What we did in class.
This is a description of what was done in each class; there is a separate listing of the homework that was assigned.
Come to class ready to discuss any examples or problems that you were not sure of.Classes are described in reverse time order.
References are to the textbook for this class, Calculus, by Stewart.
Class 57 (F 12/13): 10.6; quadratic equations in general.
Class 56 (W 12/11): 10.6; hyperbolas.
Class 55 (Tu 12/10): 10.6; ellipses
Class 54 (M 12/9): 10.6; parabolas.
Class 53 (F 12/6): Exam #3 on Appendix G (complex numbers), 8.1-3, and 10.1-5.
Classes 50, 51, and 52 (M 12/2, Tu 12/3, and W 12/4): 10.5; area and arc length for curves defined by polar equations.
Classes 48 and 49 (W 11/20 and F 11/22): 10.4; polar coordinates, especially graphing polar equations.
Class 47 (Tu 11/19): 10.3; arc length and surface area (for solids of revolution) for parametric curves.
Class 46 (M 11/18): 10:2; tangent lines of parametric curves.
Class 45 (F 11/15): 10.1; curves in the plane defined by parametric equations.
Class 44 (W 11/13): centroid and center of mass; from 8.3.
Classes 42 and 43 (M 11/11 and Tu 11/12): 8.2 and handout; area of a surface of revolution (for which we need Duhamel's Principle to prove convergence of the approximation to the integral).
Class 41 (F 11/8): 8.1; arc length formula.
Classes 38, 39, and 40 (M 11/4, Tu 11/5, and W 11/6): Appendix G; complex numbers.
Class 37 (F 11/1): Exam #2 on proofs by induction and 11.1-10.
Classes 33, 34, 35, and 36 (F 10/25, M 10/28, Tu 10/29, and W 10/30): 10.10 and handouts; Taylor's Theorem and proofs of power series representations of some familiar functions.
Classes 30, 31, and 32 (M 10/21, Tu 10/22, and W 10/23): 11.9 and handout; differentiation and integration of power series
Class 29 (F 10/18): 11.8; power series, radius of convergence.
Class 28 (W 10/16): 11.6; absolute convergence, ratio test, and root test.
Class 27 (Tu 10/15): 11.5; alternating series.
Classes 25 and 26 (F 10/11 and M 10/14): 11.4; comparison tests for positive series.
Class 24 (W 10/9): 11.3; integral test for positive series.
Class 23 (Tu 10/8): 11.2; convergence of series, geometric series.
Class 22 (M 10/7): 11.1; convergence of sequences.
Classes 18, 19, 20, and 21 (M 9/30, Tu 10/1, W 10/2, and F 10/4): cover handout chapter on proof by mathematical induction.
Class 17 (F 9/27): Exam #1 on material covered through Class 16; 50 minute exam during regular class period; there will be a Q+A session on Thursday 9/26, starting at 4:15pm, in our usual classroom.
Classes 15 and 16 (Tu 9/24 and W 9/25): 7.8; improper integrals
Classes 12, 13, and 14 (W 9/18, F 9/20, and M 9/23): 7.7; various methods of approximating a definite integral, with emphasis on error estimates.
Class 11 (Tu 9/17): finish discussing rational functions; tan(x/2) substitution to reduce certain functions of sin and cos to rational functions (not in text; there was a handout).
Classes 9 and 10 (F 9/13 and M 9/16): 7.4; integrating rational functions.
Classes 7 and 8 (Tu 9/10 and W 9/11): 7.3; inverse trigonometric substitutions.
Class 6 (M 9/9 ): 7.2; integrating products of basic trigonometric functions.
Class 5 (F 9/6): 7.1; integration by parts.
Classes 3 and 4 (Tu 9/3 and W 9/4): careful proof of the Mean Value Theorem; see 4.2 (plus 4.1 for background).
Classes 1 and 2 (W 8/28 and F 8/30): properties of the definite
integral and careful proof of the Fundamental Theorem of Calculus; see
especially 5.2 and a handout for properties of the integral and 5.3 for
the proof of the FTC.