DEPARTMENT OF MATHEMATICS & STATISTICS

MATH 3503

FINAL EXAMINATION
DECEMBER 1994
TIME: 3 HOURS

ANSWER ALL QUESTIONS

1.(a)Find where
(b)Use the Laplace Transform to solve
where is the function of part (a).
(c)Solve
2.Evaluate
(a)
(b)
(c)
(d), using the Convolution Theorem. Do not evaluate the integral.
3.Show that x = 0 is a regular singular point of the differential equation
Find the indicial equation and show that its roots differ by an integer. By considering the smaller root, show that two independent series solutions may be obtained and find the first three non-zero terms in each of the solutions.
4.(a) Find the general solution to the system
and write down a fundamental matrix for the system.
(b)Use the result of part (a) to find the general solution to the non-homogeneous system
5.(a)Find the Fourier series for the function
(b)Find the complex Fourier series for the function
6.(a)Find the Fourier cosine series for the function
(b)Solve the boundary value problem for
where is the function of part (a).