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.
Author(s): Michael D. Greenberg
Series: Dover Books on Engineering
Publisher: Dover Publications
Year: 2015
Language: English
Pages: 156
Greenberg, M.Applications of Green's functions in science and engineering (Dover Books on Engineering)(Dover,2015)(ISBN 0486797961)(T)(K)(600dpi)(156p) ......Page 3
Copyright ......Page 4
Preface vii ......Page 6
Contents ix ......Page 8
PART I Application to Ordinary Differential Equations 1 ......Page 12
1. INTRODUCTION, 2 ......Page 13
Summary of the Green’s function procedure for partial differential equations ......Page
2. THE ADJOINT OPERATOR, 6 ......Page 17
3. THE DELTA FUNCTION, 11 ......Page 22
4. THE GREEN’S FUNCTION METHOD, 21 ......Page 32
Example I. Loaded String, 22 ......Page 33
Example 2. More Complicated Operator, 27 ......Page 38
Example 3. Infinite Beam on Elastic Foundation, 30 ......Page 41
Example 4. Bessel Equation, 33 ......Page 44
Example 5. The Generalized Green's Function, 36 ......Page 47
5. THE EIGENFUNCTION METHOD, 42 ......Page 53
Application of Eigenfunction Method, 46 ......Page 57
6. SUMMARY, 50 ......Page 61
PART II Application to Partial Differential Equations 51......Page 62
1. INTRODUCTION, 52 ......Page 63
2. THE ADJOINT OPERATOR, 56 ......Page 67
3. THE DELTA FUNCTION, 60 ......Page 71
4. THE GREEN’S FUNCTION METHOD, 61 ......Page 72
Laplace Operator, 63 ......Page 74
Helmholtz Operator, 65 ......Page 76
Diffusion Operator, 66 ......Page 77
Wave Operator, 67 ......Page 78
6. GREEN’S FUNCTION METHOD FOR THE LAPLACE OPERATOR, 71 ......Page 82
Example 1. Circular Disk, 72 ......Page 83
Example 2. Half-Plane, 81 ......Page 92
Example 3. Mixed Boundary Conditions, 84 ......Page 95
Example 4. Quarter-Plane, 86 ......Page 97
Example 1. Vibrating Circular Membrane, 93 ......Page 104
Example 2. Acoustic Radiation, 94 ......Page 105
Example 1. Semi-infinite Rod, 99 ......Page 110
9. GREEN’S FUNCTION METHOD FOR THE WAVE OPERATOR, 104 ......Page 115
Example 1. Doubly-infinite Stringy 105 ......Page 116
Example 1. Poisson Equation for a Rectangle, 106 ......Page 117
Example 1. Laplace Operator in Three Dimensions, 112 ......Page 123
Example 2. Two- and Three-Dimensional Acoustics, 116 ......Page 127
Example 3. Biharmonic Equation, 125 ......Page 136
12. SUMMARY, 130 ......Page 141
Errata, 133 ......Page 144
Suggested Reading, 135 ......Page 146
Index, 137 ......Page 148
cover......Page 1
