## Math 408L (Integral Calculus), Spring 2010

This is the page for sections 56585, 56590, and 56595 of Math 408L.

The first day handout contains all of the essential organizational information about the course, including the dates of midterm exams. Some of this information is repeated below for convenience.

### Instructor

I am Andrew (Andy) Neitzke. You can contact me at neitzke@math.utexas.edu. My office hours are 1:30p-2:30p Monday and 10:00a-11:00a Friday, both in RLM 9.134.

### Teaching assistant

The teaching assistant is James Delfeld. You can contact him at jdelfeld@math.utexas.edu. His office hours are 11:00a-12:30p Monday and Wednesday in RLM 10.146.

### Homework

Homework is managed using the QUEST system. The final deadline 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. January 29.

### Extra resources

A collection of useful handouts, provided by the UT Learning Center, is available here.

### 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 (20 Jan): antiderivatives (Ch 4.9)
Lecture 2 (22 Jan): antiderivatives (Ch 4.9), estimating areas (Ch 5.1)
Lecture 3 (25 Jan): areas (Ch 5.1) [these are my notes, not the actual lecture, due to a technical glitch]
Lecture 4 (27 Jan): definite integrals (Ch 5.2)
Lecture 5 (29 Jan): Fundamental Theorem of Calculus (Ch 5.3)
Lecture 6 (01 Feb): indefinite integrals, net changes (Ch 5.4)
Lecture 7 (03 Feb): method of substitution, integration of even/odd functions on symmetrical intervals (Ch 5.5)
Lecture 8 (05 Feb): areas between curves (Ch 6.1)
Lecture 9 (08 Feb): volumes, surfaces of revolution (Ch 6.2). Animated solid of revolution.
Lecture 10 (10 Feb): volumes, exponentials, logarithms (Ch 6.2, 7.2, 7.4)
Lecture 11 (12 Feb): more volumes, exponentials, logarithms (Ch 6.2, 7.2, 7.4)
Lecture 12 (15 Feb): inverse trig functions (Ch 7.6) [paper notes from guest lecture by Prof. Daniel Allcock]
Lecture 13 (17 Feb): integration by parts (Ch 8.1)
Lecture 14 (19 Feb): more integration by parts, combined with substitution (Ch 8.1)
Lecture 15 (22 Feb): exam review (mostly questions from the class)
Lecture 16 (24 Feb): trigonometric integrals (Ch 8.2)
Lecture 17 (26 Feb): more trigonometric integrals, trigonometric substitution (Ch 8.2, 8.3)
Lecture 18 (01 Mar): more trigonometric substitution (Ch 8.3), and a tricky homework problem
Lecture 19 (03 Mar): partial fractions (Ch 8.4)
Lecture 20 (05 Mar): a little more partial fractions (Ch 8.4), strategy for integration (Ch 8.5)
Lecture 21 (08 Mar): indeterminate forms and L'Hospital's rule (Ch 7.8)
Lecture 22 (10 Mar): L'Hospital's rule continued (Ch 7.8), improper integrals (Ch 8.8)
Lecture 23 (12 Mar): improper integrals continued (Ch 8.8); happy spring break!
Lecture 24 (22 Mar): partial derivatives (Ch 15.3), with a few computer figures included inline
Lecture 25 (24 Mar): iterated and double integrals (Ch 16.2)
Lecture 26 (26 Mar): iterated and double integrals over general regions (Ch 16.3)
Lecture 27 (29 Mar): iterated and double integrals continued (Ch 15.2, 15.3) [paper notes from guest lecture by Dr. Maria Gualdani]
Lecture 28 (31 Mar): sequences (Ch 12.1) [paper notes from guest lecture by Dr. Maria Gualdani]
Lecture 29 (02 Apr): more sequences (Ch 12.1)
Lecture 30 (05 Apr): exam review
Lecture 31 (07 Apr): infinite series, especially geometric (Ch 12.2)
Lecture 32 (09 Apr): more infinite series (Ch 12.2)
Lecture 33 (12 Apr): integral test for convergence/divergence (Ch 12.3)
Lecture 34 (14 Apr): comparison tests for convergence/divergence (Ch 12.4)
Lecture 35 (16 Apr): alternating series test (Ch 12.5)
Lecture 36 (19 Apr): absolute vs. conditional convergence, ratio test (Ch 12.6)
Lecture 37 (21 Apr): more ratio test, root test (Ch 12.6), strategy for testing series (Ch 12.7)
Lecture 38 (23 Apr): power series (Ch 12.8)
Lecture 39 (26 Apr): power series as functions (Ch 12.9)
Lecture 40 (28 Apr): Taylor and Maclaurin series (Ch 12.10)
Lecture 41 (30 Apr): uses of Taylor series/Taylor polynomials (Ch 12.11)
List of tests for series convergence/divergence.
Lecture 42 (03 May): exam review
Lecture 43 (05 May): final exam review
Lecture 44 (07 May): final exam review [guest lecture by Dr. Gary Berg, no notes]

All lectures (around 200 pages).