James Cook's Calculus II with Analytic Geometry Homepage
James Cook's Calculus II Homepage

Materials and Links for Spring 2023 my Calculus II Course:
Course Planner and assignments for the whole semester:
Articles from which I teach:
• Calculus I in a Nutshell my lightning review of Calculus I with an emphasis on integral calculus
• Integration Techniques this is the heart of what I think of when I think of Calculus II. This document completes the discussion of basic integration techniques.
• Improper Integration how to integrate things involving infinity
• The First Order my notes on mostly first order ordinary differential equations.
• (I reformatted my old notes and I'm hoping to write new notes for later sections, this is a work in progress, hopefully I will post a few more articles in a few weeks)

II. Course Notes:
My lectures tend to follow these notes, however, sometimes I go deeper than classtime affords us time. Also, I do write these notes with an exceptional student in mind. I believe we are called to excellence not mediocrity. Of course, not everybody needs to understand the entirety of my notes. I just want you to do your best. Notice that I have only been able to put the first 40% or so of the notes into the LaTeX format. The last 60% are in my older, inferior, Word-based format (the whole 2nd-ed. of my notes is posted further down, and if you are really really curious you can find the first edition somewhere on this website...).

• Oldschool Calculus this pdf includes the Calculus I notes. I do reference these in many places. Most people need to read Chapter 2 again to refresh math lingo.

Posted below are problems and some solutions to problems I assigned in previous semesters. These were originally assigned in the Spring 2011 Semester:

The problems below were taken from Stewart's Calculus. The qualifier "prereq" means that I don't plan a specific lecture devoted to this topic. It is probably spread over many other lectures. I include these solutions specifically to help those of you who had a lackluster preparation before this course. OK, I hope the reason these solutions are posted here is clear enough.

