MATH 267 (Section E1) Homework No. 7
Reading
Sections 6.5, 6.6 (omit proof of Theorem 6.6.1), 7.2, 7.3.
Suggested Problems
Section 6.5: Exercise 1, 2, 5,
Section 6.6: Exercises 1,4,6,8,9,14.
Section 7.2: 10, 21, 22, 25
Section 7.3: 6,8, 12, 15,
Problems to be handed in in class on Thursday March 29-th
Problem 1 Solve the boundary value problem
y0−y=cos(t)−δ(t−4), y(0) = 0,
using the method of the Laplace transform.
Problem 2 a) Calculate the convolution integral
h(t) = et? t =Zt
0
et−ττdτ.
b) Calculate the Laplace transform H(s) of h(t).
c) Verify that H(s) = L(et)L(t) according to the convolution theorem.
Problem 3 Consider the matrix function
A(t) = cos(t)et
e−tcos(t).
a) Calculate eigenvalues and eigenvectors of A(0).
b) Calculate
d
dtA(t).
c) Calculate
Zt
0
A(τ)dτ.
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