Introduction to Partial Differential Equations with Applications

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

Publisher: Courier Corporation

ISBN: 048613217X

Category: Mathematics

Page: 432

View: 5245

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.

Introduction to Partial Differential Equations with Applications

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

Publisher: Courier Corporation

ISBN: 0486652513

Category: Mathematics

Page: 405

View: 8699

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.

Introduction to Partial Differential Equations with Applications

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

Publisher: Courier Corporation

ISBN: 9780486652511

Category: Mathematics

Page: 405

View: 2769

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.

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: 5691

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

An Introduction to Differential Equations and Their Applications

Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 0486135136

Category: Mathematics

Page: 640

View: 597

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Introduction to Partial Differential Equations

Author: Peter J. Olver

Publisher: Springer Science & Business Media

ISBN: 3319020994

Category: Mathematics

Page: 636

View: 2810

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

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: 2792

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.

Applications of Lie's Theory of Ordinary and Partial Differential Equations

Author: L Dresner

Publisher: CRC Press

ISBN: 9781420050783

Category: Science

Page: 225

View: 5926

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

An Introduction to Partial Differential Equations

Author: Yehuda Pinchover,Jacob Rubinstein

Publisher: Cambridge University Press

ISBN: 9780521848862

Category: Mathematics

Page: 371

View: 626

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

Introduction to Partial Differential Equations

Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 9780486414508

Category: Mathematics

Page: 195

View: 1384

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.

An Introduction to Partial Differential Equations with MATLAB, Second Edition

Author: Matthew P. Coleman

Publisher: CRC Press

ISBN: 1439898472

Category: Mathematics

Page: 683

View: 2824

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.

Partial Differential Equations

An Introduction

Author: David Colton

Publisher: Courier Corporation

ISBN: 0486138437

Category: Mathematics

Page: 320

View: 930

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.

Stochastic Partial Differential Equations

A Modeling, White Noise Functional Approach

Author: Helge Holden,Bernt Øksendal,Jan Ubøe,Tusheng Zhang

Publisher: Springer Science & Business Media

ISBN: 0387894888

Category: Mathematics

Page: 305

View: 2920

The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.

Introduction to Partial Differential Equations

Author: G. B. Folland

Publisher: Princeton University Press

ISBN: 9780691043616

Category: Mathematics

Page: 324

View: 1679

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

Introduction to Nonlinear Differential and Integral Equations

Author: Harold Thayer Davis

Publisher: Courier Corporation

ISBN: 9780486609713

Category: Mathematics

Page: 566

View: 8256

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

An Introduction to Nonlinear Partial Differential Equations

Author: J. David Logan

Publisher: John Wiley & Sons

ISBN: 0470225955

Category: Mathematics

Page: 397

View: 9973

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...

Numerical Partial Differential Equations in Finance Explained

An Introduction to Computational Finance

Author: Karel in 't Hout

Publisher: Springer

ISBN: 1137435690

Category: Business & Economics

Page: 128

View: 1507

This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient. The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.

Introduction to Partial Differential Equations

A Computational Approach

Author: Aslak Tveito,Ragnar Winther

Publisher: Springer Science & Business Media

ISBN: 0387227733

Category: Mathematics

Page: 392

View: 8403

Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.