Math. 487 Course Outline

This page will be modified throughout the semester.
This outline is a tentative guide, and will be updated as the course progresses.  Time will be allocated as appropriate for student presentations and discussion.

Refer to the course description for the topic and overall goals of this course.

Note: Copyrighted material or material under development referenced on this outline is available only through the Moodle pages for this course.

Home page for the course

Topic no.  Description Explanation / References / Projects
    Introduction to Matlab
  • Page 32 and subsequent pages of the manuscript for Applied Numerical Methods (to introduce Matlab).  This chapter is posted on Moodle.
  • The "Getting Started" section of the Matlab help facility.  
We will spend up to several days on this.  Things we will discuss include:
  1. interactive computations with matrices,
  2. plotting,
  3. mathematical functions and built-in higher capabilities within Matlab,
  4. Matlab as a full-featured programming language, with nice debugging capabilities.
2.  Introduction to Mathematica
(Covering of this topic is dependent on availability of licenses for Mathematica for our classroom laboratory.  If we are successful at installing the legacy version we have available on our newer machines, we will spend up to several days on this.)  
  1. Elementary features of Mathematica, including symbolic differentiation and integration.
  2. Mathematica as a functional programming language, in contrast to Matlab, C / C++, Fortran, etc., which are imperative programming languages.
  3. Some exploration of additional capabilities of Mathematica.
3.Symbolic computations in Matlab
4.  Solution of  initial value problems for systems of differential equations In this and the next topic, there is seemingly some overlap with the content of Math. 455.  However, here it is intended to examine practical aspects of solving these problems with Matlab, rather than a study of the basic underlying numerical techniques.  Also, we will cover items that were not covered or upon which assignments were not given when Math. 455 was offered in Spring, 2010.  Items covered are as follows.
  1. Introduction to the topic and systems of differential equations (Section 7.1 and 7.3 of Applied Numerical Methods). 
  2. Section 7.7 of  Applied Numerical Methods, with a focus on Example 7.10.
  3. Sections 7.9.1 and 7.9.3 of  Applied Numerical Methods.
  4. Sections 7.10 and 7.11 of  Applied Numerical Methods.
  5. A project that explores the capabilities of Matlab ODE solvers on an interesting model.
5.  Some elementary aspects of solution of partial differential equations
  1. Example 3.18 of Applied Numerical Methods.
  2. PDE capabilities in Matlab, including pdepe, and, time and interest permitting, pdenonlin.
 Solution of nonlinear algebraic systems of equations
  1. Portions of chapter 8 of  Applied Numerical Methods.
  2. Additional supplementary material.
7.  Linear and nonlinear optimization
  1.  Study of the optimization toolbox in Matlab.
  2. Additional supplementary material.