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.

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.

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.

(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).