Course Outline

The deliverables for the class project which consists of constructing a tutorial will correspond to the topics covered in class. I used the text book written by Gerald and Wheatley [8] when creating the outline and associated examples.

1. Describing/Understanding an ODE Problem
   Describe, build intuition, and analyze the software evolution model (shown in section 7.2). Also introduce the Euler method, Taylor series, and accuracy.

2. Tutorial Examples
   Describe the overall format for the tutorial project and provide at least one example tutorial.

3. Non-linear equations: Finding Roots
   Introduce Newton's method by using the software engineering example and asking "Given the rates R, F, E, and the desired rate of project size increase dm/dt, how many human hours are required?".

4. Implementation Documentation: The good, the bad, and the ugly
   As suggested by Schoenfeld [12], students can better learn by seeing the mistakes of others. Documentation is a perfect subject to allow students to evaluate what does and does not work by analyzing the work of others. In this class we will look at existing documentation for some Matlab programs and point out "the good, the bad, and the ugly". Throughout the term, students will be graded on their program comments, and their writing in the tutorial project.

5. Coming up with the model: Interpolation and Curve fitting
   We already determined a function $m(t)$ which describes the size of a software package by the number of classes over time. Let's look at some "experimental" data using interpolation to determine the size of the project where data is missing and using curve fitting methods to determine a more realistic model.

6. Visualization: The Basics
   At this point the students will have already used Matlab to do some simple graphing. This unit will introduce general visualization concepts.

7. Numerical differentiation and integration
   Using the data about the size of the software package over time we will determine the rate of change of the software package numerically.

8. The errant computer: floating point arithmetic and the error it produces
   We will look at the IEEE floating point specification and use our touchstone example to show how much error can occur due to the binary representation of numbers that a computer uses.

9. The Finite Difference Method: Discretizing time and space to solve partial differential equations
   Possible touchstone problem can be the heat on a motherboard depending on the heat generated by the chip and other elements. Will use Taylor series and solving systems of linear equations. Will cover explicit and implicit methods of time stepping and stability.

10. Brief description of Finite Element Method
    The finite element method uses interpolation, newton's method when the PDE is nonlinear, and solving a set of linear equations.