Homework for Math 421 Spring 2014
SHOW ALL YOUR WORK!!!
- Assignment 1 (Due Thursday, January 30)
- Section 2 page 5: 4
- Section 3 page 8: 1 (a), (b)
- Section 4 page 12: 4, 5 (a), (c), 6
- Section 5 page 14: 1 (c), (d), 9, and the
extra problem
- Section 7 page 22: 1 (a), 2, 3, 4, 5 (c), 5 (a), 6, 9, 10
- Section 10 page 29: 2 (a), (b), 4, 7, 8
- Section 10 page 27: Read it!
- Assignment 2 (Due Thursday, February 6)
- Section 18 page 55: 5
- Section 20 page 62: 1 (b), (d), 4, 8 (a), 9.
- Section 21,22,23 page 71: 1 (c), (d), 2 (b), (d),
3 (a),6
- Section 25 page 77: 1 (a), (b), 2 (a), 3
- Section 29 page 92: 1, 4, 7, 8 (b), (c), 14
- Assignment 3a (Due Thursday, February 20)
- Section 34 page 108: 2, 5 (a), 13, 16
(do problem 16 anyway you want, not necessarily using cosh and sinh).
- Assignment 3b (Due Tuesday, February 25)
- Section 31 page 97: 1, 2, 3, 5 (b), 7, 9
- Section 32 page 100: 2
- Assignment 4 (Due Tuesday, March 4)
- Section 33 page 104: 1, 2 (c), 3, 5, 6
- Section 26 page 81: 1 (a), (d), 4, 7, 8
Suggestion for 7: Either use the suggestion in the text, or
recall from calculus III that the tangent line to the curve
u(x,y)=constant, at a given point (a,b) on that curve, is
parallel to the line u_x(a,b)x+u_y(a,b)y=0, provided at least
one of the partials u_x(a,b) or u_y(a,b) does not vanish.
- Section 31 page 97: 10 (Method 1: check that
its first and second partials are continuous and
satisfies the laplace equation. Method 2: realize this function as the
real part of an analytic function).
- Section 38 page 121: 1 (b), 2 (b), (c), 3, 4
- Section 39 page 125: 2
- Assignment 5 (Due Thursday, March 13)
- Section 42 page 135: 1, 3, 5, 6, 7, 8, 10
- Assignment 6 (Due Thursday, March 27)
- Section 43 page 140: 1, 2, 4, 7
- Section 45 page 149: 1, 2 (a), (b), 3, 4, 5
- Assignment 7 (Due Thursday, April 3)
- Section 49 page 160: 1 All except (d), 2
ALL, 3, 4, 6, 7.
- Section 52 page 170: 1 a, b, c, 3.
- Assignment 8 (Due Tuesday, April 8)
- Section 52 page 170: 1 d, e, 2, 4, 5, 7, 8, 10
- Section 54 page 179: 1, 2, 9.
- Assignment 9 (Due Thursday, April 17)
- Section 54 page 179: 3, 4, 5, 6, 7.
- Section 56 page 188: 2, 3, 4
- Section 59 page 195: 1, 2, 3, 6, 7, 8, 11, 13
- Assignment 10 (Due Thursday, April 24)
- Section 62 page 205: 1, 2, 3, 4, 5, 6
- Section 71 page 239: 1 ALL, 2 ALL, 3 ALL,
6
Hint for 1d: Note that cot(z)sin(z)=cos(z).
Write cot(z)=sum_{n=-infinity}^infinity c_n z^n.
We already know the Taylor series of sin and cos centered at 0.
First show that c_n=0 for n<-1.
Then solve for the coefficients c_{-1}, c_0, c_1, c_2, c_3 one by one each time expressing
c_{n+1} in terms of the previous ones c_{-1}, c_0, …, c_n.
- Assignment 11 (Due Tuesday, April 29)
- Section 72 page 243: 1 ALL, 2, 3, 4
- Section 74 page 248: 1, 2 (a), (b), 3, 4, 6 (a)
- Section 76 page 255: 1, 2 (a), 3 (a), 4 (a), 5
- Assignment 12 (Due May 6 - not to be handed in,
but material is included in the final exam)
- Section 87 page 297: 1, 2, 5, 6, 7 (a), (c), 8, 9
- Section 79 page 267: 1, 2, 3, 4, 5. Recommended: 9.