## Partial Differential Equations

*An Introduction to Theory and Applications*

**Author**: Michael Shearer,Rachel Levy

**Publisher:**Princeton University Press

**ISBN:**140086660X

**Category:**Mathematics

**Page:**288

**View:**8150

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This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

## Partielle Differentialgleichungen

*Eine Einführung*

**Author**: Walter A. Strauss

**Publisher:**Springer-Verlag

**ISBN:**366312486X

**Category:**Mathematics

**Page:**458

**View:**9922

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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.

## An Introduction to Partial Differential Equations with MATLAB, Second Edition

**Author**: Matthew P. Coleman

**Publisher:**CRC Press

**ISBN:**1439898472

**Category:**Mathematics

**Page:**683

**View:**2759

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An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website.

## Bifurcation Theory

*An Introduction with Applications to Partial Differential Equations*

**Author**: Hansjörg Kielhöfer

**Publisher:**Springer Science & Business Media

**ISBN:**1461405025

**Category:**Mathematics

**Page:**400

**View:**5512

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In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.

## Differential Equations and Their Applications

*An Introduction to Applied Mathematics*

**Author**: Martin Braun

**Publisher:**Springer Science & Business Media

**ISBN:**9780387978949

**Category:**Mathematics

**Page:**578

**View:**3423

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Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book distinguishes itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show readers how to apply differential equations towards quantitative problems.

## An Introduction to Partial Differential Equations

**Author**: Yehuda Pinchover,Jacob Rubinstein

**Publisher:**Cambridge University Press

**ISBN:**9780521848862

**Category:**Mathematics

**Page:**371

**View:**5950

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

## An Introduction to Nonlinear Partial Differential Equations

**Author**: J. David Logan

**Publisher:**John Wiley & Sons

**ISBN:**0470225955

**Category:**Mathematics

**Page:**397

**View:**2260

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An Introduction to Nonlinear Partial Differential Equations is a textbook on nonlinear partial differential equations. It is technique oriented with an emphasis on applications and is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises. All software references have been updated with the latest version of [email protected], the corresponding graphics have also been updated using [email protected] An increased focus on hydrogeology...

## Introduction to Partial Differential Equations with Applications

**Author**: E. C. Zachmanoglou,Dale W. Thoe

**Publisher:**Courier Corporation

**ISBN:**048613217X

**Category:**Mathematics

**Page:**432

**View:**1493

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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

## Theory and Applications of Partial Differential Equations

**Author**: Piero Bassanini,Alan R. Elcrat

**Publisher:**Springer Science & Business Media

**ISBN:**1489918752

**Category:**Mathematics

**Page:**444

**View:**9841

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This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

## An Introduction to Nonlinear Analysis: Applications

**Author**: Zdzislaw Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou

**Publisher:**Springer Science & Business Media

**ISBN:**9780306474569

**Category:**Mathematics

**Page:**823

**View:**7224

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This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.

## An Introduction to Stochastic Differential Equations

**Author**: Lawrence C. Evans

**Publisher:**American Mathematical Soc.

**ISBN:**1470410540

**Category:**Mathematics

**Page:**151

**View:**8575

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These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

## Bifurcation Theory

*An Introduction with Applications to PDEs*

**Author**: Hansj?rg Kielh?fer

**Publisher:**Springer Verlag

**ISBN:**0387404015

**Category:**Mathematics

**Page:**346

**View:**1783

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This book presents the main theorems in bifurcation theory in an abstract setting and shows how they can be applied to partial differential equations. It will serve as an important reference for students and researchers in mathematics, physics, and engineering.

## An Introduction to the Mathematical Theory of Waves

**Author**: Roger Knobel

**Publisher:**American Mathematical Soc.

**ISBN:**0821820397

**Category:**Mathematics

**Page:**196

**View:**2880

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Linear and nonlinear waves are a central part of the theory of PDEs. This book begins with a description of one-dimensional waves and their visualization through computer-aided techniques. Next, traveling waves are covered, such as solitary waves for the Klein-Gordon and KdV equations. Finally, the author gives a lucid discussion of waves arising from conservation laws, including shock and rarefaction waves. As an application, interesting models of traffic flow are used to illustrate conservation laws and wave phenomena. This book is based on a course given by the author at the IAS/Park City Mathematics Institute. It is suitable for independent study by undergraduate students in mathematics, engineering, and science programs.

## An introduction to nonlinear partial differential equations

**Author**: John David Logan

**Publisher:**Wiley-Interscience

**ISBN:**N.A

**Category:**Mathematics

**Page:**400

**View:**6344

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Uses an analytical and techniques-oriented approach to present a concise introduction to the subject focusing on time-evolution problems. Emphasizes hyperbolic and parabolic problems and includes a range of applications--chemistry, porous media, biological problems, traffic flow, reactors, heat transfer and detonation. Packed with exercises, examples and illustrations.

## Engineering Differential Equations

*Theory and Applications*

**Author**: Bill Goodwine

**Publisher:**Springer Science & Business Media

**ISBN:**1441979190

**Category:**Mathematics

**Page:**745

**View:**4070

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This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

## Fractional Differential Equations

*An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications*

**Author**: Igor Podlubny

**Publisher:**Elsevier

**ISBN:**9780080531984

**Category:**Mathematics

**Page:**340

**View:**6688

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This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

## Introduction to Partial Differential Equations

**Author**: G. B. Folland

**Publisher:**Princeton University Press

**ISBN:**9780691043616

**Category:**Mathematics

**Page:**324

**View:**4091

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The aim of this text is to aquaint the student with the fundamental classical results of partial differential equations and to guide them into some of the modern theory, enabling them to read more advanced works on the subject

## Partial Differential Equations

*An Introduction*

**Author**: Walter A. Strauss

**Publisher:**Wiley

**ISBN:**0470054565

**Category:**Mathematics

**Page:**464

**View:**7931

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Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more. Rigorous pedagogical tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

## Difference Equations

*An Introduction with Applications*

**Author**: Walter G. Kelley,Allan C. Peterson

**Publisher:**Academic Press

**ISBN:**9780124033306

**Category:**Mathematics

**Page:**403

**View:**4256

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Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics. * Phase plane analysis for systems of two linear equations * Use of equations of variation to approximate solutions * Fundamental matrices and Floquet theory for periodic systems * LaSalle invariance theorem * Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory * Appendix on the use of Mathematica for analyzing difference equaitons * Exponential generating functions * Many new examples and exercises

## Partial Differential Equations

*An Introduction*

**Author**: David Colton

**Publisher:**Courier Corporation

**ISBN:**0486138437

**Category:**Mathematics

**Page:**320

**View:**3281

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This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Features coverage of integral equations and basic scattering theory. Includes exercises, many with answers. 1988 edition.