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Artikelmerkmale
- Artikelzustand
- Release Year
- 2013
- Book Title
- An Introduction to Partial Differential Equations with MATLAB ...
- ISBN
- 9781439898468
Über dieses Produkt
Product Identifiers
Publisher
CRC Press LLC
ISBN-10
1439898464
ISBN-13
9781439898468
eBay Product ID (ePID)
109478997
Product Key Features
Number of Pages
683 Pages
Publication Name
Introduction to Partial Differential Equations with Matlab
Language
English
Subject
Differential Equations / General, Mathematical & Statistical Software, General, Differential Equations / Partial, Applied
Publication Year
2013
Type
Textbook
Subject Area
Mathematics, Computers
Series
Chapman and Hall/Crc Applied Mathematics and Nonlinear Science Ser.
Format
Hardcover
Dimensions
Item Height
1.6 in
Item Weight
37.6 Oz
Item Length
9.4 in
Item Width
6.5 in
Additional Product Features
Edition Number
2
Intended Audience
College Audience
LCCN
2012-050932
TitleLeading
An
Reviews
Praise for the First Edition: "The strongest aspect of this text is the very large number of worked boundary value problem examples." e" SIAM "This is a useful introductory text on PDEs for advanced undergraduate / beginning graduate students of applied mathematics, physics, or engineering sciences. e a nice introductory text which certainly is of great use in preparing and delivering courses." e" Zentralblatt MATH "Readers new to the subject will find Colemane(tm)s appendix cataloguing important partial differential equations in their natural surroundings quite useful. e Colemane(tm)s more explicit, extended style would probably allow its use as an advanced graduate or reference text for UK engineers or physicists." e" Times Higher Education "The book presents very useful material and can be used as a basic text for self-study of PDEs." e" EMS Newsletter "Each chapter is introduced by a e~preludee(tm) that describes its content and gives historical background. Each section concludes with a set of exercises, many of which are marked MATLAB." e" CMS Notes, Praise for the First Edition: "The strongest aspect of this text is the very large number of worked boundary value problem examples." - SIAM "This is a useful introductory text on PDEs for advanced undergraduate / beginning graduate students of applied mathematics, physics, or engineering sciences. … a nice introductory text which certainly is of great use in preparing and delivering courses." - Zentralblatt MATH "Readers new to the subject will find Coleman's appendix cataloguing important partial differential equations in their natural surroundings quite useful. … Coleman's more explicit, extended style would probably allow its use as an advanced graduate or reference text for UK engineers or physicists." - Times Higher Education "The book presents very useful material and can be used as a basic text for self-study of PDEs." - EMS Newsletter "Each chapter is introduced by a 'prelude' that describes its content and gives historical background. Each section concludes with a set of exercises, many of which are marked MATLAB." - CMS Notes, "This is an excellent textbook e first, the book can be used by a person who has no interest in MATLAB at all, and, second, this book deserves to be considered bye"in fact, should be at the top of the list ofe"any professor looking for an undergraduate text in PDEs. e there are several reasons why I view this book as being in the upper echelon of undergraduate PDE textbooks. One is the extremely high quality of exposition. Coleman writes clearly and cleanly, with a conversational tone and a high regard for motivation. He clearly has a great deal of experience teaching this subject and has learned what points are likely to cause confusion and therefore need expanded discussion. The author also employs the nice pedagogical feature of page-long e~preludese(tm) to each chapter, which not only summarize what the chapter will cover and how it fits into the general theme of things, but also typically provide some brief historical commentary as well. In general, the overall effect of this book is like listening to a discussion by a good professor in office hours. e very highly recommended. I done(tm)t know when or if I will ever teach an undergraduate PDE course, but if I ever do, this book will certainly be on my short list of possible texts." e"Mark Hunacek, MAA Reviews, September 2013 Praise for the First Edition: "The strongest aspect of this text is the very large number of worked boundary value problem examples." e" SIAM "This is a useful introductory text on PDEs for advanced undergraduate / beginning graduate students of applied mathematics, physics, or engineering sciences. e a nice introductory text which certainly is of great use in preparing and delivering courses." e" Zentralblatt MATH "Readers new to the subject will find Colemane(tm)s appendix cataloguing important partial differential equations in their natural surroundings quite useful. e Colemane(tm)s more explicit, extended style would probably allow its use as an advanced graduate or reference text for UK engineers or physicists." e" Times Higher Education "The book presents very useful material and can be used as a basic text for self-study of PDEs." e" EMS Newsletter "Each chapter is introduced by a e~preludee(tm) that describes