Mathematics 450 Course Description and Philosophy

Mathematical Modeling, Fall, 2004

The official description in the Undergraduate Bulletin is:

450(G).  MATHEMATICAL MODELING. (3, 0, 3). Development of mathematical models arising in various areas of application in the physical, biological, and social sciences. Prereq: MATH 350 with a grade of C or better and working knowledge of a programming language
I am trying a somewhat different approach than I did in Fall, 2002.  In particular, this semester, we will be using a text (Giordano / Weir / Fox) this semester.  Depending on peoples' backgrounds, the mathematical underpinnings of this text will be rather elementary, and we will cover some material more or less quickly.  However,  the focus of this course is on setting up the models, rather than solving them, and this text provides a solid grounding in that.  You can think of this course as a course in "word problems," although we will go beyond the simple formulations you have seen in calculus. In addition to the text, we will have more advanced supplementary material, as in Fall, 2002.  We will have both assignments from the text and projects; see the required work for this course.

Depending on students' backgrounds and interests, we can cover more or less sophisticated mathematics and solution methods in addition to the text material.  This additional study will especially occur in conjunction with the projects. The course will also involve a significant amount of experimentation on the computer, with MATLAB, Mathematica, or standard programming languages such as Fortran or C++.

My (the instructor's) mathematical expertise and research interests lie in numerical analysis of nonlinear algebraic systems and in numerical optimization, especially global optimization.  I also have served on the Fortran programming language standardization committee, and I have done a major consulting project involving "C" language programming and Matlab (although I do not consider myself an expert in "C" or "C++"), and I have many years of experience with Matlab and Mathematica in conjunction with course offerings.  I have also worked on mathematical models and their solution in industry, involving chemical kinetics and the numerical solution of systems of ordinary and partial differential equations.  Students may wish to consider my expertise when deciding on how I might help them with their projects.

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