Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics
Author: Stefan Bergman
Publisher: Courier Corporation
Total Pages: 450
Release: 2005-09-01
Genre: Mathematics
ISBN: 0486445534

This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics
Author: Stefan Bergman
Publisher: Courier Corporation
Total Pages: 450
Release: 2013-01-23
Genre: Mathematics
ISBN: 0486154653

Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.

The Kernel Function and Conformal Mapping

The Kernel Function and Conformal Mapping
Author: Stefan Bergman
Publisher: American Mathematical Soc.
Total Pages: 269
Release: 1950-03
Genre: Mathematics
ISBN: 0821815059

The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of ""The Kernel Function"". The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
Author: S. L. Sobolev
Publisher: Courier Corporation
Total Pages: 452
Release: 1964-01-01
Genre: Science
ISBN: 9780486659640

This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Partial Differential Equations

Partial Differential Equations
Author: Walter A. Strauss
Publisher: John Wiley & Sons
Total Pages: 467
Release: 2007-12-21
Genre: Mathematics
ISBN: 0470054565

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Gaussian Processes for Machine Learning

Gaussian Processes for Machine Learning
Author: Carl Edward Rasmussen
Publisher: MIT Press
Total Pages: 266
Release: 2005-11-23
Genre: Computers
ISBN: 026218253X

A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Transformations, Transmutations, and Kernel Functions

Transformations, Transmutations, and Kernel Functions
Author: H Begehr
Publisher: CRC Press
Total Pages: 286
Release: 1993-09-23
Genre: Mathematics
ISBN: 9780582091092

Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.

Transformations, Transmutations, and Kernel Functions, Volume II

Transformations, Transmutations, and Kernel Functions, Volume II
Author: H Begehr
Publisher: CRC Press
Total Pages: 286
Release: 2023-06-16
Genre: Mathematics
ISBN: 1000951510

Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations
Author: Haim Brezis
Publisher: Springer Science & Business Media
Total Pages: 600
Release: 2010-11-02
Genre: Mathematics
ISBN: 0387709142

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.