Introductory Applications of Partial Differential Equations : With Emphasis on Wave Propagation and Diffusion
George L. Lamb
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
|---|---|
| Utgitt | Hoboken : : Wiley, , 2011.
|
| Omfang | 1 online resource (490 p.)
|
| Opplysninger | Description based upon print version of record.. - Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion; Contents; Preface; 1 One-Dimensional Problems-Separation of Variables; 1.1 Introduction; 1.2 One-Dimensional Heat Conduction; 1.2.1 Boundary and Initial Conditions; 1.3 Steady State Solutions; 1.4 Time Dependent Heat Flow-Separation of Variables; 1.4.1 Elementary Solutions; 1.4.2 Synthesis of Elementary Solutions-Fourier Series; 1.4.3 Changing the Boundary Conditions-Insulated Ends; 1.5 Steady State Heating by a Localized Source-Delta Function; 1.6 Inhomogeneous Boundary Conditions. - 1.7 Inhomogeneous Heat Equation-Source Terms1.8 Wave Equation-Vibrating String; 1.8.1 General Wave Equation; 1.8.2 Solution by Separation of Variables; 1.8.3 Energy Flow on the String; 1.8.4 Source Terms-Inhomogeneous Wave Equation; 1.9 d'Alembert's Solution of the Wave Equation; 2 Laplace Transform Method; 2.1 Vibrating String; 2.2 Diffusion Equation; 2.3 Miscellaneous Examples; 2.3.1 Impulse Acting on a String; 2.3.2 Long-Time Behavior; 2.3.3 Total Heat Flow through an End; 2.4 Point Source Problem-Preview of Green's Function; 3 Two and Three Dimensions; 3.1 Introduction. - 3.2 Steady State Temperature Distribution in Rectangular Coordinates-Laplace's Equation3.3 Time Dependent Diffusion in Rectangular Coordinates; 3.4 Waves on a Membrane-Rectangular Coordinates; 3.4.1 Normal Modes; 3.4.2 Guided Waves; 3.5 Orthogonal Curvilinear Coordinates; 3.5.1 Cylindrical Coordinates; 3.5.2 Spherical Coordinates; 3.5.3 Oblate Spheroidal Coordinates; 3.6 Spherical Symmetry; 3.6.1 Spherical Standing Waves; 3.6.2 Spherical Traveling Waves; 3.7 Circular and Cylindrical Symmetry; 3.7.1 Steady State Temperature in a Pie-Shaped Region; 3.7.2 Laplace's Equation in an Annular Circle. - 3.7.3 Vibrating Membrane3.7.4 Steady State Temperature in a Cylinder; 4 Green's Functions; 4.1 Introductory Example; 4.1.1 Reciprocity; 4.2 General Procedure for Constructing Green's Functions in One Dimension; 4.3 One-Dimensional Steady Waves; 4.3.1 Scattering of Waves on a String; 4.3.2 Significance of Boundary Terms; 4.4 Method of Images; 4.5 A Non-Self-adjoint Green's Function; 4.6 Green's Function for a Damped Oscillator; 4.6.1 A Generalization; 4.7 One-Dimensional Diffusion and Wave Motion; 4.7.1 Diffusion Equation; 4.7.2 Wave Equation; 4.8 Two and Three Space Dimensions-Green's Theorem. - 4.9 Green's Function in Free Space4.9.1 Boundary Condition at Infinity; 4.10 Two-Dimensional Problems; 4.11 Inversion and the Method of Images for a Circle; 4.12 Eigenfunction Expansion Methods; 4.13 Modified Green's Functions-One Dimension; 5 Spherical Geometry; 5.1 Solution of Laplace's Equation; 5.2 Source Terms and the Multiple Expansion; 5.2.1 Axial Multipoles; 5.3 Inversion-Green's Function for a Sphere; 5.4 Spherical Waves; 5.4.1 Spherical Bessel Functions; 5.4.2 Radiation from a Point Source; 5.4.3 Reduction to a Plane Wave; 5.4.4 Scattering of a Plane Wave by a Sphere. - 6 Fourier Transform Methods. - INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONSWith Emphasis on Wave Propagation and DiffusionThis is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematic
|
| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 0471311235
|
