Beginning Partial Differential Equations

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780470133903 | 0470133902
Cover: Hardcover
Copyright: 4/4/2008

Buy New

Print on Demand: 2-4 Weeks. This item cannot be cancelled or returned.

$120.18

This book provides a solid introduction to partial differential equations, particularly methods of solutions based on characteristics, separation of variables, Fourier series, integrals, and transforms. The book's approach begins with first order PDEs and characteristics, and moves on to second order linear equations, classification, and methods and properties of solutions. Next, readers are introduced to a selection of applications and more advanced techniques, and an introduction to more theoretical aspects of the subject is also provided.

First-Order Equations	p. 1
Notation and Terminology	p. 1
The Linear First-Order Equation	p. 4
The Significance of Characteristics	p. 12
The Quasi-Linear Equation	p. 16
Linear Second-Order Equations	p. 23
Classification	p. 23
The Hyperbolic Canonical Form	p. 25
The Parabolic Canonical Form	p. 30
The Elliptic Canonical Form	p. 33
Some Equations of Mathematical Physics	p. 38
The Second-Order Cauchy Problem	p. 46
Characteristics and the Cauchy Problem	p. 49
Characteristics as Carriers of Discontinuities	p. 56
Elements of Fourier Analysis	p. 59
Why Fourier Series?	p. 59
The Fourier Series of a Function	p. 60
Convergence of Fourier Series	p. 63
Sine and Cosine Expansions	p. 81
The Fourier Integral	p. 89
The Fourier Transform	p. 95
Convolution	p. 101
Fourier Sine and Cosine Transforms	p. 106
The Wave Equation	p. 109
d'Alembert Solution of the Cauchy Problem	p. 109
d'Alembert's Solution as a Sum of Waves	p. 117
The Characteristic Triangle	p. 126
The Wave Equation on a Half-Line	p. 131
A Half-Line with Moving End	p. 134
A Nonhomogeneous Problem on the Real Line	p. 137
A General Problem on a Closed Interval	p. 141
Fourier Series Solutions on a Closed Interval	p. 150
A Nonhomogeneous Problem on a Closed Interval	p. 159
The Cauchy Problem by Fourier Integral	p. 168
A Wave Equation in Two Space Dimensions	p. 173
The Kirchhoff-Poisson Solution	p. 177
Hadamard's Method of Descent	p. 182
The Heat Equation	p. 185
The Cauchy Problem and Initial Conditions	p. 185
The Weak Maximum Principle	p. 188
Solutions on Bounded Intervals	p. 192
The Heat Equation on the Real Line	p. 210
The Heat Equation on the Half-Line	p. 218
The Debate Over the Age of the Earth	p. 224
The Nonhomogeneous Heat Equation	p. 227
The Heat Equation in Two Space Variables	p. 234
Dirichlet and Neumann Problems	p. 239
The Setting of the Problems	p. 239
Some Harmonic Functions	p. 247
Representation Theorems	p. 251
Two Properties of Harmonic Functions	p. 257
Is the Dirichlet Problem Well Posed?	p. 263
Dirichlet Problem for a Rectangle	p. 266
Dirichlet Problem for a Disk	p. 269
Poisson's Integral Representation for a Disk	p. 272
Dirichlet Problem for the Upper Half-Plane	p. 276
Dirichlet Problem for the Right Quarter-Plane	p. 279
Dirichlet Problem for a Rectangular Box	p. 282
The Neumann Problem	p. 285
Neumann Problem for a Rectangle	p. 288
Neumann Problem for a Disk	p. 290
Neumann Problem for the Upper Half-Plane	p. 294
Green's Function for a Dirichlet Problem	p. 296
Conformal Mapping Techniques	p. 303
Conformal Mappings	p. 303
Bilinear Transformations	p. 308
Construction of Conformal Mappings between Domains	p. 313
An Integral Solution of the Dirichlet Problem for a Disk	p. 320
Solution of Dirichlet Problems by Conformal Mapping	p. 323
Existence Theorems	p. 327
A Classical Existence Theorem	p. 327
A Hilbert Space Approach	p. 336
Distributions and an Existence Theorem	p. 344
Additional Topics	p. 351
Solutions by Eigenfunction Expansions	p. 351
Numerical Approximations of Solutions	p. 370
Burger's Equation	p. 377
The Telegraph Equation	p. 383
Poisson's Equation	p. 390
End Materials	p. 395
Historical Notes	p. 395
Glossary	p. 398
Answers to Selected Problems	p. 399
Index	p. 473
Table of Contents provided by Ingram. All Rights Reserved.

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Beginning Partial Differential Equations

Summary

Author Biography

Table of Contents

Supplemental Materials