Math 675
Discussion Questions
Chapter #6, Part 1
Reading: Chapter 6, Section 6.4
66. Find the leading behavior of
/2
ex tan t dt
0
as x .
67. Find the leading behavior of
2
ex sinh
t
dt
0
as x .
68.
Math 675
Discussion Questions
Chapter #7, Part 1
Reading: Chapter 7, Sections 7.1, 7.2
73. Find a perturbation series solution for each of the roots of x3 + x2 x = 0 with terms up to and
including O(
Math 675
Discussion Questions
Chapter #6, Part 1
Reading: Chapter 6, Sections 6.1 - 6.3
61. Consider the integral
1
I (x) =
cos(xt) dt
x
(a) This is suciently simple that the integral can be evaluated
Math 674
Discussion Questions
Chapter #3, Part 1
Reading: Chapter 3, Sections 3.1-3.3.
23. (1.7 ). Consider the equation
x2 y + 3xy + 2y = x4 y 3 .
(a) Let = ax and = a1 y , and show that the equation
Math 674
Discussion Questions
Chapter #3, Part 2
Reading: Chapter 3, Sections 3.4
35. Prove each of the following:
1/x as x 0+.
(a) x
(b) 1/x
(c) x
2
x as x .
25 as x 0.
36. Prove or disprove: If f (x
Math 675
Discussion Questions
Chapter #3, Part 3
Reading: Chapter 3, Sections 3.5
50. Suppose that f (x)
n=0
an xn . Is it the case that
n=0
an xn converges?
51. Suppose that
(a) f (x)
(b) g (x) =
n
Math 675
Discussion Questions
Chapter #9, Part 1
Reading: Sections 9.1-9.3.
76. Consider the problem
y + 2y + 2y = 0
y (0) = 0
y (1) = 1
(a) Find the exact solution. Use a CAS or otherwise to graph th
Math 675
Discussion Questions
Chapter #9, Part 2
Reading: Sections 9.4
77. Consider the problem
y x2 y y = 0
y (0) = 1
y (1) = 1
(a) Look for an outer solution in the form
y (x) y0 (x) + y1 (x) + . .