## 2017-09-02

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

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source: James Cook     2016年1月19日
I intend to post Lectures from Math 132 at Liberty University from the Spring 2016 semester. These are from the 9:20 (M-W-F), 9:45 (T-TH) lecture section. There is a second playlist for the other second section I'm teaching in the 1st 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: inverse trig (late section) 37:12
sec2: trig and hyperbolic 52:00
sec2: hyperbolic calculus, IBP intro, Jan 21 59:51
sec2: hyperbolic calculus, IBP intro, Jan 21 (part 2) 13:00
sec2: help with IBP hwk, integrals of trig fncts, Jan 26 (part 1) 59:51
sec2: help with IBP hwk, integrals of trig fncts, Jan 26 (part 2) 16:34
sec2: integral of trig fnct, trig substitution initiated, Jan 27 50:54
sec2: trigonometric and hyperbolic subst, Jan 28 59:51
sec2: trigonometric and hyperbolic subst, Jan 28 (part 2) 15:17
sec2: hwk help, partial fractions, Jan 29 50:35
sec2: hwk help, partial fractions (867-5309) 51:01
sec2: partial fractions, rationalizing subst. , Feb 2 59:51
sec2: partial fractions, rationalizing subst. , Feb 2 (part 2) 12:28
sec2: rationalizing exp example, numerical integration, Feb 3 51:12
sec2: partial fractions help, numerical methods, Feb 4 59:51
sec2: partial fractions help, numerical methods, Feb 4 (part 2) 12:31
sec2: numerical error, integration help, Feb 5 52:45
sec2: review for Test 1, Feb 8 48:20
sec2: introduction to DEqns, integration factor method, Feb 10 49:47
sec2: separation of variables, 2nd order start, Feb 11 (part 1) 59:51
sec2: separation of variables, 2nd order start, Feb 11 (part 2) 15:29
sec2: 2nd order constant coefficient, Feb 12 47:47
sec2: help with DEqns homework, brief Test 1 overview, Feb 17 50:49
sec2: real numbers, sequences, least upper bounds, Feb 18 (part 1) 59:51
sec2: real numbers, sequences, least upper bounds, Feb 18 (part 2) 16:22
sec2: increasing and decreasing sequences, Feb 19 48:51
sec2: some theory of sequences, Feb 23 (part 1) 59:51
sec2: some theory of sequences, Feb 23 (part 2) 14:47
sec2: examples of DEqns and sequences, Feb 24 42:32
sec1: sequence theorems from 11.4, Feb 25 53:14
sec2: Lhopital Rule, Feb 26 48:09
sec 2: help with sequences, Lhop rule, Feb 29 42:36
sec2: L'Hop and Improper Integration, March 1 (part 1) 59:51
sec2: L'Hop and Improper Integration, March 1 (part 2) 14:47
sec2: L'Hop examples, March 2 26:03
sec2: quiz 2 soln, improper integrals, March 3 (part 1) 59:51
sec1: quiz 2 soln, improper integrals, March 3 (part 2) 1:35
sec2: preparing for test 2, March 4 43:52
sec2: summation notation, definition of series, March 9 53:43
sec2: series conv/div analysis, basic and limit comparison, Mar 10 (part 1) 59:51
sec2: series conv/div analysis, basic and limit comparison, Mar 10 (part 2) 3:41
sec2: series conv/div analysis, basic and limit comparison, Mar 10 (part 3) 5:07
sec2: limit comparison, integral test, p-series, March 11 50:43
sec2: root and ratio tests, March 21 52:06
sec2: alternating series, March 22 (part 1) 59:51
sec2: alternating series, March 22 (part 2) 9:44
sec2: absolute convergence, AST proofs, some hwk help, March 23 48:10
sec2: power series introduction, March 24 (part 1) 59:51
sec2: power series introduction, March 24 (part 2) 13:45
sec2: adding zero vs. direct calculation, March 25 48:50
sec2: converge or diverge, March 29 (part 1) 59:51
sec2: converge or diverge, March 29 (part 2) 15:30
sec2: Taylor's Theorem, March 30 46:34
sec2: IOC theorem, multiplication of series, March 31 (part 1) 59:51
sec2: IOC theorem, multiplication of series, March 31 (part 2) 6:06
sec2: power series calculation, April 1 47:49
sec2: applications and power series, April 4 48:59
sec2: power series calculation, April 5 (part 1) 59:51
sec2: power series calculation, April 5 (part 2) 12:49
sec2: power series calculations, April 7 (part 1) 59:51
sec2: power series calculations, April 7 (part 2) 4:53
sec2: conic sections and polar coordinates, April 8 50:04
sec2: questions for Test 3, April 11 45:11
sec2: polar graphs and area, April 13 51:56
sec2: polar graph, paths and curves, April 14 (part 1) 59:51
sec2: polar graph, paths and curves, April 14 (part 2) 16:58
sec2: arclength, April 15 46:43
sec1: arclength integral derived, area of a surface of revolution , April 18 43:51
sec2: center of mass, collisions, ninjas, tangents, April 19 (part 1) 59:51
sec2: center of mass, collisions, ninjas, tangents, April 19 (part 2) 15:01
sec2: parametric calculus, April 20 49:22
sec2: parametrized curves and their calculus, April 21(part 1) 59:51
sec2: parametrized curves and their calculus, April 21(part 2) 10:32
sec2: calculus of paths, April 22 36:18
sec2: parametric examples, April 25 52:12
sec2: review for Test 4, April 26 43:42