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.
Office hours on Wednesday to answer questions: 2-3 PM in Bradley 1-I,  3-4 PM in Bradley 1-H,   4-5 PM in Bradley 1-J.

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)