## Math 408L (Integral Calculus), Fall 2012

This is the page for sections 55460, 55465, and 55470 of Math 408L.

The first day handout contains all of the essential organizational information about the course. Especially, it contains the dates of midterm exams, and office hours for me and for the teaching assistant.

### Instructor

I am Andrew (Andy) Neitzke. You can contact me at neitzke@math.utexas.edu.

### Homework

Homework is managed using the QUEST system. The deadline for each week's homework is generally 3am Monday night (Tuesday morning). There is one extra review assignment (HW01) which is due 3am Thursday night (Friday morning) of the second week of classes, i.e. September 7.

### Lecture notes

(I will try to post these within a few hours after the lecture. They are a transcript of exactly what appeared on the screen during class, except that if errors are discovered I will correct them.)

Lecture 1 (29 Aug): integrals, Fundamental Theorem of Calculus (FTC1) (Ch 5.3)
Lecture 2 (31 Aug): Fundamental Theorem of Calculus (FTC1 and FTC2) (Ch 5.3)
Lecture 3 (5 Sep): indefinite integrals, net change (Ch 5.4)
Lectures 4-5 (7 Sep-10 Sep): method of substitution (Ch 5.5)
Lecture 6 (12 Sep): areas between curves (Ch 6.1)
Lecture 7 (17 Sep): volumes, surfaces of revolution (Ch 6.2). Extra examples of volume problems
Lecture 8 (19 Sep): integration by parts (Ch 7.1). Extra examples of integration by parts and substitution, sometimes combined
Lecture 9 (21 Sep): (more) trigonometric integrals (Ch 7.2). Extra example of trig integral
Lecture 10 (24 Sep): trigonometric substitution (Ch 7.3)
Lecture 11 (26 Sep): partial fractions (Ch 7.4)
Lecture 12 (28 Sep): more partial fractions, strategy for integration (Ch 7.5)
Lecture 13 (1 Oct): improper integrals (Ch 7.8)
Lecture 14 (3 Oct): more improper integrals (Ch 7.8)
Lecture 15 (5 Oct): partial derivatives (Ch 14.3)
Lecture 16 (8 Oct): exam review
Lecture 17 (10 Oct): volume under graphs, double and iterated integrals (Ch 15.1, 15.2)
Lecture 18 (12 Oct): double and iterated integrals over general regions (Ch 15.3)
Lecture 19 (15 Oct): more double integrals over general regions (Ch 15.3)
Lecture 20 (17 Oct): sequences (Ch 11.1)
Lecture 21 (19 Oct): more sequences (Ch 11.1)
Lecture 22 (22 Oct): series (Ch 11.2)
Lecture 23 (24 Oct): more series, Test for Divergence (Ch 11.2)
Lecture 24 (26 Oct): integral test (Ch 11.3)
Lecture 25 (29 Oct): comparison and limit-comparison tests (Ch 11.4)
Lecture 26 (31 Oct): comparison and limit-comparison tests, continued (Ch 11.4) (guest lecture by Dr. John Meth, no notes)
Lecture 27 (2 Nov): alternating series (Ch 11.5) (guest lecture by Dr. David Ben-Zvi) [notes from my lecture on the same topic given in 2010]
Lecture 28 (5 Nov): exam review (guest lecture by Dr. David Ben-Zvi, no notes)
Virtual office hours, part 1
Virtual office hours, part 2
Virtual office hours, part 3
Lecture 29 (7 Nov): absolute and conditional convergence, ratio test (Ch 11.6)
Lecture 30 (9 Nov): root test, strategy for testing series (Ch 11.7)
Lecture 31 (12 Nov): power series (Ch 11.8)
Lecture 32 (14 Nov): more power series (Ch 11.8)
Lecture 33 (16 Nov): power series as functions (Ch 11.9)
Lecture 34 (19 Nov): more power series as functions, first look at Taylor series (Ch 11.9, 11.10)
Lecture 35 (26 Nov): Taylor series (Ch 11.10)
Lecture 36 (28 Nov): Uses of Taylor series (Ch 11.11)
Lecture 37 (30 Nov): more Taylor series, Euler's formula (for fun) (Ch 11.11)
Extra example of computing a Taylor series
Lecture 38 (3 Dec): exam review
Lecture 39 (5 Dec): final exam review
Lecture 40 (7 Dec): final exam review

All lectures (long).