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E-raamat: Solution Techniques for Elementary Partial Differential Equations

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(University of Tulsa, Oklahoma, USA)
  • Formaat: 438 pages
  • Ilmumisaeg: 10-Aug-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781000629538
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Solution Techniques for Elementary Partial Differential EquationsSuurem pilt
  • Formaat: 438 pages
  • Ilmumisaeg: 10-Aug-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781000629538
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"In my opinion, this is quite simply the best book of its kind that I have seen thus far." Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition

Praise for the previous editions

An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses." Marian Aron, Plymouth University, UK

"This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended." CHOICE

Solution Techniques for Elementary Partial Differential Equations, Fourth Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing students competence in solving PDEs, and offers concise, easily understood explanations and worked examples that enable students to see the techniques in action.

New to the Fourth Edition











Two additional sections A larger number and variety of worked examples and exercises A companion pdf file containing more detailed worked examples to supplement those in the book, which can be used in the classroom and as an aid to online teaching

Arvustused

"In my opinion, this is quite simply the best book of its kind that I have seen thus far." Professor Peter Schiavone, University of Alberta, from the Foreword to the Fourth Edition

Praise for the previous editions

An ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses." Marian Aron, Plymouth University, UK

"This is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended." CHOICE

Foreword xiii
Preface to the Fourth Edition xv
Preface to the Third Edition xvii
Preface to the Second Edition xix
Preface to the First Edition xxi
Chapter 1 Ordinary Differential Equations: Brief Review
1(12)
1.1 First-Order Equations
1(2)
1.2 Homogeneous Linear Equations with Constant Coefficients
3(3)
1.3 Nonhomogeneous Linear Equations with Constant Coefficients
6(3)
1.4 Cauchy-Euler Equations
9(1)
1.5 Functions and Operators
10(3)
Chapter 2 Fourier Series
13(24)
2.1 The Full Fourier Series
13(7)
2.2 Fourier Sine and Cosine Series
20(12)
2.2.1 Fourier Sine Series
21(5)
2.2.2 Fourier Cosine Series
26(6)
2.3 Convergence and Differentiation
32(1)
2.4 Series Expansion of More General Functions
33(4)
Chapter 3 Sturm-Liouville Problems
37(40)
3.1 Regular Sturm-Liouville Problems
37(21)
3.1.1 Eigenvalues and Eigenfunctions of Some Basic Problems
41(10)
3.1.2 Generalized Fourier Series
51(7)
3.2 Other Problems
58(2)
3.3 Bessel Functions
60(6)
3.4 Legendre Polynomials
66(4)
3.5 Spherical Harmonics
70(7)
Chapter 4 Some Fundamental Equations Of Mathematical Physics
77(22)
4.1 The Heat Equation
78(6)
4.2 The Laplace Equation
84(6)
4.3 The Wave Equation
90(4)
4.4 Other Equations
94(5)
Chapter 5 The Method Of Separation Of Variables
99(64)
5.1 The Heat Equation
99(19)
5.1.1 Rod with Zero Temperature at the Endpoints
99(4)
5.1.2 Rod with Insulated Endpoints
103(4)
5.1.3 Rod with Mixed Boundary Conditions
107(4)
5.1.4 Rod with an Endpoint in a Zero-Temperature Medium
111(4)
5.1.5 Thin Uniform Circular Ring
115(3)
5.2 The Wave Equation
118(14)
5.2.1 Vibrating String with Fixed Endpoints
118(4)
5.2.2 Vibrating String with Free Endpoints
122(4)
5.2.3 Vibrating String with Other Types of Boundary Conditions
126(6)
5.3 The Laplace Equation
132(10)
5.3.1 Laplace Equation in a Rectangle
132(5)
5.3.2 Laplace Equation in a Circular Disc
137(5)
5.4 Other Equations
142(7)
5.5 Equations with More than Two Variables
149(14)
5.5.1 Vibrating Rectangular Membrane
149(5)
5.5.2 Vibrating Circular Membrane
154(4)
5.5.3 Equilibrium Temperature in a Solid Sphere
158(5)
