continuity in VIDEOS
Do Ch 9 pp 84-85 #1 a-e, 2 a-d, 4, 5, 6
Read Ch 7 and Ch 8
Short quiz on Friday on, compound interest, limits and continuity. No notes are allowed on this quiz.
Ch 5 Know all the formulas, n = finite and continuous compounding. Know how to solve for t. Effective interest rate.
Ch 6 Know how to take limits of all types, given a function and/or a graph.
Ch 7 Know the criteria of 'f is continuous at a point x = a' to use when you justify whether a function is continuous or fails. Be able to Graph a piecewise function. The video has two clear examples.
Fri-Sun Do Ch 7 Exercises p 72 #1, 2, 3 a-d
Mon Read Ch 8. Then, view the video, where Patrick finds the equation of the tangent line to f(x), but already has the derivative function f'(x) and evaluates it at the given point to get slope m. (Rather than doing the calculation of the limit of the DQ). This gives you the overall picture: Finding equation of tangent line to the curve
Homework on limit of difference quotient to hand in on Wednesday! Remember, it's easier to find the general limit at x = a, then substitute the three values -1, 0, 1 into this (the derivative!)
Do Ch 8 Exercises p 78 #1, 2, 3, 4 using the derivative formulas
Tues-Wed Review worksheets for Exam 1
I've extracted and entitled Supplemental Materials worksheets here. Practice what you need:
Solutions are found at Solutions to worksheets
Wed-Thurs Exam 1 Topics:
Essential graphs; function of a domain (interval notation); piecewise functions; intercepts (y and roots); limits; continuity; linear cost, revenue, profit; compound interest (solving for various unknowns, whether F, P or t); slope of tangent using definition of derivative (limit of DQ etc.) and equation of tangent line at a point of f(x).
As usual, some interpretation of answers, like marginal cost, time to double with finite vs continuous compounding, word problems on derivatives.
I meant to post this: Compound interest summary
WEEKEND HW Fri-Sun Read Ch 10 (derivative rules) and view relevant videos:
Mon-Tues Watch again Shortcuts to the derivative
Do Ch 10, p 91 #3-6 and #16 a, b, c, d, o
I've moved some previous videos down, for Mon-Tues viewing:
Finally, view Chain rule explained
Read Ch 11
Wed Do Ch 10 p 91, #8-13 and #16 d-n
HELPFUL READING (not to hand in) The derivative and marginal cost, revenue and profit
View these short videos:
Do Ch 11 p 96 #1, and in each of the multi-part #2, 3, 4 EVERY OTHER DERIVATIVE
Read Ch 12 (easy chapter on Leibniz notation and higher derivatives)
QUIZ ON FRIDAY Ch 10 and Ch 11
Here are the derivative worksheets again, and their solution files:
Fri-Sun Do Ch 11 p 97 #6-9, and in the multi-part #13 EVERY OTHER DERIVATIVE
Do Ch 12 p 107 #1, 2, 4, 5, 7, 9
To hand in Monday:
WORK INDEPENDENTLY OR NO CREDIT. More credit is gained for personal–even if faulty–work that has effort and time behind it than you get for copying a friend's, which gets no credit at all.
In the pdf, please ignore the note at the end, 'Compare to sketch we did in class on Wednesday'.
Feel free to use graphing program like Desmos to make your graph. It needs to be accurate, so you will want to scale your axes smartly.
Mon Read Ch 13. View both Implicit Differentiation videos at VIDEOS
Do Ch 13 exercises #1, 2, 3, 4, 8 (Tip: worked examples in the book will help you do homework problems)
Wed-Thurs First read related rates overview on Video page)
Finally, read Ch 14 and another text chapter on ID and RR
Do Ch 14 pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14 (again, videos and worked examples in text will help)
PRACTICE QUIZ Friday, to test how you handle derivative computation without formula sheet. Includes implicit differentiation. To mark at desks and keep to study for quiz that counts on Monday.
