Exams

Final exam:   

• final_exam_sample
• final_exam_sample_answers
• improved_euler_practice_exam (code used to generate the table at the end of the answer document, not an official part of the exam)

(30%) Chapters 1 and 2:

• part I of exam 1: rearranged and with different equations;
• part V of exam 1:  identify type and give first few steps of solution for one equation.

(40%) Chapters 3 and 6.

• part I of exam 2: rearranged and with different equations;
• For an underdamped mass spring system with damper or RLC circuit
  1. for the homogeneous equation
     1. find the form of the solution
     2. find natural and quasi periods and use example to discuss affect of damping on period
  2. for a cosine or sine forcing function: find form of particular solution.
  3. for a discontinuous forcing function with initial conditions: use Laplace Transform methods to solve.

(15%) Chapter 5:  find the recursive formula and the first few terms of a series solution to a 2nd order homogeneous equation.

(15%) Chapter 8: write down the pseudo-code for the improved Euler method with specific h and initial and target values. Perform the first 2 iterations by hand.

Exam 3:

• sample_exam3
• sample_exam3_solns
• As you will see from the solutions, there is too much computation to do in an hour and 15 minutes, so the actual problems on the exam will involve the same steps; however, they will be easier (smaller numbers) so that you will be able to finish the exam. Also note, that I changed the damping in problem to 2 Ns/m so that the problem has resonance. The original value 10 is too large for practical resonance.
• For up to 25% of whatever points you had lost, up to a maximum of 15 points; on separate paper:
  1.  for each problem you lost points on:
     1. write a sentence explaining what you did wrong (if you did not work on the problem, then explain the general procedure for solving the problem);
     2. complete the solution
  2.  insert the corrections into your exam  and submit by the beginning of class on Th 12/12.

Exam 2:

• exam2_guide
• exam2_practice
• exam2_red_of_order_solns
• exam2_practice_solns (with last problem’s solution corrected)
• For up to 25% of whatever points you had lost, up to a maximum of 15 points, on separate paper:
  1.  for each problem you lost points on:
     1. write a sentence explaining what you did wrong (if you did not work on the problem, then explain the general procedure for solving the problem);
     2. complete the solution
  2. for problem 2,  graph and printout the solution using your favorite software (MATLAB, maple, etc.) and discuss the longterm behavior.
  3. for problem 3, use the initial conditions y(1)=1, y'(1)=1 to solve the corresponding IVP.  Graph and printout the solution using your favorite software (MATLAB, maple, etc.) and discuss the longterm behavior.
  4. for problem 4, find the particular solution, not just the form (i.e., identify the coefficients).
  5. for problems 5, use the initial conditions x(0)=0.5 and x'(0)=1 to solve the corresponding IVP. Write the solution as a cosine function with phase. Graph and printout the solution using your favorite software (MATLAB, maple, etc.) and discuss the longterm behavior.
  6.  staple to your exam  and submit by the beginning of class on T 11/19.

Exam 1:

• Exam I study guide: ch01_02
• Guide to part V of exam I part V exam 1 including solutions to p. 133 #1-32
• exam1_practice
• exam1_practice_solutions
• exam1_solutions
• Exam 1 results
• As a way to encourage you to study the solutions carefully and to complete the partial solutions, for up to 10 points plus 10% of whatever points you had lost, on separate paper:
  1.  for each problem you lost points on for parts II-V, write a sentence explaining what you did wrong (if you did not work on the problem, then explain the general procedure for solving the problem);
  2. complete the solutions for part V;
  3. staple items 1 and 2 to the back of your exam  and submit by the beginning of class on Th 10/24.