its content and gives historical background. Each section concludes with a set of exercises, many of which are marked MATLAB." e" CMS Notes, Praise for the First Edition: "The strongest aspect of this text is the very large number of worked boundary value problem examples." -- SIAM "This is a useful introductory text on PDEs for advanced undergraduate / beginning graduate students of applied mathematics, physics, or engineering sciences. ... a nice introductory text which certainly is of great use in preparing and delivering courses." -- Zentralblatt MATH "Readers new to the subject will find Coleman's appendix cataloguing important partial differential equations in their natural surroundings quite useful. ... Coleman's more explicit, extended style would probably allow its use as an advanced graduate or reference text for UK engineers or physicists." -- Times Higher Education "The book presents very useful material and can be used as a basic text for self-study of PDEs." -- EMS Newsletter "Each chapter is introduced by a 'prelude' that describes its content and gives historical background. Each section concludes with a set of exercises, many of which are marked MATLAB." -- CMS Notes, "This is an excellent textbook ... first, the book can be used by a person who has no interest in MATLAB at all, and, second, this book deserves to be considered by--in fact, should be at the top of the list of--any professor looking for an undergraduate text in PDEs. ... there are several reasons why I view this book as being in the upper echelon of undergraduate PDE textbooks. One is the extremely high quality of exposition. Coleman writes clearly and cleanly, with a conversational tone and a high regard for motivation. He clearly has a great deal of experience teaching this subject and has learned what points are likely to cause confusion and therefore need expanded discussion. The author also employs the nice pedagogical feature of page-long 'preludes' to each chapter, which not only summarize what the chapter will cover and how it fits into the general theme of things, but also typically provide some brief historical commentary as well. In general, the overall effect of this book is like listening to a discussion by a good professor in office hours. ... very highly recommended. I don't know when or if I will ever teach an undergraduate PDE course, but if I ever do, this book will certainly be on my short list of possible texts." --Mark Hunacek, MAA Reviews, September 2013 "... a pick for any college-level collection strong in applied mathematics and nonlinear science, and provides a thorough assessment updated for the latest mathematical applications. From modeling problems ranging from heat flow to sound waves and algae spread to equations based on methods of solution and physical and mathematical applications, this reviews PDEs and their applications and is a pick for advanced math collections whose patrons have an basic knowledge of multivariable calculus and ODEs. Any working with MATLAB codes and problem-solving applications need this!" --California Bookwatch, November 2013 Praise for the First Edition: "The strongest aspect of this text is the very large number of worked boundary value problem examples." -- SIAM "This is a useful introductory text on PDEs for advanced undergraduate / beginning graduate students of applied mathematics, physics, or engineering sciences. ... a nice introductory text which certainly is of great use in preparing and delivering courses." -- Zentralblatt MATH "Readers new to the subject will find Coleman's appendix cataloguing important partial differential equations in their natural surroundings quite useful. ... Coleman's more explicit, extended style would probably allow its use as an advanced graduate or reference text for UK engineers or physicists." -- Times Higher Education "The book presents very useful material and can be used as a basic text for self-study of PDEs." -- EMS Newsletter "Each chapter is introduced by a 'prelude' that describes its content and gives historical background. Each section concludes with a set of exercises, many of which are marked MATLAB." -- CMS Notes, "This is an excellent textbook ... first, the book can be used by a person who has no interest in MATLAB at all, and, second, this book deserves to be considered by--in fact, should be at the top of the list of--any professor looking for an undergraduate text in PDEs. ... there are several reasons why I view this book as being in the upper echelon of undergraduate PDE textbooks. One is the extremely high quality of exposition. Coleman writes clearly and cleanly, with a conversational tone and a high regard for motivation. He clearly has a great deal of experience teaching this subject and has learned what points are likely to cause confusion and therefore need expanded discussion. The author also employs the nice pedagogical feature of page-long 'preludes' to each chapter, which not only summarize what the chapter will cover and how it fits into the general theme of things, but also typically provide some brief historical commentary as well. In general, the overall effect of this book is like listening to a discussion by a good professor in office hours. ... very highly recommended. I don't know when or if I will ever teach an undergraduate PDE