 Section # My Notes Lecture Date Assignment Label and content Description Sec. 7.8 . prereq. H40 = 5, 11, 13, 15, 19, 21, 25, 27, 43 L'Hopital's Rule (p. 478) Sec. 7.8 . prereq. H41 = 49, 55, 59, 63, 85, 93, 94 L'Hopital's Rule (p. 478) Sec. 7.6 . prereq. H1 = 63, 64 u-substitution Sec. 7.7 Ch. 9 prereq. H2 = 9, 30, 31, 57, 58, 60, 63, 64 calculus of hyperbolic functions. Sec. 8.1 Ch. 9 Jan. 24 H5 = 3, 4, 7, 8, 10, 12, 17, 33 Integration By Parts (IBP) Sec. 8.1 Ch. 9 Jan. 24 H6 = 34, 49, 64 Integration By Parts (IBP) Sec. 8.2 Ch. 9 Jan. 25 H3 = 2, 7, 8, 16, 20, 25, 41, 43, 44 integrals of trig functions Sec. 8.3 Ch. 9 Jan. 26 H4 = 1, 2, 3, 10, 18, 24, 31, 32, 38 trig substitution Sec. 8.4 Ch. 9 Jan. 28 H7 = 2, 4, 6, 7, 8, 10, 13, 19, 20, 29, 34, 35, 48, 51, 69 partial fractions Sec. 8.7 Ch. 10 Feb. 2 H9 = 5, 22, 40 (use Mathematica to calculate finite sums for each of these.) numerical integration and error Sec. 8.8 Ch. 11 Feb. 4 H8 = 2, 6, 9, 16, 17, 18, 27, 31, 35, 38, 78 improper integration Sec. 11.1 Ch. 12 Feb. 11 H29 = 2, 4, 6, 8, 12, 14, 18, 34, 35, 46 Parametric Curves Sec. 11.2 Ch. 14 Feb. 15 H30 = 1, 42, 44, 48, 52 Arclength Sec. 9.1 Ch. 14 Feb. 15 H31 = 9, 12, 38, 40 Arclength Sec. 9.2 Ch. 14 Feb. 17 H32 = 5, 6, 12, 14, 15 Area of a surface of revolution Sec. 9.3 Ch. 14 Feb. 21 TBA (nothing to post here, but you ought to work some of these) Calculus in Physics Sec. 9.5 . . H33 = 5, 6 Probability*(optional topic) Sec. 11.3 Ch. 15 Feb. 23 H28 = 4, 6, 8, 10, 15, 16, 18, 20, 22, 24, 26, 30, 36, 40, 44, 48 Polar Coordinates Sec. 11.4 Ch. 14 Feb. 24 TBA (nothing to post here, but you ought to work some of these) polar coordinate calculus Sec. 11.5 Ch. 15 Feb. 28 H27 = 2,4,12,16,20,24,26,30,40,48, 55 Basics of Conic Sections Sec. 10.1 Ch. 16 Mar. 4 H10 = 7 basic concepts for differential equations Sec. 10.3 Ch. 16 Mar. 7 H11 = 1, 2, 8, 11, 12, 16, 22, 30 separation of variables Sec. 10.5 Ch. 16 Mar. 9 H12 = 8, 10, 17, 18, 23, 26, 27, 29 integrating factor method Sec. 10.4 Ch. 16 . H13 = 7, 8 population growth*(optional topic) Supplemental Stewart Sec. Ch. 16 . H14 = Click Here for the Problems (2, 4, 6, 7, 9, 10, 18, 21, 22, 34) homogeneous 2nd order constant coefficient ODEs*(optional topic) Sec. 12.1 Ch. 17 Mar. 11 H15 = 5, 15, 22, 25, 30, 33, 62, 64 sequences, limits of sequence Event . Mar. 14-18 . Spring Break (The Holidays) Appendix E Ch. 17 Mar. 22 H16 = 11, 12 sigma notation Sec. 12.2 Ch. 17 Mar. 22 H17 = 10, 15, 31, 34, 42, 48, 56, 60, 67, 68, 70 geometric series, n-th term test. Sec. 12.3 Ch. 17 Mar. 24 H18 = 7, 12, 17, 31, 34 p-series and integral test Sec. 12.4 Ch. 17 Mar. 25 H19 = 3, 5, 8, 12, 13, 16, 28, 30 limit and direct comparison tests Sec. 12.5 Ch. 17 Mar. 28 H20 = 5, 7, 12, 19, 28 alternating series test and error Sec. 12.6 Ch. 17 Mar. 29 H21 = 2, 3, 6, 12, 14, 18, 29, 38 absolute convergence, ratio test Sec. 12.8 Ch. 18 Apr. 6 H22 = 4, 6, 12, 25, 30, 32, 38, 41 power series Sec. 12.9 Ch. 18 Apr. 7 H23 = 4, 9, 10, 11, 17, 18, 23, 26, 28, 32 power series expansions via geometric series tricks Sec. 12.10 Ch. 19 Apr. 8 H24 = 9, 11, 15, 25, 28, 29, 33, 36, 39, 41, 47, 50, 59 Taylor Series Event . Apr. 13 . Assessment Day Party Sec. 12.11 Ch. 19 Apr. 15 H25 = 4, 8, 28 Taylor Polynomials (also, see my Section 6.5) N/A Fourier Section . H26 = 1, 4, 7, 11, 13, 15, 17 (from the linked pdf) Fourier Series*(optional topic) Sec. 6.5 . . H34 = 2, 7, 8, 20, Averages*(optional topic)

IV. Previous Semesters Test Solutions:
These give you some idea of the difficulty of the course. Also, while tests change from semester to semester these show you certain things you might expect.

Test Solutions from Fall 2009:

Test Solutions from Spring 2009:

V. Old Course Notes (circa 2009):
We start with Chapter 9 in calculus II. You do not need to print these. These are not the notes for this semester. That said, my approach in these notes is less formal than the approach I am currently applying to the calculus sequence. I expect more of my students in the current edition of my notes.

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.

Integration Examples:
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)

Differential Equation Examples:

Convergence and Divergence of sequences and series:
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

Power Series Techniques:
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)

Arclength, Averages, Probablility, Center of Mass, Select Applications:

Modified 1-7-2023

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