Written homework will generally be due on Wednesday in class. You are encouraged to discuss the homework with other members of the class, but you will be expected to write up your solutions without any assistance. It is appropriate to acknowledge the assistance of others. I reserve the right to refuse to accept late homework for any reason.

Note that some of the homework problems in this course have been assigned in other classes.  Copying work from published solutions (or solutions of past students) is a violation of the HMC Honor Code and will be dealt with accordingly. 

Homework should be formatted in accordance with the Math Department Homework Policy.

• Define the Laplace Transform.
• Take the Laplace Transform of simple functions.
• Solve linear constant coefficient initial value problems using the Laplace Transform.
• Define the δ-function and determine it's Laplace Transform
• Define a Green's Function.
• Define the convolution and use it to solve certain linear DE's with an arbitrary forcing.

Reading:

• Problems for Homework 4 (.pdf)
• Problems for Homework 4 (.tex)

• Describe and be able implement Euler's Numerical Method and explain its relationship to the tangent line.
• Describe and be able to implement Taylor Numerical Methods of low orders and explain their relationship to Euler's Methods
• Describe and be able to implement various Runge-Kutta Methods (Midpoint method, fourth-order Runge-Kutta)
• Define local truncation error and determine the local truncation error for various numerical schemes.
  
• Define global error and estimate it for various numerical schemes.
• Determine for which stepsizes a numerical scheme is stable.
• Given an IVP, find an appropriate numerical method to solve it and solve it to a particularly accuracy.
• Use the provided MAPLE worksheets to implement various numerical methods (Euler's Method, Runge-Kutta, etc.) in MAPLE.

Reading:

MAPLE:

• The Final Exam is a three hour take-home.
• You can use any class materials distributed during the course, and your own notes.
• You can use this table of Laplace Transforms.
• You can NOT use any internet resources other than the course website.
• You can use Mathematica, MAPLE or Wolfram Alpha for calculations.

• Here is a practice midterm from Spring 2012.
• Here are the solutions to the practice midterm.