Math 251

  Ordinary and Partial Differential Equations  

        Sample Exams        

 

 

Exam I

  1. Exam I, Spring 2000            answer key

  2. Exam I, Fall 2000            answer key
    Question 6 on this exam is among the trickiest application problems to appear on a Math 251 exam in the past decade... It is not quite the mixing problem as given in the textbook, but with a slight twist. You'll need to think a little to come up with the correct model/initial value problem.

  3. Exam I, Fall 2001            answer key
    The graphs are missing from question 6b. You can ignore the part, or sketch the correct direction field yourself.

  4. Exam I, Spring 2002            answer key and complete solutions

  5. Exam I, Summer 2002            answer key

  6. Exam I, Fall 2002            answer key and complete solutions

  7. Exam I, Spring 2003            answer key

  8. Exam I, Summer 2003            answer key

  9. Exam I, Fall 2003            answer key

  10. Exam I, Spring 2004            answer key

  11. Exam I, Fall 2004            answer key

  12. Exam I, Spring 2005            answer/grading key and solutions

  13. Exam I, Fall 2005 (questions and answer key) - Professor Glasner's sections

  14. Exam I, Fall 2005 - common exam for other sections            questions and answer/grading key

  15. Exam I, Summer 2006            answer key

  16. Exam I, Spring 2007            answer key

  17. Exam I, Summer 2007            answer key

  18. Exam I, Fall 2007            answer key

  19. Exam I, Spring 2008            answer key

  20. Exam I, Summer 2008            answer key

  21. Exam I, Fall 2008            answer key

  22. Exam I, Spring 2009            answer key

  23. (Math 251H Honors section) Mock/Practice Exam I, Spring 2009

  24. Exam I, Summer 2009            answer key
    There was only one midterm exam during the Summer semester, 2009. This is that exam. It covers up to section 6.2.

  25. Exam I, Fall 2009           

  26. Exam I, Spring 2010            answer key

  27. Exam I, Summer 2010            answer key

  28. Exam I, Fall 2010            answer key

  29. Exam I, Spring 2011            answer key

  30. Exam I, Summer 2011            answer key

  31. Exam I, Fall 2011            answer key

  32. Exam I, Spring 2012            answer/grading key

  33. Exam I, Summer 2012            answer key

  34. Exam I, Fall 2012            answer key

  35. Exam I, Spring 2013            answer key

  36. Exam I, Summer 2013           

  37. Exam I, Fall 2013            answer/grading key and complete solutions

  38. Exam I, Spring 2014            answer key and solution

 

 

Exam II

  1. Exam II, Spring 2000

  2. Exam II, Fall 2000            answer key

  3. Exam II, Fall 2001

  4. Exam II, Summer 2002            answer key

  5. Exam II, Fall 2002            answer key

  6. Exam II, Spring 2003            answer key
    It says Exam 1 on the cover, but it is indeed the second exam.

  7. Exam II, Summer 2003            answer key

  8. Exam II, Fall 2003            answer/grading key and complete solutions (very detailed).
    Due to an error in putting together the exam package, the table of Laplace transforms was unavailable to students taking the conflict exam. Therefore, a separate set of Laplace transform problems was made as a mini re-test and given to the affected students as a remedy. Here is the Laplace re-test.
    Exam II Laplace transforms make-up test, Fall 2003            answer key and complete solutions

  9. Exam II, Spring 2004            answer key

  10. Exam II, Spring 2005            answer key

  11. Exam II, Fall 2005 (questions and answer key) - Professor Glasner's sections

  12. Exam II, Fall 2005 (questions and answer/grading key) - common exam for other sections

  13. Exam II, Summer 2006            answer key

  14. Exam II, Spring 2007

  15. Exam II, Summer 2007            answer key

  16. Exam II, Fall 2007            answer key

  17. Exam II, Spring 2008            answer key

  18. Exam II, Summer 2008            answer key

  19. Exam II, Fall 2008            answer/grading key (interim).
    This was a draft version of the grading key - there was a mistake in #12 (the correct answer is y(t)=e^{-3t} + u(t-2)(5/9+(t-2)/3-5/9 e^{-3(t-2)}) + u(t-3)e^{-3(t-3)}); in addition, also acceptable as an answer to #2(a) was "none", since the eigenvectors do not match what's given in the saddle point phase portrait.

  20. Exam II, Spring 2009            answer key

  21. (Math 251H Honors section) Mock/Practice Exam II, Spring 2009            answer key

  22. There was not a second midterm exam during the summer 2009 semester, only the exam I and final exam.

  23. Exam II, Fall 2009           

  24. Exam II, Spring 2010           

  25. Exam II, Summer 2010            answer key

  26. Exam II, Fall 2010            answer key

  27. Exam II, Spring 2011            answer key

  28. Exam II, Summer 2011            answer key

  29. Exam II, Fall 2011            answer/grading key

  30. Exam II, Spring 2012            answer key

  31. Exam II, Summer 2012            answer key

  32. Exam II, Fall 2012            answer key

  33. Exam II, Spring 2013            answer key

  34. Exam II, Summer 2013            answer key and complete solutions

  35. Exam II, Fall 2013            answer/grading key

 

 

Final Exam

  1. Final Exam, Fall 1999

  2. Final Exam, Spring 2000

  3. Final Exam, Fall 2000            answer key

  4. Final Exam, Fall 2001

  5. Final Exam, Summer 2002

  6. Final Exam, Spring 2003            answer key

  7. Final Exam, Summer 2003            answer key

  8. Final Exam, Fall 2003            answer key

  9. Final Exam, Spring 2004            answer key

  10. Final Exam, Spring 2005 (questions and answer key)

  11. Final Exam, Fall 2005 - Professor Glasner's sections

  12. Final Exam, Fall 2005 - common exam for other sections            questions and answer/grading key

  13. Final Exam, Spring 2007            answer key            complete solution (detailed)

  14. Final Exam, Fall 2007            answer key

  15. Final Exam, Spring 2008            answer key

  16. Final Exam, Fall 2008            answer key

  17. Final Exam, Spring 2009            answer key

  18. (Math 251H Honors section) Mock/Practice Final Exam (version 1), Spring 2008/2009

  19. (Math 251H Honors section) Mock/Practice Final Exam (version 2), Spring 2008/2009

  20. Final Exam, Summer 2009            answer key
    This exam is shorter and simpler than usual. It is not a typical representative of the comprehensive final exams like the others.

  21. Final Exam, Fall 2009           

  22. Final Exam, Spring 2010            answer key

  23. Final Exam, Summer 2010            answer key

  24. Final Exam, Fall 2010            answer key

  25. Final Exam, Spring 2011            answer/grading key

  26. Final Exam, Summer 2011            answer key

  27. Final Exam, Fall 2011            answer key

  28. Final Exam, Spring 2012            answer/grading key

  29. Final Exam, Summer 2012           

  30. Final Exam, Fall 2012            answer key

  31. Final Exam, Spring 2013            answer/grading key and complete solutions

  32. Final Exam, Summer 2013           

  33. Final Exam, Fall 2013            answer/grading key and complete solutions

 

 

Additional sample problems can be found here: Math 250 Sample Exams Page


Send any question/comment about this page to: tseng@math.psu.edu

Last modified: March 20, 2014