# Past Exam for MTH 3326 - Partial Differential Equations with Littlejohn at Baylor (BU)

## Exam Information

 Material Type: Final Professor: Littlejohn Class: MTH 3326 - Partial Differential Equations Subject: Mathematics University: Baylor University Term: Spring 2009 Keywords: CalculatorsTransformationBonus ProblemTransformation (1)Partial CreditHeat Equation

## Sample Document Text

MATH 3326 FINAL EXAMINATION SPRING SEMESTER 2009 Lance L. Littlejohn Name SCLW"nDN.\$. Instructions: Show all work. Partial credit can only be given if sufficient work accompa nies each answer. Calculators may be used but exact answers are required. This examination is out of 70 points. GOOD LUCK! Problem No. L 2. 3. 4. 5. 6. Grade L (10 POINTS) Using d'Alembert's formula, solve the Cauchy problem Utt - c 2 u xx (-00 < X < 00, t> 0) u(x,O) - cos x, 11t(X,0) = e- x (-00 < x < 00) with c = 4. Simplify your answer as much as possible. \ Y\ --It \ s Q.o,:;,e.,~ 'f l~) "" c.'Os X ~ "-f !x)-=- e.::-'" d\M~\1f1~t\s. Se.\,vAiovv in fu0 Q.C<~Q-\~~Ud::; {,{u<;c):::. '{?\X,+4-b)+'f(X-'-tt)+-t-~ e-Ucl-v-.- ~ ~-4-t Points /70 2. Consider the first-order linear PDE U x + xU y + 3u = 2. (1) (a) (3 POINTS) Find, and solve, the characteristic equation associated with (1). SO ~= ~~'-4-C ~ \t;--t"= ~J (b) (4 POINTS) Using ~(x,y) = x, find a transformation 1) ...