Introduction to partial differential equations with MATLAB
type: Item
instance of: scholarly article
title: Introduction to partial differential equations with MATLAB
zbMATH Open document ID: 0887.35001
author: Jeffery Cooper
published in: Applied and Numerical Harmonic Analysis
publication date: 1998-01-12T00:00:00Z
review text: The text is intended for a first course in partial differential equations at the undergraduate level for students in mathematics, science, and engineering. It is assumed that the student has had the standard three semester calculus sequence including multivariable calculus and a course in ordinary differential equations. Some exposure to matrices and vectors is helpful, but not essential. No prior experience with MATLAB is assumed, although many engineering students will have already seen MATLAB. The material is organized by physical setting and by equation rather than by technique of solution. Each equation is placed in the appropriate physical context with a careful derivation from physical principles. This is followed by a discussion of qualitative properties of the solutions without boundary conditions. Then a nonlinear version of the equation and an appropriate numerical scheme are introduced. Thus Chapter 2 deals with linear first-order equations and the method of characteristics, an example of a scalar nonlinear conservation law, and numerical methods for these equations. Chapter 3 follows the same strategy for the heat equation, while Chapter 4 treats boundary value problems for the heat equation. The wave equation is studied in Chapter 5. Fourier series and the Fourier transform are studied in Chapter 6. Chapter 7 is perhaps novel for this level course. It deals with the method of stationary phase and dispersive equations. The Schrödinger equation is discussed as a dispersive equation. Chapter 8 has fairly standard material on the linear heat and wave equations in higher dimensions. Chapter 9 treats the Laplace and Poisson equations, and includes some examples of nonlinear variational problems. Finally, Chapter 10 provides more numerical methods, suitable for computations in higher dimensions, including an introduction to the finite element method and Galerkin methods. The computer is used extensively in the text with many exercises, although it is possible…
Mathematics Subject Classification ID: 35-01
Mathematics Subject Classification ID: 65Mxx
Mathematics Subject Classification ID: 65Nxx
zbMATH DE Number: 1102779
zbMATH Keywords: undergraduate level
zbMATH Keywords: method of characteristics
zbMATH Keywords: Fourier series
zbMATH Keywords: Fourier transform
zbMATH Keywords: method of stationary phase
zbMATH Keywords: dispersive equations
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: linear heat and wave equations
zbMATH Keywords: nonlinear variational problems
zbMATH Keywords: finite element method
zbMATH Keywords: Galerkin methods
reviewed by: I. N. Katz
describes a project that uses: Matlab
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1102779