MATH 132 section 2: Calculus II with Analytic Geometry
MATH 132 section 2 Homepage

Welcome, please note that the offical syllabus is linked here. Please note this webpage is where test solutions and further assignments are to be posted. For your convenience, I have provided a few links to points further down this page.

I. Course Contact Information:
• Instructor: Dr. James S. Cook
• Office: Applied Science 105
• Office Hours: M-T-W-R-F from 11:00am-12:00pm
• Email: jcook4@liberty.edu
• Office Phone: 434-582-2476
• Lectures and tests are in Science Hall 134
• Lecture Times: MWF 8:50 am - 9:40 am, and TR 9:15 am - 10:30 am

I'll probably post Mathematica templates and small notes about particular lectures here if need be.

If you surf through these documents you'll find over a dozen old tests, numerous quiz solutions and just plain old solved homework problems. There are solved problems like your homework for most of the sections we cover. Exceptions to this rule are the material in my Chapter 13 and 14 this semester. I am attempting to organize these so you can find the sort of problem you are working on without too much searching. Unfortunately there are some irrelevant problems, but those should be fairly obvious and I certainly don't mind if you email to ask if a given problem has anything to do with your homework or not... On the other hand, there is more than likely a number of solved homework problems in the mix. This is not on purpose. It's just the inevitable consequence of Stewart's Calculus never changing it's problems from edition to edition or decade to decade if I had to speculate...

Solutions relevant to material on our test 1 (my Chapter 9)
1. Test I solution
2. Test I solution
3. Test one solution
4. Test one solution
5. U-subst. , 7-3-07
6. U-subst. in-class exercise, 1-10-06
7. U-substitution, 1-13-06
8. Trig-subst./Partial Fractions , 7-6-07
9. Trig-subst. in-class exercise, 1-17-06
10. trig. substitution, 1-20-06
11. IBP(5.6), 1-23-06
12. partial fractions, 1-26-06
13. Partial fractions make-up quiz (add's maximum of 5+1 points to test one)
14. Final Exam and solution
15. Solution to old extra credit project
16. Older extra credit project Solutions by Ginny. Warning, she's my wife so she doesn't have to show all her work. You do not have this privilige on the tests. Please ask me if you don't understand some step she made since her work is very concise.
17. quizzes integration, differential equations, series ( best of collection)

Solutions relevant to DEQns material on our test 2 (my Chapter 10)

Solutions sequences and series material on our test 2 (my Chapter 11)
1. series convergence and divergence(8.1-8.4)
2. convergence/divergence test guidewith box to put in an example of your own
3. convergence/divergence test guidewith box filled with the wise guidance of a fellow TA and a warning about what my focus is on for our section of ma 241.
4. Sequences and series, basics
5. Test IV solution
6. Test IV practice test and solution
7. Test IV solution
8. Test four solution
9. Test four solution

Solutions for power series representations of functions covered on Test 3 (my Chapters 12 and 13),
1. Power Series, Interval of Convergence and Geometric Series Techniques
2. geometric series trick chart my graphical representation of how to use the geometric series indirectly. This trick should be combined with some common sense to solve problems in section 8.6. Of course some problems are just plain-old geometric series, so try that first when attacking 8.6 questions.
3. a selection of homework problems worked I work out a few of your homework problems. I deal with the endpoints for an example or two, but then focus on the main part which is the open interval of convergence. That just requires careful application of the ratio test. The endpoints require more thought sometimes.
4. a selection of homework problems worked mostly even numbered problems, I hope these help you understand how to get started. These sort of problems reflect what I think is the most important element of power series. This is the part that you can use in other courses ( convergence and divergence is fine and all but if you can't calculate the power series representation of a function then the question of where it converges seems somewhat pointless ). Also the fact we can integrate almost anything with power series is just fantastic.
5. power series extra examples ( E6 thru E13 relevant to ma241-006 )
6. Test IV solution
7. Test IV practice test and solution
8. Test IV solution
9. Test four solution
10. Test four solution
11. Final Exam and solution
12. quizzes integration, differential equations, series ( best of collection)

Solutions relevant to material on our test 4 (my Chapters 14,15 and 16)

IV. Test Reviews and Solutions:
I will post reviews and solutions for our course here once it's time.

Test Solutions from this Semester:

Test Reviews:

V. Course Notes:
Lectures often closely follow these notes (I expect you to have a copy with you in lecture). Sometimes there is not time to say everything during class, I try to stick to the most important parts in lecture. We start with Chapter 9 in calculus II.

