Facets analysis

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Facets analysis

Logarithm, Powers, Zeros and isolated singularities, The calculus of residues, The maximum modulus principle, Mobius transformations. Krantz PDF Pages English This text will illustrate and teach all facets of the subject in a lively manner that will speak to the needs of modern students.

It will give them a powerful toolkit for future work in the mathematical sciences, and will also point to new directions for additional learning. University of Oxford Online NA Pages English This lecture note begins by introducing students to the language of topology before using it in the exposition of Facets analysis theory of holomorphic functions of a complex variable.

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The central aim of the lecture note is to present Cauchy's Theorem and its consequences, particularly series expansions of holomorphic functions, the calculus of residues and its applications. Number systemAlgebra of Complex Numbers, Inequalities and complex exponents, Functions of a Complex Variable, Sequences and Series, Complex Integration, Consequences of complex integration, Residue calculus, Conformal Mapping, Mapping of Elementary transformation, Applications of conformal mapping, Further theory of analytic functions.

MacRobert Online Pages English This book is designed for students who, having acquired a good working knowledge of the calculus, desire to become acquainted with the theory of functions of a complex variable, and with the principal applications of that theory.

Numerous examples have been given throughout the book, and there is also a set of Miscellaneous Examples, arranged to correspond with the order of the text. This book covers the following topics: Complex numbers and inequalities, Functions of a complex variable, Mappings, Cauchy-Riemann equations, Trigonometric and hyperbolic functions, Branch points and branch cuts, Contour integration, Sequences and series, The residue theorem, Evaluation of integrals, Introduction to potential theory, Applications, Fourier, Laplace and Z-transforms.

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Facets analysis

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Facets analysis
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