Introduction to Partial Differential Equations with MATLAB by Jeffery M. Cooper
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Synopsis
Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coefficients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular, there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore, nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter."The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience. This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes. Topic and Features: * Nonlinear equations including nonlinear conservation laws; * Dispersive wave equations and the Schrodinger equation; * Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform; * Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this website. This text/reference is an excellent resource designed to introduce advanced students in mathematics, engineering, and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.
Product Identifiers
ISBN-10
1461272661
ISBN-13
9781461272663
Key Details
Author
Jeffery M. Cooper
Number Of Pages
541 pages
Series
Applied and Numerical Harmonic Analysis
Format
EBOOK
Publication Date
2012-10-31
Language
English
Publisher
Birkhäuser Boston
Publication Year
2012
Additional Details
Number of Volumes
1 vol.
Copyright Date
1998
Illustrated
Yes
Dimensions
Weight
29.9 Oz
Height
0.4 In.
Width
6.1 In.
Length
9.3 In.
Target Audience
Group
Scholarly & Professional
Classification Method
LC Classification Number
QA71-90QA403.5-404.5
Reviews
"Cooper's book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of MATLAB routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations... One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty." -Choice
Synopsis
Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coefficients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular, there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore, nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter."The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience. This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes. Topic and Features: * Nonlinear equations including nonlinear conservation laws; * Dispersive wave equations and the Schrodinger equation; * Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform; * Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this website. This text/reference is an excellent resource designed to introduce advanced students in mathematics, engineering, and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.
Product Identifiers
ISBN-10
1461272661
ISBN-13
9781461272663
Key Details
Author
Jeffery M. Cooper
Number Of Pages
541 pages
Series
Applied and Numerical Harmonic Analysis
Format
EBOOK
Publication Date
2012-10-31
Language
English
Publisher
Birkhäuser Boston
Publication Year
2012
Additional Details
Number of Volumes
1 vol.
Copyright Date
1998
Illustrated
Yes
Dimensions
Weight
29.9 Oz
Height
0.4 In.
Width
6.1 In.
Length
9.3 In.
Target Audience
Group
Scholarly & Professional
Classification Method
LC Classification Number
QA71-90QA403.5-404.5
Reviews
"Cooper's book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of MATLAB routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations... One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty." -Choice