ABSTRACT

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they

chapter 1|4 pages

The Starting Point

chapter 5|8 pages

Symmetry and Periodicity

chapter 6|16 pages

Elementary Complex Analysis

chapter 7|22 pages

Functions of Several Variables

chapter 9|20 pages

The Trigonometric Fourier Series

chapter 11|14 pages

Inner Products, Norms, and Orthogonality

chapter 12|10 pages

The Complex Exponential Fourier Series

chapter 13|24 pages

Convergence and Fourier’s Conjecture

chapter 15|18 pages

Derivatives and Integrals of Fourier Series

chapter 16|32 pages

Applications

chapter 18|22 pages

Integrals on Infinite Intervals

chapter 19|18 pages

The Fourier Integral Transforms

chapter 22|20 pages

Differentiation and Fourier Transforms

chapter 24|24 pages

Convolution and Transforms of Products

chapter 26|20 pages

Identity Sequences

chapter 28|16 pages

Fourier Analysis in the Analysis of Systems

chapter 31|22 pages

Gaussian Test Functions

chapter 32|30 pages

Generalized Functions

chapter 36|24 pages

Periodic Functions and Regular Arrays

chapter 38|12 pages

Periodic, Regular Arrays

chapter 39|40 pages

Sampling and the Discrete Fourier Transform