Fri-Sun Read Chapter 13.
At the VIDEOS view first video on critical numbers.
Related rates take home Please do this neatly so I may mark quickly and return it before exam.
Exam 2 is this Friday.
Topics are Chapters 10-15.
Mon-Wed Do Exercises in Ch 15
Do Ch 15 pp 129-130 #1, 2, 4 a-i
Tues-Wed Study these items for Exam 2, on Friday:
Ch 10-11 Derivative (the 'u-forms', product, quotient, chain rules); study both word problems and computation of derivatives.
Marginal analysis: the meaning of marginal cost, revenue and profit
Graphs of parabolas and lines
Ch 10-11: Derivatives (the 'u-forms', product, quotient, chain rules); both word problems and computation
Here's some extra reading with worked examples on log and exponential derivatives
Marginal analysis: meaning of marginal cost, revenue and profit
Graphs of parabolas and lines
Ch 12: Leibniz notation, meaning of dy vs delta y (dy does not equal delta y unless the f is linear); higher order derivatives
Ch 13-14: Implicit differentiation and related rates: finding eqn of all tangent lines to curve at given x (be able to find y's); word problems in related rates, including geometric (circle, cylinder, triangle) and application to commerce: df/dt = (df/dx)(dx/dt) where f = C, R, P, and so on
Ch 15: Local extremes of a function and critical numbers: identify local extremes from sketch, know definition of critical numbers, find critical numbers c such that f'© = 0 and what c give DNE for f' (review domain so you know what to discard as a possible critical number), identify if, for critical number c whether f© is local max or local min by applying def of loc ext (that is, check f(x) for a NEARBY x < c and x > c)
Mon-Tues View Ch 16 and Ch 17 videos:
The lecturer presents the general IVT: f is cts on [a, b], f(a) < f(b), though the function doesn't change sign. I showed the particular case, where f(a) < f(b) because the function changes sign on the interval. It's a useful form of the IVT, since most applications concern zeros of function.
Read Ch 17 only!
Re-read Solutions Ch 15
I posted Ch 17 solutions–to guide your Ch 17 exercises. Refer to videos above as well (first)
Do Ch 17 p 141 #1, 2 a-m
Do like 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. (This is a little flippy in terms of learning, but it's straightforward.)
In place of the quiz tomorrow, you will have a take home problem to work out and I will collect. Quiz upon your return.
Read Ch 18
Fri On the following video, pay close attention to a good technique (3:45 onward) for creating the curve above the number line. He draws an actual rough sketch of the function!
And, my Summary of Ch 15, 17, 18 The alternate text and the videos are the best.
Do exercises Ch 18 (in this order) #1, 3 a-e, 2 a, b, e, f, h
WEEK 9 HOMEWORK FOR THE WEEK OF SPRING BREAK
Mon-Sun of Spring Break You are responsible to read Chapters 19-21 over the break, covering the three classes of curves: polynomials, rational and root functions
Read Ch 19; Do exercises Ch 19 #1 a b c, #2 a b c d f i
Read Ch 20
Mon Do exercises Ch 20 pp 167-168 #1 a b c, #3, 4 a-g #5 c d e f
Read Ch 21; do exercises p 174 #1, 2, 3
Read Ch 22, absolute extreme
Wed View Absolute Extrema
Do Ch 22 exercises p 185 #3, 4-8 (absolute min/max with business application questions)
The calculus of Ch 23-29 facilitates one of the main areas of problem-solving in the fields in economics and management. To optimize is to either maximize or minimize factors like cost, revenue, profit, demand, price, and so on. There are three categories of problems:
Fri-Sun I shifted much of the Wed HW line down to here—plenty to do!
