Mathematics 162A,D :: Spring 2007 ::
Techniques of Integration, Introduction to Infinite Series, and Multivariable Calculus

Instructor: Michael Bolt, 292 North Hall, x6-6719, mbolt@calvin.edu.

This course is a continuation of Mathematics 161, Differential and Integral Calculus. The course also involves a laboratory component using Mathematica.

Topics include: Techniques of integration; rectangular, cylindrical, and spherical coordinate systems; vectors; partial derivatives; multiple integrals; and an introduction to sequences and series. Prerequisite: Mathematics 160 or 161.
Important Dates

There will be four in-class tests on the following days:

The final exam will be Monday, May 14 at 6:30pm.

Problem Sets
PS 01: p. 310#100,105,110,115,120; 7.1#2,5,6,8,9,13,16,22,25,39 (due Friday, Feb. 2)
PS 02: 7.2#1,7,11,34,37; 7.3#1,2,7,8,9 (due Tuesday, Feb. 6)
PS 03: 7.4#1,3,5,10,14,19,21,23,30,35 (due Friday, Feb. 9)
PS 04: 7.7#2,5,10,12,15,20,28,39; 7.6#3,25,26,27b,37 (due Tuesday, Feb. 13)
PS 05: 8.2#7-14,23,27,28,29,45; 8.3#1-9 (due Tuesday, Feb. 20)
Suggested review problems for Midterm 1: Review 1
PS 06: 8.4#1,2,8,20; 8.5#2-5,8,17-20; 8.7#7a,9a,14a,17a,24a,43ab,44ab (due Friday, Feb. 23)
PS 07: 8.8#3,7,8,10,13,17 (due Tuesday, Feb. 27)
Suggested review problems for Midterm 2: Review 2
PS 08: 9.1#1,6,9,11,12,33,34,37,46; 9.2#21a,22b,23b,26,27 (due Tuesday, Mar. 6)
PS 09: 9.2#18,19,25; 9.3#1,6,7,14,16; p. 499#62,65,75 (due Friday, Mar. 9)
PS 10: 10.1#9,10,19,24,35,38; 10.2#5,6,9,11,12,13,17,24,25 (due Tuesday, Mar. 13)
PS 11: 10.2#45,46; 10.3#3,4,13,14,18,41; 10.4#1,7,12 (due Friday, Mar. 16)
PS 12: 10.4#15,16,35,36; 10.5#2,3,6,9,21,22,23 (due Wednesday, Mar. 28)
PS 13: 10.6#1-12; 11.1#1,2,8,9,13,17,18; p.453#1; p.460#1; p.463#1 (due Friday, Mar. 30)
Suggested review problems for Midterm 3: Review 3
PS 14: 12.1#2,5,10,13-18,19,25; 12.2#2,6,7,9,13,22,28,39; p.453#3; p.464#7; p.469#11 (due Tuesday, Apr. 10)
PS 15: 12.3#4,6,9,13,14,16,17,43,44,48; 12.4#2,5,15,20,24,25,28,33; p.552#41ab; p.558#7; p.567#7,12 (due Friday, Apr. 13)
PS 16: 12.5#3,6,9,12,14,17,18; 12.6#3,7,10,11,13,14,19,22; p.470#15; p.495#27 (due Tuesday, Apr. 17)
PS 17: 12.7#1,2,3,11,21,24,29; p.670#5,7; p.384#55,57 (due Friday, Apr. 20)
PS 18: 13.1#3,4,14,17,18,22,25; p.642#38; p.499#65 (due Monday, Apr. 23)
PS 19: 13.2#19,24,25,30,37,38; 13.3#4,11,12; 13.6#3,6,13 (due Monday, Apr. 30)
PS 20: 13.4#3,7,9,20,31; 13.5#8,9,13,19 (due Wednesday, May 2)
Suggested review problems for Midterm 4: Review 4
PS 21: 13.5#22,24,26,36; 13.7#15,17,21,33,39,49 (due Tuesday, May 8)

Solutions for Quizzes and Tests
Quiz 1: [solutions]
Test 1: [solutions]
Test 2: [solutions]
Quiz 2: [solutions]
Quiz 3: [solutions]
Test 3: [solutions]
Test 4: [solutions]

Handouts, Demonstrations, etc.
[lab 01: notebook]
[8.2: examples of power series]
[power series applet]
[8.7: examples of power series]
[Taylor polynomials applet]
[9.2: polar graphs]
[9.2: polar calculus, day 1]
[10.4: cross product]
[10.6: Interactive Gallery of Quadric Surfaces]
[11.1: demo]
[11.1: demo 2]
[12.1: How to Make a Contour Plot (Prof. Louis Talman)]
[12.1: contour plots .nb]
[12.1: contour plot; see p.10]
[12.1: Topographic Maps]
[12.1 : Color Coded Maps]
[12.2: contour plots .nb]
[12.3: A Partial Derivatives Applet]
[12.7: Extreme values and saddle points]
[12.7: constrained max/min]
[13.1: Riemann Sums Approach to Volume]
[13.1: Fubini's Theorem 1]
[13.1: Fubini's Theorem 2]

Second Lab
[lab2: surface plots and contour plots]
[lab2: example of global extrema]
[lab2: integration; iterated integrals]
[lab2: limits of functions; paths of approach]

[13.4: Double Integrals in Polar Coordinates]
[13.7: cylindrical & spherical coordinates]

You can view notebook (.nb) files using the free program MathReader, available at http://www.wolfram.com/products/mathreader/.
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