# Ordinary and Partial Differential Equations

## Sample Exams

Exam I

1. Exam I, Spring 1998

2. Exam I, Spring 2000            answer key

3. 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.

4. 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.

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

6. Exam I, Summer 2002            answer key

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

8. Exam I, Spring 2003            answer key

9. Exam I, Summer 2003            answer key

10. Exam I, Fall 2003            answer key

11. Exam I, Spring 2004            answer key

12. Exam I, Fall 2004            answer key

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

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

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

16. Exam I, Summer 2006            answer key

17. Exam I, Spring 2007            answer key

18. Exam I, Summer 2007            answer key

19. Exam I, Fall 2007            answer key

20. Exam I, Spring 2008            answer key

21. Exam I, Summer 2008            answer key

22. Exam I, Fall 2008            answer key

23. Exam I, Spring 2009            answer key

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

25. 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.

26. Exam I, Fall 2009

27. Exam I, Spring 2010            answer key

28. Exam I, Summer 2010            answer key

29. Exam I, Fall 2010            answer key

30. Exam I, Spring 2011            answer key

31. Exam I, Summer 2011            answer key

32. Exam I, Fall 2011            answer key

33. Exam I, Spring 2012            answer/grading key

34. Exam I, Summer 2012            answer key

35. Exam I, Fall 2012            answer key

36. Exam I, Spring 2013            answer key

37. Exam I, Summer 2013

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

39. Exam I, Spring 2014            answer key and solution

40. Exam I, Summer 2014

41. Exam I, Fall 2014            answer key

42. Exam I, Spring 2015            answer key

43. Exam I, Summer 2015            answer key

44. Exam I, Fall 2015

45. Exam I, Spring 2016            answer key

46. (Math 251H Honors section) Exam I, Spring 2016            answer key and solutions

47. Exam I, Summer 2016            answer key

48. Exam I, Fall 2016

49. Exam I, Spring 2017

50. Exam I, Fall 2017            answer key and solution

51. Exam I, Spring 2018

52. Exam I, Summer 2018            answer key

53. Exam I, Fall 2018            answer key

54. Exam I, Spring 2019            answer key

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

36. Exam II, Spring 2014            answer key

37. Exam II, Summer 2014            answer key

38. Exam II, Fall 2014            answer key
The missing answer at the very end is: #12(c) "saddle point, unstable".

39. Exam II, Spring 2015            answer key

40. Exam II, Summer 2015            answer key

41. Exam II, Fall 2015            answer key and solutions

42. (Math 251H Honors section) Exam II, Spring 2016            answer key and solutions

43. Exam II, Spring 2016            answer key

44. Exam II, Summer 2016

45. Exam II, Fall 2016

46. Exam II, Spring 2017            answer key

47. Exam II, Fall 2017

48. Exam II, Spring 2018            answer key and solutions

49. Exam II, Summer 2018            answer key

50. Exam II, Fall 2018            answer 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

34. Final Exam, Spring 2014            answer/grading key and complete solutions

35. Final Exam, Summer 2014

36. Final Exam, Fall 2014            answer key

37. Final Exam, Spring 2015            answer/grading key

38. Final Exam, Summer 2015

39. Final Exam, Fall 2015            answer/grading key and complete solutions

40. Final Exam, Spring 2016            answer/grading key and complete solutions

41. Final Exam, Summer 2016

42. Final Exam, Fall 2016

43. Final Exam, Spring 2017            answer/grading key and complete solutions
The correct answer to 16(c) should be "true" since the case h(x) = j(x) = 0 is not ruled out by the question, in fact in part 16(d) it is explicitly stated that either function could be 0.

44. Final Exam, Fall 2017

45. Final Exam, Spring 2018            answer key

46. Final Exam (Exam III), Summer 2018
This exam is the third (noncomprehensive) midterm exam of the semester. It covers only phase portraits and PDE topics. It is not simpler, just shorter than usual. Nevertheless, it is not a typical representative of the comprehensive final exams like the others.

47. Final Exam, Fall 2018            answer key

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