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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:
  • Calculators
  • Transformation
  • Bonus Problem
  • Transformation (1)
  • Partial Credit
  • Heat Equation
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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) ...
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