An Introduction to Differential Equations: With Difference Equations, Fourier Series, and Partial Differential Equations
The same, refined Ordinary Differential Equations with Modern Applications by Finizio and Lades is the backbone of this text. In addition to this are included applications, techniques and theory of partial difference equations, difference equations and Fourier analysis.
The general aim of this book is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. The more particular goal is to cover John Tate's visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries--technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist.
This text is appropriate for students from across the engineering and science disciplines. Topics include: Periodicity and Fourier series; The Fourier transform and its basic properties; Convolution and its applications; Distributions and their Fourier transforms; Sampling and interpolation; Linear systems; The discrete Fourier transform; Higher dimensional Fourier transforms and applications.
The author has provided a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy, and electrical engineering.
Detailed derivation of the Discrete Fourier Transform (DFT) and its associated mathematics, including elementary audio signal processing applications and matlab programming examples.
