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This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value problems. Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.  Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.

Green's functions --- Products, Infinite --- Conformal mapping --- Eigenfunction expansions --- Engineering & Applied Sciences --- Physics --- Physical Sciences & Mathematics --- Applied Mathematics --- Atomic Physics --- Green's functions. --- Products, Infinite. --- Infinite products --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Analysis. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Applications of Mathematics. --- Algebra --- Processes, Infinite --- Differential equations --- Potential theory (Mathematics) --- Global analysis (Mathematics). --- Differential Equations. --- Differential equations, partial. --- Math --- Science --- Partial differential equations --- 517.91 Differential equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Conformal mapping. --- Eigenfunction expansions. --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics --- classical Euler representations --- Hilbert's theorem --- method of images --- method of variation

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• Reference Manager
• EndNote
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Partial differential equations --- Differential equations --- Mathematical analysis --- Mathematics --- differentiaalvergelijkingen --- analyse (wiskunde) --- toegepaste wiskunde

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value problems. Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.  Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.

Partial differential equations --- Differential equations --- Mathematical analysis --- Mathematics --- differentiaalvergelijkingen --- analyse (wiskunde) --- toegepaste wiskunde