An Introduction to Partial Differential Equations

Author: Yehuda Pinchover,Jacob Rubinstein

Publisher: Cambridge University Press

ISBN: 9780521848862

Category: Mathematics

Page: 371

View: 8117

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A complete introduction to partial differential equations. A textbook aimed at students of mathematics, physics and engineering.

Numerical Solution of Partial Differential Equations

Finite Difference Methods

Author: Gordon D. Smith

Publisher: Oxford University Press

ISBN: 9780198596509

Category: Mathematics

Page: 337

View: 5541

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Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Numerical Data Fitting in Dynamical Systems

A Practical Introduction with Applications and Software

Author: Klaus Schittkowski

Publisher: Springer Science & Business Media

ISBN: 1441957626

Category: Computers

Page: 396

View: 1968

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Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Theory and Computation of Hydrodynamic Stability

Author: W. O. Criminale,T. L. Jackson,Ronald Douglas Joslin

Publisher: Cambridge University Press

ISBN: 9780521632003

Category: Mathematics

Page: 441

View: 8809

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Graduate text/reference with exercises, computer code on basic topic in fluid dynamics.

Applying Maths in the Chemical and Biomolecular Sciences

An Example-based Approach

Author: Godfrey Beddard

Publisher: Oxford University Press

ISBN: 0199230919

Category: Mathematics

Page: 786

View: 8839

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Applying Maths in the Chemical and Biomolecular Sciences uses an extensive array of examples to demonstrate how mathematics is applied to probe and understand chemical and biological systems. It also embeds the use of software, showing how the application of maths and use of software now go hand-in-hand.

Mathematical Handbook for Scientists and Engineers

Definitions, Theorems, and Formulas for Reference and Review

Author: Granino A. Korn,Theresa M. Korn

Publisher: Courier Corporation

ISBN: 0486320235

Category: Technology & Engineering

Page: 1152

View: 3392

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Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.

Partielle Differentialgleichungen

Eine Einführung

Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 368

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Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Mathematical Models in Applied Mechanics

Author: Alan B. Tayler

Publisher: Oxford University Press

ISBN: 9780198515593

Category: Mathematics

Page: 280

View: 545

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Mathematical Models in Applied Mechanics is perfectly designed for final year undergraduate and graduate students. This textbook utilizes the power of mathematics in solving practical, scientific and technical problems through mathematical modeling techniques. Taken from real-life situations, the text includes twenty-one ordered problems, which gives students the ability to develop the skills necessary to create new situational models.

Wissenschaftliches Rechnen mit MATLAB

Author: Alfio Quarteroni,Fausto Saleri

Publisher: Springer-Verlag

ISBN: 3540293078

Category: Mathematics

Page: 269

View: 2774

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Aus den Rezensionen der englischen Auflage: Dieses Lehrbuch ist eine Einführung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewöhnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Übungsaufgaben sowie deren Lösung präsentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code. MATLAB select 2003, Issue 2, p. 50. [Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nützliche Sammlung von MATLAB Funktionen für die Lösung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. [...] Die Präsentation des Stoffs ist durchgängig gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzellenter Neuzugang für Universitätsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Ergänzung zu anderen MATLAB-basierten Büchern von großem Nutzen sein. Alles in allem: Sehr empfehlenswert. Für Studenten im Erstsemester wie für Experten gleichermassen. S.T. Karris, University of California, Berkeley, Choice 2003.