Do those exercises concerning the two topics we covered (straightforward and container problems) from among Ch 23 exercises p 192 #2-5, 6, 9, 10, 12, 15, 16
Be ready with questions from these two categories of HW problems on Monday
View the third category of optimization problem videos:
Computer software sales This video's two examples are similar to the lamp sales problem in the text (y-intercept in first example of the video is incorrect; it wouldn't be that n = 0 price reductions means $0 revenue–more about that in class)
The famous Hot dog problem
Slightly different approach to hot dog problem Optimizing revenue given two points of data
Mon If you need extra help on Optimization, you'll find excellent coverage in Bittinger et al. textbook and read in Ch 2, Sec 2.5, pp 262-272 in the pdf (the actual textbook pp, not the pdf pp)
1. Do Practice problems for optimization quiz to prepare for Wednesday; print the sheet of problem sheet, too, to bring in for the desk check
2. Finish Ch 23 exercises concerning the third category
3. AND DO THIS, TOO, NO KIDDING:
View Elasticity of Demand, a good video lecture
4. Read Ch 24 Elasticity
5. Read Price Elasticity of Demand
Wed Do Ch 24 exercises, p 199 #1-9
Fri Do Supp Mat'ls elasticity exercises on Elasticity worksheet
Skip Ch 25
Ch 26-27 covers multi-dimensional functions of the form z = f(x,y) (two independent variables, that is, two input; one output, as usual!)
Watch as much of the video Multivariable functions as you need to get the picture of how z = f(x,y) represents surfaces in 3-space. Though a advanced as a graphing exercise, it is insightful in terms of input (x, y) and output z = f(x, y).
Read Ch 26 (notation of z = f(x,y)
Do Ch 26 p 212 #1-8
First, view this pretty good Khan academy partial derviatives, and don't worry about the trig term. (The derivative of y = sin x is y' = cos x, and the derivative of y = cos x is y' = -sin x. No problem!)
Then, view this rather old-fashioned sounding teacher in a Super cool graphics explaining partial derivatives
Then, view Partial derivatives up to 11:07. You might not get it on the first read, but that's ok.
Go on to read: Ch 27 (Partial Derivatives)
Mon Watch again, this time to the end: Partial derivatives
Read again Ch 27 and study the text's examples. We prefer spare notation f sub x and f sub y to the Leibniz notation
Do Ch 27 exercises p 219 #1 a b c e f i, 2, 3, 4
[A word about Ch 28: Although we're skipping it, finding local extremes of surfaces in 3-space can be visualized because it's analogous to finding extremes in 2-space, though more complicated, because of the first and second degree partials. In fact, there are infinite possible directions a particle on a surface can move in the z direction with respect to x and y that are not parallel to x and y.]
Wed Patrick's Lagrangian multiplier method for solving optimization with constraint uses the same set up as our book. He begins with the general algorithm for three variables, x,y,z. But don't worry, as his example uses only two variables, x,y.
Read Ch 29 and the following scan Goldstein et al. (Wait for it.) Study the examples.
Start reviewing for the test.
Fri Now you can see the second method, which is a bit shorter and cleaner.
Do pp 233-234 #1-4 Solutions are posted now.
Quiz will be a take home, to be gone over as a review on Monday.
Do Ch 29 p 234 #6, 7
[MORE PROBLEMS TO BE POSTED HERE FROM THE SCANNED MATERIAL]
Exam 3 on Wednesday. First set of practice problems are filled in. Other topics will have problems later.
1. Review and practice optimization by Lagrange in Ch 7.5 of TEXT, Hoffman & Bradley
Cobbs-Douglas examples are well done and show how x and y are easily isolated. It would not be out of the question to see one on the exam, as long as the numbers are reasonable.
You may ignore any problems that entail f(x,y,z).
Practice end-of-chapter exercises: #1-11, 17-22. The answers to odd numbered ones are at end of text. Page numbers of the pdf don't match the page numbers of the actual book, so use the point and click on TOC to get to the sections you need.
2. Partial derivative short answer
4. Curve sketching
5. Optimization (other than by Lagrange)
Tues To study besides various materials and the text and my HW solutions:
Do a few from each of the Worksheets 23/24/25, 28, 30, 40, 41, 44, 45 at SUPPLEMENTAL MATERIALS
Skipping absolute max/min this time.
