Ebook: Methods of Applied Mathematics with a MATLAB Overview

Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.

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Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.

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Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-4
Fourier Series....Pages 5-78
Elementary Boundary Value Problems....Pages 79-161
Sturm-Liouville Theory and Boundary Value Problems....Pages 163-278
Functions of a Complex Variable....Pages 279-343
Laplace Transforms....Pages 345-409
Fourier Transforms....Pages 411-542
Discrete Variable Transforms....Pages 543-634
Additional Topics....Pages 635-684
Linear Algebra Overview ....Pages 685-691
Software Resources ....Pages 693-710
Transform Tables....Pages 711-715
Back Matter....Pages 716-721

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Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-4
Fourier Series....Pages 5-78
Elementary Boundary Value Problems....Pages 79-161
Sturm-Liouville Theory and Boundary Value Problems....Pages 163-278
Functions of a Complex Variable....Pages 279-343
Laplace Transforms....Pages 345-409
Fourier Transforms....Pages 411-542
Discrete Variable Transforms....Pages 543-634
Additional Topics....Pages 635-684
Linear Algebra Overview ....Pages 685-691
Software Resources ....Pages 693-710
Transform Tables....Pages 711-715
Back Matter....Pages 716-721
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