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Applications of Green's Functions in Science and Engineering First Edition, First ed. [Pehme köide]

  • Formaat: Paperback / softback, 160 pages, kõrgus x laius x paksus: 229x8x153 mm, kaal: 229 g
  • Sari: Dover Books on Engineering
  • Ilmumisaeg: 31-Jul-2015
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486797961
  • ISBN-13: 9780486797960
  • Formaat: Paperback / softback, 160 pages, kõrgus x laius x paksus: 229x8x153 mm, kaal: 229 g
  • Sari: Dover Books on Engineering
  • Ilmumisaeg: 31-Jul-2015
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486797961
  • ISBN-13: 9780486797960
In addition to coverage of Green's function, this concise introductory treatment examines boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics. Suitable for undergraduate and graduate students. 1971 edition.


Concise and highly regarded, this treatment of Green's functions and their applications in science and engineering is geared toward undergraduate and graduate students with only a moderate background in ordinary differential equations and partial differential equations. The text also includes a wealth of information of a more general nature on boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics.
The two-part treatment begins with an overview of applications to ordinary differential equations. Topics include the adjoint operator, delta function, the Green's function method, and the eigenfunction method. The second part, which explores applications to partial differential equations, covers functions for the Laplace, Helmholtz, diffusion, and wave operators. A full index, exercises, suggested reading list, a new preface, and a new brief errata list round out the text.
PART I Application to Ordinary Differential Equations
1 Introduction
2(4)
Operators; linearity; superposition
2 The Adjoint Operator
6(5)
Formal adjoint; adjoint; formal self-adjointness; self-adjointness; inner product
3 The Delta Function
11(10)
Introduction to generalized functions; delta function; Heaviside function
4 The Green's Function Method
21(21)
Development of Green's function method; symmetry property; Fourier transform; generalized Green's function; integral equations
Example 1 Loaded String
22(5)
Example 2 A More Complicated Operator
27(3)
Example 3 Infinite Beam on Elastic Foundation
30(3)
Example 4 A Bessel Equation
33(3)
Example 5 The Generalized Green's Function
36(6)
5 The Eigenfunction Method
42(8)
Eigenvalue problem; Sturm-Liouville systems; orthogonality; completeness; Fourier series; expansion of Green's function
Application of Eigenfunction Method
46(4)
6 Summary
50(2)
Summary of the Green's function procedure for ordinary differential equations
PART II Application to Partial Differential Equations
1 Introduction
52(4)
General second order linear equation with two independent variables; classification; examples
2 The Adjoint Operator
56(4)
Formal adjoint; adjoint; formal self-adjointness; self-adjointness; inner product
3 The Delta Function
60(1)
Two-dimensional delta function
4 The Green's Function Method
61(2)
Outline of method; principal solutions; "splitting" technique
5 Principal Solutions
63(8)
Calculation of principal solutions; Fourier transform
Laplace Operator
63(2)
Helmholtz Operator
65(1)
Diffusion Operator
66(1)
Wave Operator
67(4)
6 Green's Function Method For The Laplace Operator
71(22)
Images; conformal mapping; Poisson integral formula; symmetry; Dirichlet, Neumann, and mixed boundary conditions
Example 1 Circular Disk
72(9)
Example 2 Half-Plane
81(3)
Example 3 Mixed Boundary Conditions
84(2)
Example 4 Quarter-Plane
86(7)
7 Green's Function Method For The Helmholtz Operator
93(6)
Separation of variables; radiation condition; images
Example 1 Vibrating Circular Membrane
93(1)
Example 2 Acoustic Radiation
94(5)
8 Green's Function Method For The Diffusion Operator
99(5)
Images; iteration
Example 1 Semi-infinite Rod
99(5)
9 Green's Function Method For The Wave Operator
104(2)
D'Alembert formula
Example 1 Doubly-infinite String
105(1)
10 The Eigenfunction Method
106(6)
Illustration of the method
Example 1 Poisson Equation for a Rectangle
106(6)
11 Additional Examples
112(18)
More than two independent variables; higher order equations; images; Poisson integral formula; Laplace transform; Lienard-Wiechert potential; plate theory
Example 1 Laplace Operator in Three Dimensions
112(4)
Example 2 Two- and Three-Dimensional Acoustics
116(9)
Example 3 Biharmonic Equation
125(5)
12 Summary
130(3)
Summary of the Green's function procedure for partial differential equations
Errata 133(2)
Suggested Reading 135(2)
Index 137