Partial Differential Equations for Scientists and Engineers
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| Autore: |
Farlow Stanley J
|
| Titolo: |
Partial Differential Equations for Scientists and Engineers
|
| Pubblicazione: | Newburyport, : Dover Publications, 2012 |
| Edizione: | 1st ed. |
| Descrizione fisica: | 1 online resource (663 p.) |
| Disciplina: | 515.3/53 |
| 515.353 | |
| Soggetto topico: | Differential equations, Partial |
| Mathematics | |
| Physical Sciences & Mathematics | |
| Calculus | |
| Note generali: | Description based upon print version of record. |
| Nota di contenuto: | Title Page; Copyright Page; Preface; Table of Contents; PART 1 - Introduction; LESSON 1 - Introduction to Partial Differential Equations; What Are PDEs?; Why Are PDEs Useful?; How Do You Solve a Partial Differential Equation?; Kinds of PDEs; PART 2 - Diffusion-Type Problems; LESSON 2 - Diffusion-Type Problems (Parabolic Equations); A Simple Heat-Flow Experiment; The Mathematical Model of the Heat-Flow Experiment; More Diffusion-Type Equations; LESSON 3 - Boundary Conditions for Diffusion-Type Problems; Type 1 BC (Temperature specified on the boundary) |
| Type 2 BC (Temperature of the surrounding medium specified)Type 3 BC (Flux specified-including the special case of insulated boundaries); Typical BCs for One-Dimensional Heat Flow; LESSON 4 - Derivation of the Heat Equation; Derivation of the Heat Equation; LESSON 5 - Separation of Variables; Overview of Separation of Variables; Separation of Variables; LESSON 6 - Transforming Nonhomogeneous BCs into Homogeneous Ones; Transforming Nonhomogeneous BCs to Homogeneous Ones; Transforming Time Varying BCs to Zero BCs; LESSON 7 - Solving More Complicated Problems by Separation of Variables | |
| Heat-Flow Problem with Derivative BCLESSON 8 - Transforming Hard Equations into Easier Ones; Transforming a Heat-Flow Problem with Lateral Heat Loss into an Insulated Problem; LESSON 9 - Solving Nonhomogeneous PDEs (Eigenfunction Expansions); Solution by the Eigenfunction Expansion Method; Solution of a Problem by the Eigenfunction-Expansion Method; LESSON 10 - Integral Transforms (Sine and Cosine Transforms); The Spectrum of a Function; Solution of an Infinite-Diffusion Problem via the Sine Transform; Interpretation of the Solution; LESSON 11 - The Fourier Series and Transform | |
| Discrete Frequency Spectrum of a Periodic FunctionThe Fourier Transform; LESSON 12 - The Fourier Transform and Its Application to PDEs; Useful Properties of the Fourier Transform; Example of a Convolution of Two Functions; Solution of an Initial-Value Problem; LESSON 13 - The Laplace Transform; Properties of the Laplace Transform; Sufficient Conditions to Insure the Existence of a Laplace Transform; Definition of the Finite Convolution; Heat Conduction in a Semi Infinite Medium; LESSON 14 - Duhamel's Principle; Heat Flow within a Rod with Temperature Fixed on the Boundaries | |
| The Importance of Duhamel's PrincipleLESSON 15 - The Convection Term ux in the Diffusion Problems; Laplace Transform Solution to the Convection Problem; PART 3 - Hyperbolic-Type Problems; LESSON 16 - The One-Dimensional Wave Equation (Hyperbolic Equations); Vibrating-String Problem; Intuitive Interpretation of the Wave Equation; LESSON 17 - The D'Alembert Solution of the Wave Equation; D'Alembert's Solution to the One-Dimensional Wave Equation; Examples of the D'Alembert Solution; LESSON 18 - More on the D'Alembert Solution; The Space-Time Interpretation of D'Alembert's Solution | |
| Solution of the Semi-infinite String via the D'Alembert Formula | |
| Sommario/riassunto: | Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th |
| Titolo autorizzato: | Partial differential equations for scientists and engineers |
| ISBN: | 9780486134734 |
| 0486134733 | |
| 9781621985846 | |
| 1621985849 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9911006803503321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Dover Books on Mathematics