VI. Bonus Point Policy:
It is possible to earn bonus points by asking particularly good questions or suggesting corrections to errors in notes and materials on the course website. This does not include spelling or grammatical errors, those are provided for your amusement. Once I notify the class of the error you may no longer ask for that point.
I also provide a little bonus project from time to time. These are not required. It is entirely possible to earn an A without completing these. If you scan through the notes you'll find a number of bonus opportunities already available. In contrast to previous semesters I will not offer bonus points on the in-class portion of the test. Instead, you have the choice to do them outside class at your leisure. I will usually be able to take these as late as the final exam day, just ask.

VII. Required Homework List:
It is important to both complete and understand the homework. I encourage you to form study groups, however, it is very important that in the end you come to an understanding of the material for yourself. You will most likely find the homework in this course challenging at times, so it is important to begin early and give yourself a chance to talk to others (for example me) before the due date. You may also email me reasonable questions.

It is not enough to find the answer - you must be able to justify each step. Imagine that you are writing the solution for a person who doesn't know calculus. On our tests I will expect you to explain your work since presentation and proper notation are arguably as important as the answer itself. In my lectures I strive to present calculations in a coherent and logical manner and I will expect you to do the same. So, take some time to notice what the notation means and don't just scribble the bare amount to get the answer. It's a bad habit and it will most likely knock a letter grade or two off of your tests.

I am always happy to look over your derivations of homework during office hours. Additionally, most days (time permitting), I'll answer a question about the homework. I try to give you all the tools you need to do the homework, but it is you who must put those tools to work. Think.

The homework is posted below. Notice I have indicated which portion of my lecture notes as well as which part of the textbook is most relevant to the assigment. Beware, sometimes the homework is not exactly matched up with the lecture notes link, sometimes you need to look at the next few pages. The pdf's of my lecture notes are chopped up Chapter by Chapter, usually you can find what you need somewhere in that chapter. If you are lost send me an email, I'll try to point you in the right direction. I expect you to print out a copy of the lecture notes - you will find them helpful for certain homework problems.

