Physics 3513, Final exam: solution
(1) Let z = x + iy , then we have x2 y 2 + 2xyi = x iy , or x2 y 2 = x, 2xy = y . The
second equation has two solutions y = 0 and x = 1/2. Substituting them to the
r
Physics 3513, Homework #5 (due 10/1)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 1.5) For w = 8x4 + y 4 2xy 2 , nd 2 w/x2 and 2 w/y 2 at the poin
Physics 3513, Homework #4 (due 9/24)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 5.10) Find symmetric and parametric equations of a line through
Physics 3513, Homework #3 (due 9/17)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 2.7) Solve
2x +
3y = 1
+ 2y = 2
+ 3y = 5
x
x
P2(10) (Boas 2.10)
Physics 3513, Homework #1 (due 9/3)
The numbers in parentheses after the problem number indicate points for each problem.
1
n ln n
n=2
P1(10) (Boas 6.7) Test for convergence using the integral test:
3
Physics 3513, Homework #2 (due 9/10)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 5.6) Calculate
1+i
1i
2
P2(10) (Boas 5.47) Solve z 3 = 1
P3(10)
Physics 3513, Homework #6 (due 10/15)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) Find the ratio of the hatched area to the area of the band |y | < 1.
Physics 3513, Homework #7 (due 10/29)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 3.1) If A = (2, 1, 1), B = (2, 3, 1), C = (0, 1, 1), nd (AB)C,
Physics 3513, Midterm I: solutions
an+1
= |x 1|, so the series converges if 0 < x < 2 and diverges if x < 0
an
(1)n
1
(n 1)!
(1)n =
= ln 2 and
=e
or x > 2. At x = 0, both
n!
n
n!
n=1
n=1
n=1
1
1
diver
Physics 3513, Midterm II: solutions
1
(1) V =
(x2 x3 )2 dx =
0
.
105
(2) F = (ey ey )i + (ez ez )j + (ex ex )k = 0, so the function is conservative.
y
x
(x,y,z )
dx +
F dr =
The potential =
(0,0,0)
Physics 3513, Homework #11 (due 12/10)
The numbers in parentheses after the problem number indicate points for each problem.
P1(20) (Boas 1.5,7) Solve by series and by an elementary method and verify
Physics 3513, Homework #10 (due 12/3)
The numbers in parentheses after the problem number indicate points for each problem.
P1(20) (Boas 5.7, 6.14)
(a) Expand in a Fourier series: f (x) =
(b) Using th
Physics 3513, Homework #8 (due 11/5)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 2.5) Solve by separating variables: xy xy = y , y (1) = 1
P2(10)
Physics 3513, Homework #9 (due 11/29)
The numbers in parentheses after the problem number indicate points for each problem.
P1(10) (Boas 1.21) Find the real and imaginary parts u(x, y ) and v (x, y )