Study your notes! Make sure you can answer briefly and clearly on things like the meaning of partials of business functions. Practice finding intercepts! Be able to do certain sketches without calculus, as we've often discussed.
Fri-Mon Read pp 372-376 of Ch 5 Integration in TEXT, Hoffman and Bradley
Read also you text, Ch 30. But the other book first
Bring last week's take-home assignment for me to collect and grade
Wed Do Ch 30 p 242 #1 and 2 (watch Fri-Mon videos again if you need to)
Do #1-25 on p 381 of TEXT, Hoffman and Bradley
Finish reading about initial (boundary) conditions in our book, Ch 30
Fri-Sun Do rest of our book's Ch 30 problems, and do p 382 of Hoffman #31-34, 41-47
Continue reading Hoffman Ch 5 to p 403 ( skip Ex. 5.2.8, 5.2.9 and 5.2.10)
Read Ch 31; know rules for anti-differentiation on pp 237-238 (basically the same as the video examples)
Do Ch 31 p 248 #1 a b c e f g i j k l
Read Ch 32 in our text and Ch 6.1 pp 475-479 in Hoffman
1. View Integration by parts
Do Ch 32 in our text, p 255 #1 a b c d e g h i k (rely on examples in text as well as video and notes and Hoffman)
After reading Hoffman pp 475-479, do pp 486-487, #1-13 odd and #23, 24
2. DEFINITE INTEGRALS: The definite integral calculation of the Fundamental Theorem of Calculus is quite straightforward. First watch some example videos:
Read Ch 33 of our text and Hoffman pp 403-408 through Example 5.3.10;
Hoffman p 404 has a box with the rules for definite integrals!
Do in our text Ch 33 p 260 #1 a-e i j k o p q and in Hoffman pp 410-411, #1-20
Wed Prof Dave Videos on the FTC:
Here's Prof Dave's Indefinite integral, which he does after the definite integral! You should find this to be a good review.
Read Ch 34, catch up on previous HW
Fri-Sun Prof Dave's Area between curves
Read Hoffman pp 414-427 on area between curves and study its examples
Do in our book p 268 #1 a b e f, 4, 5, 6 a c g, 8, 9
Do Hoffman pp 427-428 #1-12, 17, 18
Ch 35 is DENSE, covering far more than the title suggests. It's about total and average value of a function on an interval (in one way or another). The independent value is mainly t = time now. Here is a road map:
1. View applications of the definite integral:
Prof Dave's Average value of a fcn (MVT for Integrals)
A super low tech but very short and very understandable Present and future value of a continuous income stream
2. Continue with Hoffman p 428 #19-22 and p 429 word problems #35-38, 46, 48, 50, 52
Do Ch 35 problems p 278, #1 d, 2, 5, 7, 11, 12, 14, 15
[ Make sure you did the Friday problems in our text and Hoffman ]
3. Now, read Hoffman pp 434-436; do a selection of the word problems on p 443 #24, 25, 27-32
Here is my detailed Summary of the integration unit
PREPARE FOR WEDNESDAY QUIZ: IBP, AREA UNDER AND BETWEEN CURVES, TOTAL AND AVERAGE VALUE OF A FUNCTION IN WORD PROBLEMS
Wed-Thurs My Exam 4 from Spring 2018 is a good review tool for the new material
STUDY THESE TOPICS FOR THE FINAL EXAM
Derivatives–all types with chain rule, products, quotients, implicit, partial
Marginal cost, profit, revenue–break even, critical numbers, max/min values
Compound interest of a bank account–one-time deposit or loan; n finite (monthly, quarterly, etc) and continuous
Optimization–Lagrange method when constraints are present and the hot dog problem
Integration–all types with u-sub and IBP
Indefinite integrals with initial (boundary) conditions
Area under and between curves
Total value of a function
Area between curves
Average value of a function