Chapter 6 Linear Nqnhqmogenequs Problems
163(12)
6.1 Equilibrium Solutions
163(5)
6.2 Nonhomogeneous Problems
168(7)
6.2.1 Time-Independent Sources and Boundary-Conditions
168(1)
6.2.2 The General Case
169(6)
Chapter 7 The Method Of Eigenfunction Expansion
175(40)
7.1 The Nonhomogeneous Heat Equation
175(11)
7.1.1 Rod with Zero Temperature at the Endpoints
175(6)
7.1.2 Rod with Insulated Endpoints
181(3)
7.1.3 Rod with Mixed Boundary Conditions
184(2)
7.2 The Nonhomogeneous Wave Equation
186(8)
7.2.1 Vibrating String with Fixed Endpoints
186(4)
7.2.2 Vibrating String with Free Endpoints
190(2)
7.2.3 Vibrating String with Mixed Boundary Conditions
192(2)
7.3 The Nonhomogeneous Laplace Equation
194(13)
7.3.1 Equilibrium Temperature in a Rectangle
194(9)
7.3.2 Equilibrium Temperature in a Circular Disc
203(4)
7.4 Other Nonhomogeneous Equations
207(8)
Chapter 8 The Fourier Transformations
215(34)
8.1 The Full Fourier Transformation
215(15)
8.1.1 Cauchy Problem for an Infinite Rod
219(4)
8.1.2 Vibrations of an Infinite String
223(3)
8.1.3 Equilibrium Temperature in an Infinite Strip
226(4)
8.2 The Fourier Sine and Cosine Transformations
230(13)
8.2.1 Heat Conduction in a Semi-Infinite Rod
231(3)
8.2.2 Vibrations of a Semi-Infinite String
234(3)
8.2.3 Equilibrium Temperature in a Semi-Infinite Strip
237(6)
8.3 Other Applications
243(6)
Chapter 9 The Laplace Transformation
249(30)
9.1 Definition and Properties
249(7)
9.2 Applications
256(23)
9.2.1 The Signal Problem for the Wave Equation
256(7)
9.2.2 Heat Conduction in a Semi-Infinite Rod
263(4)
9.2.3 Finite Rod with Temperature Prescribed on the Boundary
267(2)
9.2.4 Diffusion-Convection Problems
269(6)
9.2.5 Dissipative Waves
275(4)
Chapter 10 The Method Of Green's Functions
279(30)
10.1 The Heat Equation
279(12)
10.1.1 The Time-Independent Problem
279(6)
10.1.2 The Time-Dependent Problem
285(6)
10.2 The Laplace Equation
291(6)
10.3 The Wave Equation
297(12)
Chapter 11 General Second-Order Linear Equations
309(22)
11.1 The Canonical Form
309(4)
11.1.1 Classification
309(2)
11.1.2 Reduction to Canonical Form
311(2)
11.2 Hyperbolic Equations
313(5)
11.3 Parabolic Equations
318(4)
11.4 Elliptic Equations
322(2)
11.5 Other Problems
324(7)
Chapter 12 The Method Of Characteristics
331(32)
12.1 First-Order Linear Equations
331(11)
12.2 First-Order Quasilinear Equations
342(3)
12.3 The One-Dimensional Wave Equation
345(9)
12.3.1 The d'Alembert Solution
345(5)
12.3.2 The Semi-Infinite Vibrating String
350(2)
12.3.3 The Finite String
352(2)
12.4 Other Hyperbolic Equations
354(9)
12.4.1 One-Dimensional Waves
354(4)
12.4.2 Moving Boundary Problems
358(3)
12.4.3 Spherical Waves
361(2)
Chapter 13 Perturbation And Asymptotic Methods
363(28)
13.1 Asymptotic Series
363(3)
13.2 Regular Perturbation Problems
366(16)
13.2.1 Formal Solutions
366(13)
13.2.2 Secular Terms
379(3)
13.3 Singular Perturbation Problems
382(9)
Chapter 14 Complex Variable Methods
391(12)
14.1 Elliptic Equations
391(7)
14.2 Systems of Equations
398(5)
Appendix
403(8)
A.1 Useful Integrals
403(1)
A.2 Eigenvalue-Eigenfunction Pairs
404(1)
A.3 Table of Fourier Transforms
405(1)
A.4 Table of Fourier Sine Transforms
406(1)
A.5 Table of Fourier Cosine Transforms
407(1)
A.6 Table of Laplace Transforms
408(1)
A.7 Second-Order Linear Equations
409(2)
Further Reading 411(2)
Index 413
Christian Constanda, MS, PhD, DSc, is the Charles W. Oliphant Endowed Chair in Mathematical Sciences and director of the Center for Boundary Integral Methods at the University of Tulsa. He is also an emeritus professor at the University of Strathclyde and chairman of the International Consortium on Integral Methods in Science and Engineering. He is the author/editor of more than 30 books and more than 150 journal papers. His research interests include boundary value problems for elastic plates with transverse shear deformation, direct and indirect integral equation methods for elliptic problems and time-dependent problems, and variational methods in elasticity.
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