Hilbert Space Methods in Partial Differential Equations PDF Download
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Author: Ralph E. Showalter
Publisher: Courier Corporation
ISBN: 0486135799
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Author: Ralph E. Showalter
Publisher: Courier Corporation
ISBN: 0486135799
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Author: Karl E. Gustafson
Publisher: Courier Corporation
ISBN: 0486140873
Category : Mathematics
Languages : en
Pages : 500
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Book Description
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Author: Ralph E. Showalter
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: R. E. Showalter
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 196
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Book Description
Author: Jaak Peetre
Publisher:
ISBN:
Category :
Languages : en
Pages : 394
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Book Description
Author: Krzysztof Kowalski
Publisher: World Scientific
ISBN: 9814502057
Category : Science
Languages : en
Pages : 148
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Book Description
This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrödinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the “quantal” Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bäcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.
Author: Martin Schechter
Publisher: Courier Corporation
ISBN: 0486492966
Category : Mathematics
Languages : en
Pages : 259
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Book Description
When first published in 1977, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Now it remains a permanent, much-cited contribution to the ever-expanding literature.
Author: R. E. Showalter
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 298
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Book Description
Lecture notes.
Author: Karl E. Gustafson
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Wolfgang Arendt
Publisher: Springer Nature
ISBN: 303113379X
Category : Mathematics
Languages : en
Pages : 463
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Book Description
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
