course information

Mathematics 8                 Fall 2005                  tentative Syllabus

 Day Date Topic Homework

 1 9-21 12.1  Sequences 12.1:  14, 22, 25, 32, 49, 57, 58 2 9-23 12.2  Series 12.2:  14, 20, 24, 27, 30, 37, 45, 60

 3 9-26 8.8  Improper integrals (through Ex. 4, p. 569) 12.3  Integral test, Estimate of sums 8.8:  5, 16, 21, 22;     12.3:  12, 17, 19, 25, 33(Just say how many terms of the series are needed to approximate its sum to wihin .01) 4 9-28 12.4  Comparison test 12.4:  6, 9, 10, 26, 27(changed from 29), 35(Just estimate the error.  Do not compute the sum  of the first 10 terms.), 37 5 9-30 12.5  Alternating series 12.6  Absolute convergence (up to ratio test, p. 778) 12.5:  2, 4, 8, 16, 24, 33;   12.6:  7, 8, 20

 6 10-3 12.6  Ratio test (p.778 to middle of p.780) 12.7  Strategy for testing series 12.6:  14  12.7:  7, 8, 10, 14, 16, 18, 20, 24 7 10-5 12.8  Power series 12.8:  6, 8(hint: p. 474), 12, 18, 26, 30 8 10-7 12.9  Functions as power series 12.9:  4, 8, 14, 16, 23, 26, 28(The approximation you find may be left in the form of a finite sum.), 38ab

 9 10-10 12.10  Taylor and Maclaurin series (skip multiplication and division of power series) 12.10:  5, 12, 14, 27, 31, 60 10 10-12 12.12  Applications of Taylor series (up to bottom of p. 816) 12.10: 18, 43, 47, 49 12.12: 16ab, 25,  26, 28 (don't do the graphing) 11 10-14 Review No homework due, but there are many good review problems on pp. 823-824.

Question and answer review session from 2:00-4:00 pm on Saturday in 102 Bradley.

The first exam on Sunday, Oct. 16th, in Silsby 28, from 5:00 to 7:00pm, covers up to and including day 10.
solutions to the first test

 12 10-17 8.1  Integration by parts 8.1:  4, 10, 16, 21, 27, 29, 34, 35 13 10-19 8.2  Trigonometric integrals (up to the boxed formula on p. 523) 8.3  Trigonometric substitution 8.2:  2, 14, 26, 28 8.3:  4, 5, 10, 15 14 10-21 13.1 Three-dimensional coordinates 13.2  Vectors 13.1:  6(a), 8, 10, 20, 28, 32(sketch the region rather than describing it in words) 13.2:  4ac, 20, 22, 24, 26

 15 10-24 13.3  Dot product 13.3:  12, 18 (only the exact expression), 24, 27, 38, 43, 44, 48, 51(the diagonal of a cube goes from one vertex to the opposite one) 16 10-26 13.4  Cross product 13.4:  5, 9abc, 12, 14, 15, 24, 27, 32,  33 17 10-28 13.5  Equations of lines and planes 13.5:  4, 12, 18, 20, 26, 30, 33, 41, 45, 65

 18 10-31 14.1  Vector functions and space curves (Up to the bottom of p. 888) 14.2  Derivatives and integrals of vector functions 14.1:  2, 6, 12(just the portion in the first octant), 22, 34;                 14.2:  14, 20, 26, 30(a), 40 19 11-2 14.3  Arc length (up to curvature, p. 900) 14.4  Motion in space (through middle of p. 910) 14.3:  4, 5; 14.4:  10, 11, 16, 18(a), 25(use g=10m/s^2), 28(use g=32ft/s^2) Show all work on problems 25 and 28. 20 11-4 15.1  Functions of several variables 15.2  Limits and continuity 15.1:  14, 26, 28, 30, 34, 38; 15.2:  6, 10, 12, 36

The second exam on Wednesday,  Nov. 9, in Murdough Cook Auditorium (changed from Silsby 28), from 5:00-7:00pm, covers days 12 through 21.

It is a violation of the honor code to look at these solutions to the second test if you have not yet taken the test.

No tutorial on Thursday the 10th.

 21 11-7 15.3  Partial derivatives  (to top third of p. 953) 15.3: 10, 14, 17, 31, 37, 46b, 51, 54, 55 22 11-9 Review 23 11-11 15.4  Tangent planes and linear approximation 15.4: 2, 4, 6, 15(Just find the linearization), 17, 24, 30, 31

 24 11-14 15.5  The chain rule (up to implicit differentiation on p. 972) 15.5:  2, 6, 8, 10, 14, 16, 21, 35, 42, 45 25 11-16 15.6  Directional derivative and the gradient vector 15.6:  4, 7, 10, 14, 16, 20, 21, 24 26 11-18 15.6  More directional derivative and gradient 15.6:  28, 33, 39, 42, 48, 52

 27 11-21 15.7  Maximum and minimum values 15.7:  4, 12, 27, 30, 40          solutions

 28 11-28 15.8 LaGrange multipiers 15.8: 4, 10, 19;  p. 1013: 64           solutions 29 11-30 Review

Final exam:  Saturday, December 3, 11:30-2:30, in Murdough Cook Auditorium.

office hours:  Wednesday, Nov. 30     4-6 PM        Nicholas Scoville (Bradley 1-J)
Thursday, Dec. 1    2-4 PM        Jonathan Bayless (Bradley 1-H)
Friday, Dec. 2    11:15 AM-1:15 PM    Annalies Vuong (Bradley 1-I)