Partial Differential Equations 3150
Final Exam
Exam Date: Thursday, May 2, 2013
Instructions: This exam is timed for 120 minutes. You will be given extra time to complete
the exam. No calculators, notes, tables or books. Problems use only Chapters 1, 2, 3, 4, 7 of the
textbook. No answer check is expected. Details count 3/4, answers count 1/4.

1. (CH3. Heat Conduction in a Bar)
(a) [20%] Find the steady-state temperature
(b) [60%] Solve the bar problem
(c) [20%] Display an answer check


2. (Fourier Series)
(a) [40%] Find and display the nonzero terms in the Fourier series expansion of f(x)
(b) [60%] Compute the Fourier sine or cosine series coefficients for the function g(x)


3. (CH3. Finite String: Fourier Series Solution)
(a) [50%] Display the series formula, complete with derivation details, for the solution
          u(x, t) of the finite string problem
(b) [25%] Display explicit formulas for the Fourier coefficients
(c) [25%] Evaluate the Fourier coefficients


4. (CH4. Poisson Problem)
 [100%] Solve for u(x, y) in the Poisson problem, to obtain an explicit formula.


5. (CH7. Heat Equation and Gauss' Heat Kernel)
Solve the insulated rod heat conduction problem

Hint: Use the heat kernel, the error function erf (x), and Fourier transform
rules to solve the problem. The answer is expressed in terms of the error function.