Partial Differential Equations of Parabolic Type

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Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 0486318265

Category: Mathematics

Page: 368

View: 9006

With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Numerical Methods for Partial Differential Equations

An Introduction

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Author: Vitoriano Ruas

Publisher: John Wiley & Sons

ISBN: 1119111374

Category: Technology & Engineering

Page: 376

View: 3730

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Equations of Mathematical Physics

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Author: A. N. Tikhonov,A. A. Samarskii

Publisher: Courier Corporation

ISBN: 0486173364

Category: Science

Page: 800

View: 5045

DIVThorough, rigorous advanced-undergraduate to graduate-level treatment of problems leading to partial differential equations. Hyperbolic, parabolic, elliptic equations; wave propagation in space, heat conduction in space, more. Problems. Appendixes. /div

Partielle Differentialgleichungen und numerische Methoden

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Author: Stig Larsson,Vidar Thomee

Publisher: Springer-Verlag

ISBN: 3540274227

Category: Mathematics

Page: 272

View: 9484

Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.

Introduction to Partial Differential Equations

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Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 9780486414508

Category: Mathematics

Page: 195

View: 7838

Rigorous presentation, designed for use in a 1-semester course, explores basics; Fourier series; 2nd-order partial differential equations; wave, potential, and heat equations; approximate solution of partial differential equations, more. Exercises. 1961 edition.

Partial Differential Equations for Scientists and Engineers

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Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 0486134733

Category: Mathematics

Page: 414

View: 4432

Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

A Collection of Problems in Mathematical Physics

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Author: Boris Mikha?lovich Budak,Aleksandr Andreevich Samarski?,Andre? Nikolaevich Tikhonov

Publisher: Courier Corporation

ISBN: 0486658066

Category: Science

Page: 768

View: 2662

Outstanding, wide-ranging material on classification and reduction to canonical form of second-order differential equations; hyperbolic, parabolic, elliptic equations, more. Bibliography.

Introduction to Partial Differential Equations and Hilbert Space Methods

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Author: Karl E. Gustafson

Publisher: Courier Corporation

ISBN: 9780486612713

Category: Mathematics

Page: 448

View: 1430

This volume offers an excellent undergraduate-level introduction to the main topics, methods, and applications of partial differential equations. Chapter 1 presents a full introduction to partial differential equations and Fourier series as related to applied mathematics. Chapter 2 begins with a more comprehensive look at the principal method for solving partial differential equations — the separation of variables — and then more fully develops that approach in the contexts of Hilbert space and numerical methods. Chapter 3 includes an expanded treatment of first-order systems, a short introduction to computational methods, and aspects of topical research on the partial differential equations of fluid dynamics. With over 600 problems and exercises, along with explanations, examples, and a comprehensive section of answers, hints, and solutions, this superb, easy-to-use text is ideal for a one-semester or full-year course. It will also provide the mathematically inclined layperson with a stimulating review of the subject's essentials.

Selected Papers on Noise and Stochastic Processes

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Author: Nelson Wax

Publisher: Courier Corporation

ISBN: 0486798267

Category: Technology & Engineering

Page: 352

View: 784

These six classic papers on stochastic process were selected to meet the needs of professionals and advanced undergraduates and graduate students in physics, applied mathematics, and engineering. Contents include: "Stochastic Problems in Physics and Astronomy" by S. Chandrasekhar from Reviews of Modern Physics, Vol. 15, No. 1 "On the Theory of Brownian Motion" by G. E. Uhlenbeck and L. S. Ornstein from Physical Review, Vol. 36, No. 3 "On the Theory of the Brownian Motion II" by Ming Chen Wang and G. E. Uhlenbeck from Reviews of Modern Physics, Vol. 17, Nos. 2 and 3 "Mathematical Analysis of Random Noise" by S. O. Rice from Bell System Technical Journal, Vols. 23 and 24 "Random Walk and the Theory of Brownian Motion" by Mark Kac from American Mathematical Monthly, Vol. 54, No. 7 "The Brownian Movement and Stochastic Equations" by J. L. Doob from Annals of Mathematics, Vol. 43, No. 2

Physics of Fully Ionized Gases

Second Revised Edition

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Author: Lyman Spitzer

Publisher: Courier Corporation

ISBN: 0486151581

Category: Science

Page: 192

View: 6441

An introductory course in theoretical physics is the sole prerequisite for this general but simple introduction to the fields of plasma and fusion research. 1962 edition.

The Geometry of René Descartes

with a Facsimile of the First Edition

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Author: René Descartes

Publisher: Courier Corporation

ISBN: 0486158179

Category: Mathematics

Page: 272

View: 4115

The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill.

An Introduction to the Theory of Elasticity

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Author: R. J. Atkin,N. Fox

Publisher: Courier Corporation

ISBN: 0486150992

Category: Science

Page: 272

View: 1035

Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.

Atomic Physics: 8th Edition

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Author: Max Born

Publisher: Courier Corporation

ISBN: 0486318583

Category: Science

Page: 544

View: 5340

Nobel Laureate's lucid treatment of kinetic theory of gases, elementary particles, nuclear atom, wave-corpuscles, atomic structure and spectral lines, much more. Over 40 appendices, bibliography.

Differentialgleichungen und ihre Anwendungen

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Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642973418

Category: Mathematics

Page: 596

View: 2647

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#

Mathematical Logic

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Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 4406

Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Vorlesungen über partielle Differentialgleichungen

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Author: Vladimir I. Arnold

Publisher: Springer-Verlag

ISBN: 3540350314

Category: Mathematics

Page: 174

View: 7442

Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss. Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende. Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.

Modern Mathematics for the Engineer: Second Series

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Author: Edwin F. Beckenbach

Publisher: Courier Corporation

ISBN: 0486316122

Category: Technology & Engineering

Page: 480

View: 4275

The second in this two-volume series also contains original papers commissioned from prominent 20th-century mathematicians. A three-part treatment covers mathematical methods, statistical and scheduling studies, and physical phenomena. 1961 edition.

A Bridge to Advanced Mathematics

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Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

View: 5403

This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

An Introduction to Differential Geometry

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Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

View: 9186

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.