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This comprehensive exposition on analytic methods for solving problems in science and engineering is grounded in distribution theory and features many modern topics relevant to practitioners and researchers. It aims to provide both specialists and non-specialists with practical mathematical tools for research and analysis. Volume 1 focuses on asymptotic methods, including stationary phase and steepest descent techniques for Fourier and other integral transforms, alongside topics such as fractional calculus, the uncertainty principle, wavelets, and multiresolution analysis. Volume 2 analyzes the three basic types of linear PDEs—elliptic, parabolic, and hyperbolic—and includes discussions on first-order nonlinear PDEs and conservation laws, along with nonlinear waves, Burger's equations, KdV equations, and gas dynamics. Volume 3 explores distributional tools in generalized stochastic processes and fields, covering probability distributions, Brownian motion, stochastic differential equations, and multiscale anomalous fractional dynamics. With clear explanations, an accessible writing style, and numerous illustrations/examples, this work serves as a valuable self-study reference for anyone looking to enhance their understanding and proficiency in these problem-solving methods. It is tailored for a broad scientific and engineering audience while maintaining mathematical precision.
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Distributions in the Physical and Engineering Sciences, Alexander I. Saichev
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- Année de publication
- 2018
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