Methods of Applied Mathematics with a Software Overview (Applied and Numerical Harmonic Analysis)

This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and signal processing.Replete with helpful 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. Key features of the software overview: * Now relies solely on the free software tools Octave, Maxima, and Python. * Appendix introduces all of these tools at a level suitable to those with some programming experience * Provides references to sources of further learning. * Code snippets incorporated throughout the text. * All graphics and illustrations generated using these tools. Praise for the first edition: “The author mixed in a remarkable way theoretical results and applications illustrating the results. Flexibility of presentation (increasing and decreasing level of rigor, accessibility) is a key feature...The book contains extensive examples, presented in an intuitive way with high quality figures (some of them quite spectacular)...” **– Mathematica** “...Davis's book has many novel features being quite different from most other textbooks on applied mathematics.... Mainly it has a clear and consistent exposition with a strong focus on mathematical fundamentals and useful techniques. It has numerous extensive examples, illustrations, comments, and a very modern graphical presentation of results.“...The book has style. Every theorem and mathematical result has a wonderful appealing comment.” **– Studies in Informatics and Control** This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and signal processing. Replete with helpful 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. Key features of the software overview: Now relies solely on the free software tools Octave, Maxima, and Python. Appendix introduces all of these tools at a level suitable to those with some programming experience Provides references to sources of further learning. Code snippets incorporated throughout the text. All graphics and illustrations generated using these tools. Praise for the first edition: zThe author mixed in a remarkable way theoretical results and applications illustrating the results. Flexibility of presentation (increasing and decreasing level of rigor, accessibility) is a key feature ... The book contains extensive examples, presented in an intuitive way with high quality figures (some of them quite spectacular) ... y - Mathematica z ... Davis's book has many novel features being quite different from most other textbooks on applied mathematics ... Mainly it has a clear and consistent exposition with a strong focus on mathematical fundamentals and useful techniques. It has numerous extensive examples, illustrations, comments, and a very modern graphical presentation of results. z&#x٢٠٢٦؛The book has style. Every theorem and mathematical result has a wonderful appealing comment.y - Studies in Informatics and Control Methods of Applied Mathematics with a MATLAB Overview is devoted to the applications of Fourier analysis; topics encompass the 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 covered, along with the necessary background in complex variables and Sturm-Liouville theory. The final chapter provides an examination of wavelets, short-time Fourier analysis, and geometrically-based transforms. The use of the computer program MATLAB has been integrated throughout the text, with particular emphasis on the program's numerical and graphing capabilities. Key topics and features: • Clear, consistent exposition with a strong focus on mathematical fundamentals and useful techniques • Extensive examples, illustrations, and modern applications • A variety of problems of wide-ranging difficulty, many with solutions • Numerous MATLAB exercises and routines, with an introduction to MATLAB provided in an appendix • Comprehensive references and index Requiring only familiarity with calculus and linear algebra and some introductory acquaintance with differential equations and vector calculus, this work can be used flexibly, either for a one-semester survey or an in-depth, year-long course. With its broad scope and careful pedagogy, this treatment will serve students in pure and applied mathematics, physical sciences, and engineering. Solutions manual available upon adoption of text. 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.