Fourier analysis is a mathematical technique for decomposing a signal into identifiable components. It is used in the study of all types of waves. This book explains the basic mathematical theory and some of the principal applications of Fourier analysis in areas ranging from sound and vibration to optics and CAT scanning. The author provides in-depth coverage of the techniques and includes exercises that demonstrate straightforward applications of formulas as well as more complex problems.
PART I: Introduction to Fourier Series PART II: Convergence of Fourier Series PART III: Applications of Fourier Series PART IV: Some Harmonic Function Theory PART V: Multiple Fourier Series PART VI: Basic Theory of the Fourier Transform PART VII: Applications of Fourier Transforms 1. Partial Differential Equations 2. Fourier Optics PART VIII: Legendre Polynomials and Spherical Harmonics PART IX: Some Other Transforms 1. The Laplace Transform 2. The Radon Transform PART X: A Brief Introduction to Bessel Functions A. Divergence of Fourier Series B. Brief Tables of Fourier Series and Integrals
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