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Zusatztext ". . . presents various topics which rarely appear in a textbook form . . . proofs are carefully chosen . . . has many illustrations which clarify key concepts from complex variable theory . . . strongly recommended to everybody interested in modern complex analysis." - Marek Jarnicki! in Zentralblatt Math! 2008/2009! Vol. 1131 Informationen zum Autor Washington University! St. Louis! Missouri! USA Klappentext From the algebraic properties of a complete number field to the Cauchy integral formula to conformal mapping! this text explores all facets of complex variables! with particular emphasis on using theory in practice. It presents complex analysis as a natural continuation of calculus! discusses the use of computer algebra systems in complex analysis! and integrates MATLAB exercises and examples throughout. Each chapter features applications from physics and engineering! including those involving differential equations. The text also includes stimulating exercises at the drill! theory! and exploration levels as well as numerous figures to clarify key concepts in complex variable theory. Zusammenfassung From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, Maple™, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences. Inhaltsverzeichnis Preface. Basic Ideas. Holomorphic and Harmonic Functions. The Cauchy Theory. Applications of the Cauchy Theory. Isolated Singularities. The Argument Principle. The Geometric Theory. Applications of Conformal Mapping. Harmonic Functions. Transform Theory. PDEs and Boundary Value Problems. Computer Packages. Appendices. Bibliography. Index....