course, but if I ever do, this book will certainly be on my short list of possible texts." --Mark Hunacek, MAA Reviews, September 2013 Praise for the First Edition: "The strongest aspect of this text is the very large number of worked boundary value problem examples." -- SIAM "This is a useful introductory text on PDEs for advanced undergraduate / beginning graduate students of applied mathematics, physics, or engineering sciences. ... a nice introductory text which certainly is of great use in preparing and delivering courses." -- Zentralblatt MATH "Readers new to the subject will find Coleman's appendix cataloguing important partial differential equations in their natural surroundings quite useful. ... Coleman's more explicit, extended style would probably allow its use as an advanced graduate or reference text for UK engineers or physicists." -- Times Higher Education "The book presents very useful material and can be used as a basic text for self-study of PDEs." -- EMS Newsletter "Each chapter is introduced by a 'prelude' that describes its content and gives historical background. Each section concludes with a set of exercises, many of which are marked MATLAB." -- CMS Notes
Dewey Edition
23/eng/20240326
Series Volume Number
27
Illustrated
Yes
Dewey Decimal
515/.353028553
Table Of Content
Introduction What are Partial Differential Equations? PDEs We Can Already Solve Initial and Boundary Conditions Linear PDEs--Definitions Linear PDEs--The Principle of Superposition Separation of Variables for Linear, Homogeneous PDEs Eigenvalue Problems The Big Three PDEs Second-Order, Linear, Homogeneous PDEs with Constant Coefficients The Heat Equation and Diffusion The Wave Equation and the Vibrating String Initial and Boundary Conditions for the Heat and Wave Equations Laplace's Equation--The Potential Equation Using Separation of Variables to Solve the Big Three PDEs Fourier Series Introduction Properties of Sine and Cosine The Fourier Series The Fourier Series, Continued The Fourier Series--Proof of Pointwise Convergence Fourier Sine and Cosine Series Completeness Solving the Big Three PDEs Solving the Homogeneous Heat Equation for a Finite Rod Solving the Homogeneous Wave Equation for a Finite String Solving the Homogeneous Laplace's Equation on a Rectangular Domain Nonhomogeneous Problems Characteristics First-Order PDEs with Constant Coefficients First-Order PDEs with Variable Coefficients The Infinite String Characteristics for Semi-Infinite and Finite String Problems General Second-Order Linear PDEs and Characteristics Integral Transforms The Laplace Transform for PDEs Fourier Sine and Cosine Transforms The Fourier Transform The Infinite and Semi-Infinite Heat Equations Distributions, the Dirac Delta Function and Generalized Fourier Transforms Proof of the Fourier Integral Formula Bessel Functions and Orthogonal Polynomials The Special Functions and Their Differential Equations Ordinary Points and Power Series Solutions; Chebyshev, Hermite and Legendre Polynomials The Method of Frobenius; Laguerre Polynomials Interlude: The Gamma Function Bessel Functions Recap: A List of Properties of Bessel Functions and Orthogonal Polynomials Sturm-Liouville Theory and Generalized Fourier Series Sturm-Liouville Problems Regular and Periodic Sturm-Liouville Problems Singular Sturm-Liouville Problems; Self-Adjoint Problems The Mean-Square or L 2 Norm and Convergence in the Mean Generalized Fourier Series; Parseval's Equality and Completeness PDEs in Higher Dimensions PDEs in Higher Dimensions: Examples and Derivations The Heat and Wave Equations on a Rectangle; Multiple Fourier Series Laplace's Equation in Polar Coordinates: Poisson's Integral Formula The Wave and Heat Equations in Polar Coordinates Problems in Spherical Coordinates The Infinite Wave Equation and Multiple Fourier Transforms Postlude: Eigenvalues and Eigenfunctions of the Laplace Operator; Green's Identities for the Laplacian Nonhomogeneous Problems and Green's Functions Green's Functions for ODEs Green's Function and the Dirac Delta Function Green's Functions for Elliptic PDEs (I): Poisson's Equation in Two Dimensions Green's Functions for Elliptic PDEs (II): Poisson's Equation in Three Dimensions; the Helmholtz Equation Green's Functions for Equations of Evolution Numerical Methods Finite Difference Approximations for ODEs Finite Difference Approximations for PDEs Spectral Methods and the Finite Element Method Appendix A: Uniform Convergence; Differentiation and Integration of Fourier Series Appendix B: Other Important Theorems Appendix C: Existence and Uniqueness Theorems Appendix D: A Menagerie of PDEs Appendix E: MATLAB Code for Figures and Exercises Appendix F: Answers to Selected Exercises References Index
Edition Description
Revised edition,New Edition
Synopsis
An Introduction to Partial Differential Equations with MATLAB(R), 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., 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., Updated throughout, this second edition of a bestseller illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. It 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. The text also contains many exercises, including standard ones and graphical problems using MATLAB(R).
LC Classification Number
QA371.35.C66 2013
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