## 2017-09-02

### Calculus II of 2016 (the early section) by James Cook at Liberty University

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source: James Cook     2016年1月18日
Calculus II of 2016 (the early section)
I intend to post Lectures from Math 132 at Liberty University from the Spring 2016 semester. These are from the 8:15 lecture section. There is a second playlist for the other second section I'm teaching in the 2nd period. Sometimes these are identical, other times I may use this layering as an opportunity to add examples. Of course, I only expect students to carefully study their own section's Lecture set.

We follow Salas and Hille's text in part, but, I try to keep these Lectures independent from the text. I have many notes posted and I will refer to those from time to time. They can be found in the webpage for Calculus II at www.supermath.info. Eventually, I'd like to mature these notes into an open source calculus text so I appreciate your input where there are errors. I hope to post some new notes as the semester progresses. Thanks!

Topics: we begin with inverse trig and hyperbolic functions, then IBP, partial fractions, integrals of trig. functions, trig and hyperbolic substitutions, first and second order DEqns, theory of sequential convergence, convergence of series, power series, Taylor's Theorem, calculus of parametrized curves, conic sections, polar coordinates and, perhaps special to my sections, 2D vector math. This list is not quite comprehensive and not quite in order, but this essentially captures the course; we assume integration through u-substitution was covered in the previous course and we cover material up to, but not including, 3D vector algebra. Past this you can see my multivariable calculus Lectures if you wish.

sec1: introductory comments 11:21 Ok, this is not even the real course introduction. I need to talk to you all about homework and such in person. However, this does serve to review those things we all should know cold from calculus I.
sec1: inverse trig 34:59
sec1: trig and hyperbolic 51:54
sec1: hyperbolic calculus, IBP intro, Jan 21 59:51
sec1: hyperbolic calculus, IBP intro, Jan 21 (part 2) 17:39
sec1: help with IBP hwk, integrals of trig fncts, Jan 26 (part 1) 59:51
sec1: help with IBP hwk, integrals of trig fncts, Jan 26 (part 2) 9:52
sec1: integral of trig fnct, trig substitution initiated, Jan 27 50:16
sec1: trigonometric and hyperbolic subst, Jan 28 59:51
sec1: trigonometric and hyperbolic subst, Jan 28 (part 2) 17:33
sec1: hwk help, partial fractions, Jan 29 49:11
sec1: hwk help, partial fractions 46:12
sec1: partial fractions, rationalizing subst. , Feb 2 59:51
sec1: partial fractions, rationalizing subst. , Feb 2 (part 2) 12:22
sec1: rationalizing exp example, numerical integration, Feb 3 48:10
sec1: partial fractions help, numerical methods, Feb 4 59:51
sec1: partial fractions help, numerical methods, Feb 4 (part 2) 12:12
sec1: numerical error, integration help, Feb 5 44:12
sec1: review for Test 1, Feb 8 43:11
sec1: introduction to DEqns, integration factor method, Feb 10 50:03
sec1: separation of variables, 2nd order start, Feb 11 (part 1) 59:51
sec1: separation of variables, 2nd order start, Feb 11 (part 2) 16:35
sec1: 2nd order constant coefficient, Feb 12 50:41
sec1: help with DEqns homework, Feb 17 43:02
sec1: real numbers, sequences, least upper bounds, Feb 18 (part 1) 59:51
sec1: real numbers, sequences, least upper bounds, Feb 18 (part 2) 17:31
sec1: increasing and decreasing sequences, Feb 19 50:56
sec1: some theory of sequences, Feb 23 (part 1) 59:51
sec1: some theory of sequences, Feb 23 (part 2) 15:12
sec1: examples of DEqns and sequences, Feb 24 42:48
sec1: sequence theorems from 11.4, Feb 25 59:51
sec1: Lhopital Rule, Feb 26 47:27
sec 1: help with sequences, Lhop rule, Feb 29 46:13
sec1: L'Hop and Improper Integration, March 1 (part 1) 59:51
sec1: L'Hop and Improper Integration, March 1 (part 2) 11:43
sec1: L'Hop examples, March 2 23:44
sec1: quiz 2 soln, improper integrals, March 3 (part 1) 59:51
sec1: quiz 2 soln, improper integrals, March 3 (part 2) 10:18
sec1: preparing for test 2, March 4 38:27
sec1: summation notation, definition of series, March 9 51:27
sec1: series conv/div analysis, basic and limit comparison, Mar 10 (part 1) 59:51
sec1: series conv/div analysis, basic and limit comparison, Mar 10 (part 2) 7:14
sec1: limit comparison, integral test, p-series, March 11 53:16
sec1: root and ratio tests, March 21 47:16
sec1: alternating series, March 22 59:51
sec1: alternating series, March 22 (part 2) 17:38
sec1: another try at proofs from 12.5, some hwk help, March 23 38:07
sec1: power series introduction, March 24 (part 1) 59:51
sec1: power series introduction, March 24 (part 2) 8:33
sec1: geometric series tricks, March 25 48:43
sec1: converge or diverge, March 29 (part 1) 59:51
sec1: converge or diverge, March 29 (part 2) 4:32
sec1: Taylor's Theorem, March 30 50:40
sec1: power series calculation, April 1 50:28
sec1: applications and power series, April 4 45:53
sec1: power series calculation, April 5 (part 1) 59:51
sec1: power series calculation, April 5 (part 2) 9:41
sec1: power series calculations, April 7 (part 1) 59:51
sec1: power series calculations, April 7 (part 2) 1:19
sec1: conic sections and polar coordinates, April 8 41:33
sec1: questions for Test 3, April 11 45:12
sec1: polar graphs and area, April 13 49:49
sec1: polar graph, paths and curves, April 14 (part 1) 59:51
sec1: polar graph, paths and curves, April 14 (part 2) 15:57
sec1: arclength, April 15 49:30
sec1: arclength in polar coordinates, April 18 47:13
sec1: surface area, center of mass, tangents, April 19 (part 1) 59:51
sec1: surface area, center of mass, tangents, April 19 (part 2) 15:09
sec1: parametric calculus, April 20 44:02
sec1: parametrized curves and their calculus, April 21(part 1) 59:51
sec1: parametrized curves and their calculus, April 21(part 2) 8:29
sec1: calculus of paths, April 22 59:14
sec1: parametric examples, April 25 58:02
sec1: review for Test 4, April 26 42:27