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Tutorial Section:
Math 211 Assignment 7
1. Using the convolution theorem, determine the following inverse Laplace transform (you
should not use partial fractions in this question).
1
1
L
(s 2)2 (s + 3)2
(AMEM 5.6.8 49(b)
2. Express the solution x(t)

Name:
Tutorial Section:
Math 211 Assignment 6
1. Obtain the inverse Laplace transform of
s2 1
s2 + 4
(AMEM 5.5.12 25(b)
2. Solve for t > 0 the following IVP:
x + 6x + 13x = (t 2),
subject to x = 0 and dx/dt = 0 at t = 0. (AMEM 5.5.12 26(b)
3. Note the con

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Math 211 Assignment 5
1 Find the Laplace transform, L [f ], of the following functions and determine the domain of
convergence:
i) f (t) = cos t + 4
ii) f (t) = e t [c1 sin t + c2 cos t]
iii) f (t) = t4 + 4t3 + 6t2 + 4t + 1
iv) f (

Math 211 Assignment 11 Solutions
1. Solve the heat equation
u
2u
=2 2
t
x
for x [0, 7] and t [0, ) subject to the conditions that
u(t, 0) = 0, u(t, 7) = 2, u(0, x) = H(x 2) H(x 5).
Answer: We can deal with non-zero boundary conditions as follows: find one

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Tutorial Section:
Math 211 Assignment 8
1. Explain why a circuit with transfer function T (s) = s is called a differentiator. What
would be the transfer function of an integrator?
2. Prove the following orthogonality relation for arbitrary natural n

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Math 211 Assignment 3
1. Find the general solution of the following differential equations:
dx
d2 x
2
3x = t
dt2
dt
d2 x dx
(b)
x = 5et
dt2
dt
(a)
2. Solve the following equation:
d2 x
dx
+ 16x = e4t
+8
2
dt
dt
3. Solve the follo

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Math 211 Assignment 4
1. In this problem, you may assume the following result without proof:
lim T k esT = 0,
T
provided Re(s) > 0. Here k 0 is any non-negative integer.
Use the integral definition of Laplace transform to obtain t

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Tutorial Section:
Math 211 Assignment 10
1. Compute the complex Fourier series of the function which is the periodic extension of t2 on the interval
[1, 1].
2. Let f (x) be an arbitrary real-valued, periodic function. f (x) has a real FS with coeffi

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Tutorial Section:
Math 211 Assignment 1
1. Fill in the table with the attributes of each equation.
Equation
Dep. Indep. Order Partial/
Var(s) Var(s)
Ordinary
a)
dx
+ 2x = 0
dt
b)
f
f
+
=0
x y
c)
dx
d2 x
+ t5
+ 3x = 5
2
dt
dt
d)
d2 y
dx
+c 2 =0
dt
dt

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Tutorial Section:
Math 211 Assignment 9
1. Simplify sin( n
) + cos( n
) 1 under the assumption that n is an integer. This means,
2
2
write out the possible values for this expression as n varies among the integers.
2. Let f (x) = H(x 1) defined on x