Department of Mathematics

Syllabus

**Math 03.400 - Applications of Mathematics**

**CATALOG DESCRIPTION:**

Math 03.400 Applications of Mathematics
3 s.h.

Prerequisites: (Math 01.230 Calculus III or Math 01.141 Accelerated Calculus II) and [(Math 01.210 Linear Algebra and Math 01.231 Ordinary Differential Equations) or Math 01.235 Math for Engineering Analysis I] with a grade of C- or better in all prerequisites

This course may include examples of mathematical models applied to various
fields of the biological, physical, or social sciences. The process of
building a mathematical model to describe a real world system will be demonstrated.
Emphasis will be placed on the value of mathematical models for solving
problems and obtaining new results. Computers and graphing calculators
will be used.

**OBJECTIVES:**

This course will introduce the student to the techniques used in the
construction of mathematical models of real world systems. This will
include a discussion on fitting the model to data and on model validation.
Specific mathematical models and their applications to different disciplines
will be included. Emphasis will be placed on the relationship between
discrete and continuous models and between deterministic and stochastic
models.

**CONTENT:**

**PART ONE:**

CREATIVE MODEL CONSTRUCTION AND THE MODELING PROCESS

The discussion will center on the types of mathematical models and their classification in terms of deterministic versus stochastic and discrete versus continuous. The description of the iterative nature of model construction will be followed by examples of model construction.

**PART TWO:**

MODEL FITTING AND VALIDATION

The least square method of fitting a model to data will be presented.
Model validation with newly acquired data is discussed and used to adjust
the model in the iterative approach.

**PART THREE:**

SPECIFIC MATHEMATICAL MODELS AND THEIR APPLICATIONS

Models used in the physical, social, and life sciences will be introduced
and the mathematics used in the analysis of these models will be discussed.
The mathematics may include topics in Differential and Difference Equations,
Linear Algebra, Modern Algebra, Number Theory, Probability, Complex Analysis,
Graph Theory, or Numerical Analysis.

**TEXT:**

Frank R. Giordano and Maurice D. Weir, A FIRST COURSE IN MATHEMATICAL
MODELING L.F., 1997, Brooks/Cole Publishing Co.

Meerschaert, M., Mathematical Modeling, 2nd Ed., Academic Press, 1999.

Mesterton-Gibbons, M., A concrete Approach to Mathematical Modeling, John Wiley & Sons, Inc., 1995.

(Note: The instructor may chose to emphasize a series of individual
models from a certain branch of mathematics and may find less general text,
more useful.)