Let me just recall the homework policies.
You are encouraged to work on homework together, but you must write up
the solutions by yourself. Please indicate with whom you worked
together. If you stumble across the solution to a homework problem in a
book or somewhere else, you may write up this solution,
but you have to give the reference where you got it from.
No late homework will be accepted.
Please order and staple your solutions together and put your name on
it. Unreadable homework will not be corrected.
|
Due
|
Homework
Assignment
|
|
04 Oct 06
|
DON'T WORRY, IT LOOKS LIKE A LOT, BUT MOST PROBLEMS ARE JUST ONE COMPUTATION.
1) Read pages 14-18 about finding equations of a line given by a vector or by two points.
Solve Problems 26, 28 on page 21.
Solve Problems 2, 3 on page 35, Problems 7, 8, 10, 14 on page 36, and Problems 22, 24 on page 37.
2) Read Section 1.3 and 1.4 (pages 39-57), in particular get familiar with Cramer's rule explained in
the historical note on page 43 (see also Exercise 14 on page 46).
Solve Problems 2,4,6,8, on page 45.
Solve Problem 16 on page 46 (apply Cramer's rule - check your result by putting the numbers into the equations).
Solve Problems 2,4,6 on page 57, Problems 24, 26 on page 58 and Problem 34 on page 59.
3) Solve Problems 2,8,10,14 on page 82 and Problem 18 on page 83.
Bonus Problem: If you are familiar with chemical notation, solve Problem 37 and 38 on page 21.
Problem 30 on page 37/38.
|
|
11 Oct 06
|
1) Consider the function from Problem 8 on page 107:
f(x,y) = 2-x^2-y^2
a) Sketch the graph of f and its level curves f(x,y)=c for c= -1,0,1,2
b) Compute the partial derivatives of f and the derivative matrix Df.
c) Find the equation for the tangent planes to the graph of f at the point (0,0,2)
and at the point (1,1,0)
d) Give a path c(t) lying on the graph of f.
2) Computing partial derivatives: Problems 6,8,10 on pages 122 and 123,
Limits: Problem 20,24 on p. 123
3)Derivatives and Chain rule: Problems 12,14,16 on p. 132; Problems 10,16 on p.144/145
4) Problem 24 on p. 145.
5) Gradients and Implicit Functions: Problem 12,30 on p.157 to 159; Problem 51 on p. 169;
Problems 4,10 on p.165
Bonus Problems: Problems 18,19 on p.166; Problem 65 on p.170; Problem 43 on p.160.
|
|
18 Oct 06
|
1) Higher Order Partial Derivative: Problem 2 on p.180, Problem 16 (a) (c) on p.181/182
2) Taylor's Formula: Problem 4, 8 on p.189
3) Finding Local Extrema: Problem 12 p.199, Problem 4, 6 on p. 209, Problem 21, 22 on p.210
4) Constrained Extrema: Problem 2, 10, 18 on p.220, Problem 22 on p. 221, Problem 32 on p. 225
Bonus:
Problem 16 (b) on p.181/182, Problem 40 on p. 226, Problem 12 on p.190
(For Problem 12 use that for |r|<1 you can write 1/(1-r) = 1+r+r^2+ r^3 +..... )
|
|
25 Oct 06
|
1) Speed and Acceleration: Problem 2 on p. 233, Problem 9 on p. 234
2) Length of Paths: Problem 8, 10 on p. 240
3) Vector Fields: Problem 4 on p. 247, Problem 10, 14 on p.248
4) Divergence of Vector Fields: Problem 2, 6 on p. 261, Problem 10, 26 on p.262
Bonus: Problem 8 on p. 261, Problem 11 on p. 264
|
|
01 Nov 06
|
1) Vectorfields and Curl: Problem 14, 16, 18 on p. 262. Problem 22, 27 on p. 262, Problem 28 on p. 263
2) Cavalieri's principle: Problem 2,4 on p. 278. Problem 6,10,12 on p. 279
3) Integrals over rectangles: Problem 2,6,10 on p. 290. Problem 16 on p. 291
4) Double integrals over more general regions: Problem 2,4 on p. 303. Problem 6 on p. 304. Problem 14, 20, 22 on p. 305
Bonus: Problem 32 on p. 263, Problem 24 on p. 305.
|
|
08 Nov 06
|
1) Triple Integral: Problem 2 on p. 315, Problem 6,10 on p. 316, Problem 20 on
p. 317
2) Change of Variables: Problems 2,4,10,13 on p. 337, Problems 18,20,24 on p. 338, Problem 34 on p. 339, Problem 40 on p. 353
3) Applications of Integrals: Problem 2, 4, 8 on p. 348, Problem 10,12 on p. 349
Bonus: Problem 6 on p. 348. Read Example 3 on pages 321/322 about the computation of the Gaussian integral, which plays an important role in probability and statistics. Then solve Problem 8 on p. 337.
|
|
15 Nov 06
|
1) Line Integrals: Problem 2,6 on p. 371, Problem 10,12,16 on p. 372.
2) Parametrized surfaces: Problem 2,7,8,10 on pages 381/382. (For Problem 8 read Example 4 on page 380.)
3) Surface Area: Problem 4,6,12 on p. 395, Problem 18 on p. 396, Problem 20 on p. 397.
Bonus: Problem 18 on p. 372, Problem 22 on p. 373, Problem 10 on p. 395.
|
|
22 Nov 06
|
1) Surface integrals: Problem 4, 8, 10, 14 on p. 409/410, Problem 32 on p. 414.
2) Green's Theorem: Problem 2, 6 on p. 427, Problem 20 on p. 428.
3) Divergence Formula: Problem 18 on p. 428.
4) Stokes' Theorem: Problem 2 on p. 442, Problem 6, 12 on p. 443, Problem 20 on p. 444 (For Problem 12 p.443
remember that the circulation of a vector field F
along a closed (oriented) curve C is the line integral of F along C.)
Bonus: Problem 16 on p. 410/411, Problem 29 on p. 429.
|
|
29 Nov 06
|
1) Gauss' divergence theorem: Problem 2 on p.455, Problem 4,5,6 on p. 456.
2) Review Chapter 7: Problem 4, 10, 12, 18 on p. 473/474/475.
3) Review Chapter 6: Problem 2 on p. 411 and Problem 28 on p. 414, Problem 16 on p. 412
4) Look at the page: http://www.math.umn.edu/~nykamp/m2374/readings
Bonus: Problem 13 on p. 457
|
Remark: I stole the code of this page from Uri Bader, who stole it from
Miklos Abert – who stole it from someone else.