MATH3705 D Test 3:
Friday, March 7, 14:3515:25
Name and Student Number:
Total points: 15. There are 6 Questions in total.
Closed book! Nonprogrammer calculators are allowed!
cfw_
[1]
x + x2 x3 , 0 x < 1;
1. Let f (x) =
Let fodd (x) be the 4periodic odd
MATH 3705 * B
Test 2  Solutions.
February 2012
Questions 14 are multiple choice. Circle the correct answer. Only the answer will be marked.
1
1. [2 marks] The equation 3(x 1)y + x2 y + y = 0 has
4
(a) two regular singular points x = 1 and x = 3.
(b) one
MATH3705 D Test 1:
Friday, Jan 31, 14:3515:25
Name and Student Number:
Total points: 15. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
[1]
1. Lcfw_t sin 3t =
(a)
3s
(s2 +3)2
3s
s2 +9
(b)
(c)
2 sin s
(s2 +9)2
s
(d
MATH3705 A Test 3:
5:35pm6:25pm, July 10
Name and Student Number:
Total points: 15. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
cfw_
[1]
1 x,
0 x < 1;
Let fodd (x) be the 4periodic odd extension of f (x).
2 x,
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MATH 3705* A
Test 1
January 2012
LAST NAME: ID#:
Questions 16 are multiple choice. Circle the correct answer. Only the answer will be marked.
1. [2] Lcfw_e2t cos(3t) =
(a)
s+2
(s + 2)2 + 9
(b)
s2
s
+9
(c)
s2
(s 2)2 + 9
(d) None of the above
2. [2] Lcfw_t
m
1
q
;
p.
A
u
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MATH 3705* A
Test 1
January 2012
LAST NAME: ID#:
Questions 16 are multiple choice. Circle the correct answer. Only the answer will be marked.
1. [2] Lcfw_e2t cos(3t) =
(a)
s+2
(s + 2)2 + 9
(b)
s2
s
+9
(c)
s2
(s 2)2 + 9
(d) None of the above
2. [2] Lcfw_t
MATH3705 A Test 2:
5:35pm6:25pm, June 12
Name and Student Number:
Total points: 15. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
1. (1.5 points) Find the general solution of x2 y 4xy + 6y = 0 for x = 0.
(a) c1 
MATH3705 A Test 4:
5:35pm6:25pm, July 31
Name and Student Number:
Total points: 15. No partial marks for Questions 12.
Closed book! Nonprogrammer calculators are allowed!
1. (1.5 points) Consider the wave equation utt = c2 uxx , 0 < x < L, t > 0, subjec
Student ID: 
Solution b)
Finding the polar and Area moments of inertia
=
= .460 in4 for d = 1.75 in
=
= .921 in4 for d = 1.75 in
Deflection in bending
=
+ ( ) ( ) + ( )
=
.
Torsional Deflection
=
=
8 + (8 4) (8 8) + 4(8 4)8 = 0.0031 in
.
.
= .0015 Ra
MATH3705 Tutorial 6
1. Consider the SturmLiouville problem y + 4y + 2y = 0, 2y(0) + y (0) = 0, y(2) = 0.
(a) Find all eigenvalues n and corresponding eigenfunctions yn (x).
(b) Place the equation in the SturmLiouville form (py ) qy + ry = 0, and determi
MATH3705 A Test 3
Name and Student Number:
Total points: 20. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
cfw_
[1]
1 x, 0 x < 1;
Let fodd (x) be the 4periodic odd extension of f (x).
0,
1 x < 2.
Which of the fo
MATH3705 Tutorial 4
cfw_
1. Let
f (x) =
2, for x [, 0);
,
1, for x (0, ).
and let f (x) be 2periodic. Find the Fourier series of f (x) and determine the sums to
which the series converges at x = 0, 101, 88.1.
Solution:
a0
an
bn
( 0
)
1
1
=
f (x)dx =
2
MATH3705 A Test 2
Name and Student Number:
Total points: 20. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
[2]
1. Find the general solution of x2 y 4xy + 6y = 0 for x = 0.
(a) c1 x2 + c2 x3
(b) c1 x2 + c2 
MATH 3705C
Test 4 Solutions
March 18, 2011
[Marks]
[4]
Questions 12 are multiple choice. Circle the correct answer. Only the answer will be marked.
1. The solution of Laplaces equation uxx + uyy = 0 within the rectangle
0 < x < 2, 0 < y < 3, which satise
MATH3705A  Test 4:
Surname
17:3518:25, July 26, Tuesday
First Name
Student #
Total points: 15. No partial marks for Questions 12.
Closed book! Nonprogrammer calculators are allowed!
1. (2 points) To solve the equation urr + 1r ur + r12 u = 0, we use Se
MATH3705A  Test 3:
Surname
17:3518:25, July 12, Tuesday
First Name
Student #
Total points: 15. No partial marks for Questions 12.
Closed book! Nonprogrammer calculators are allowed!
1. (4.5 points = 1.5+1.5+1.5) Let f (x) =
2,
0 x 1;
x + 3, 1 < x < 3.
MATH3705A  Test 2:
Surname
17:35cfw_18:25, June 14, Tuesday
First Name
Student #
Total points: 15. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
1. (1.5 points) The regular singular points of x2 y 00
(a) 0; 1; 2
Table of Laplace Transforms
Z
f (t)est dt, s > 0
F (s) = Lcfw_f (t) =
0
Lcfw_tn =
L cfw_tp =
n!
(p + 1)
, p > 1
sp+1
Lcfw_sin(at) =
Lcfw_cos(at) =
Lcfw_eat =
if n 0 is an integer
sn+1
s2
a
+ a2
s2
s
+ a2
1
, s>a
sa
Lcfw_f (t) =
1 s
F
, >0
Lcfw_eat f (t
MATH3705A Test 1:
Surname
17:3518:25, May 31
First Name
Student #
Total points: 15. No partial marks for Questions 14.
Closed book! Nonprogrammer calculators are allowed!
[2]
1. Lcfw_t cos(3t) =
(a)
s2 9
(s2 +9)2
(b)
3s
s2 +9
(c)
3s2 +9
(s2 +9)2
s
(d) (