MA 460

Undergraduate Courses

MA 460/561, Introduction to Fourier Analysis

Catalog Description

Brief development of trigonometric and exponential Fourier series, derivation of the classical Fourier transform from Fourier series, classical properties of Fourier transforms, transforms of functions, convolution, elementary development of the delta function, transforms of periodic functions, use of transforms to solve systems, introduction to the discrete transform and/or multidimensional transforms, as time permits.

Prerequisites

MA 244, Introduction to Linear Algebra and MA 238, Applied Differential Equations

Course Materials

The text is Principles of Fourier Analysis by Howell, published by CRC Press. The computer algebra package Maple is recommended for this course.

Credit

3 Semester Hours

Grading System

This course is graded A, B, C, D, F. The grade typically depends on a combination of class tests, homework assignments, quizzes, and a comprehensive final exam. Course completion and/or grade requirements for the MA 561 course will differ from those for the MA 460 course

Course Content

This is an introduction to the mathematics of Fourier analysis. The goal is that you will come to understand the mathematics well enough that you will be able to intelligently apply the basic tools of Fourier analysis in the applications which arise in your own particular fields of study. Here is a thumbnail syllabus for the course:

  1. Fourier series for periodic functions and functions defined on finite intervals. Includes derivation of the series and basic notions of convergence.
  2. Classical Fourier transforms. Includes derivation, definitions of transformability, basic properties, transforms of basic functions, elementary identities, convolution, and, maybe, the Fundamental Identity.
  3. Elementary generalized transforms. The delta function and transforms of periodic functions.
  4. Introduction to linear systems, the impulse response function, and the transfer function. A rather general discussion of applications.