Contents: *Introduction *Linear Partial Differential Equations *The Wave Equation *Green's Function & Sturm-Liouville Problems *Fourier Series and Fourier Integral *The Heat Equation *Laplace's Equation *References *Solutions of the Exercises *Index
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Nonlinear Ocean Waves & the Inverse Scattering Transform
For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves.
The New Physical Optics Notebook: Tutorials in Fourier Optics
Approaches the topic of physical optics with examples drawn from the physical processes described. Includes chapters on Fourier transforms, image formation, optical coherence, diffraction, interference, holography, interferometry, analog optical computing, synthetic aperture imaging, and others. Contains more than 600 photographs and line drawings and more than 650 references.
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study.