• WARNING: some of the later problems are difficult. I warn you now, I have no pity for procrastination this semester. I have built some delay between lecture and the collection date for the homework. Make good use of this delay. There is too much homework for most of you to do in a day, however there is not too much homework. I would expect at least 10 hours/week are needed to study and complete homework for this course.
•  Section # My Notes Due Date Assignment Description Sec. 7.6 . Jan. 16 63, 64 u-substitution Sec. 7.7 Ch. 9 Jan. 16 9, 30, 31, 57, 58, 60, 63, 64 calculus of hyperbolic functions. Sec. 8.2 Ch. 9 Jan. 16 2, 7, 8, 16, 20, 25, 41, 43, 44 integrals of trig functions Sec. 8.3 Ch. 9 Jan. 23 1, 2, 3, 10, 18, 24, 31, 32, 38 trig substitution Sec. 8.1 Ch. 9 Jan. 23 3, 4, 7, 8, 10, 12, 17, 33 Integration By Parts (IBP) Sec. 8.1 Ch. 9 Jan. 30 34, 49, 62*, 64 Integration By Parts (IBP) Sec. 8.4 Ch. 9 Jan. 30 2, 4, 6, 7, 8, 10, 13, 19, 20, 29, 34, 35, 48, 51, 57*, 69 partial fractions Sec. 8.8 Ch. 9 Jan. 30 2, 6, 9, 16, 17, 18, 27, 31, 35, 38, 71*, 78 improper integration Test I . Feb. 5 Test I covers most of chapter 9 in my notes integration, improper integration Sec. 8.7 Ch. 9 Feb. 9 5, 22, 40 (use Mathematica to calculate finite sums for each of these.) numerical integration and error Sec. 10.1 Ch. 10 Feb. 13 7, basic concepts for differential equations Sec. 10.3 Ch. 10 Feb. 13 1, 2, 8, 11, 12, 16, 22, 30, 48* separation of variables Sec. 10.5 Ch. 10 Feb. 13 8, 10, 17, 18, 23, 26, 27, 29, 35*, 36* integrating factor method Sec. 10.4 Ch. 10 Feb. 20 7*, 8* population growth Supplemental Stewart Sec. Ch. 10 Feb. 20 Click Here for the Problems (2, 4, 6, 7, 9, 10, 18, 21, 22, 34) homogeneous 2nd order constant coefficient ODEs Sec. 12.1 Chap. 11 Feb. 20 5, 15, 22, 25, 30, 33, 62, 64 sequences, limits of sequence Appendix E Chap. 11 Feb. 20 11, 12 sigma notation Sec. 12.2 Chap. 11 Feb. 20 10, 15, 31, 34, 42, 48, 56, 60, 67, 68, 70 geometric series, n-th term test. Sec. 12.3 Chap. 11 Feb. 27 7, 12, 17, 31, 34 p-series and integral test Sec. 12.4 Chap. 11 Feb. 27 3, 5, 8, 12, 13, 16, 28, 30 limit and direct comparison tests Sec. 12.5 Chap. 11 Feb. 27 5, 7, 12, 19, 28, 35* alternating series test and error Sec. 12.6 Chap. 11 Feb. 27 2, 3, 6, 12, 14, 18, 29, 38 absolute convergence, ratio test Test II . Mar. 3 covers Chapters 10 and 11 of my notes differential equations, sequences, conv/div tests Event . Mar. 9-13 no lectures, spring break The "Hollidays" Sec. 12.8 Chap. 12 Mar. 20 4, 6, 12, 25, 30, 32, 38, 41 power series Sec. 12.9 Chap. 12 Mar. 20 4, 9, 10, 11, 17, 18, 23, 26, 28, 32 power series expansions via geometric series tricks Sec. 12.10 Chap. 13 Mar. 27 9, 11, 15, 25, 28, 29, 33, 36, 39, 41, 47, 50, 59 Taylor Series Sec. 12.11 Chap. 13 Mar. 27 4, 8, 28, 35* Taylor Polynomials Test III . Mar. 31 chapter 12 and 13 of my notes power series representation of functions, IOC and ROC, Taylor Polynomials Sec. 11.5 Chap. 14 Apr. 10 6, 12, 20, Prove Theorems 14.1.1, 14.1.2, 14.1.3 (worth 6 problems) Conic Sections Sec. 11.3 Chap. 14 Apr. 10 4, 6, 8, 10, 15, 16, 18, 20, 22, 24, 26, 30, 36, 40, 44, 48 Polar Coordinates Sec. 11.1 Chap. 15 Apr. 17 2, 4, 6, 8, 12, 14, 18, 34, 35, 46 Parametric Curves Sec. 11.2 Chap. 15 Apr. 24 1, 42, 44, 48, 52, 69*, 70*, 72* Arclength Sec. 9.1 Chap. 15 Apr. 24 9, 12, 38, 40 Arclength Sec. 9.2 see Stewart. Apr. 24 5, 6, 12, 14, 15 Area of a surface of revolution Sec. 9.5 Chap. 16 Apr. 24 5, 6 Probability Sec. 6.5 Chap. 16 Apr. 24 2, 7, 8, 20, Averages Sec. 6.4 Chap. 16 Apr. 29 14*, 22* Work, Force, Physics Sec. 9.3 Chap. 16 Apr. 29 6*, 9* Hydrostatic Force Test IV . Apr. 28 parts of chapters 14, 15 and 16 of my notes coordinates, conic sections, parametric curves, arclength, surface area, averages, probability density definition Final . May 6 comprehensive 8-10am, Wed. May 6, usual room.

• *-exercises can be turned in anytime before the last test. They will earn bonus points towards your homework/quiz total. They should be turned in directly to me, separate from the required problems so we don't confuse the grader. Thanks.

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