ANALYTIC METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS By G. Evans & J. Blackledge
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ANALYTIC METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS By G. Evans & J. Blackledge
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eBay-Artikelnr.:226741882992
Artikelmerkmale
- Artikelzustand
- Sehr gut
- Hinweise des Verkäufers
- ISBN-10
- 3540761241
- Book Title
- Analytic Methods for Partial Differential Equations (Springer
- ISBN
- 9783540761242
Über dieses Produkt
Product Identifiers
Publisher
Springer London, The Limited
ISBN-10
3540761241
ISBN-13
9783540761242
eBay Product ID (ePID)
1621300
Product Key Features
Number of Pages
Xii, 316 Pages
Publication Name
Analytic Methods for Partial Differential Equations
Language
English
Publication Year
1999
Subject
Differential Equations / General, Numerical Analysis, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Series
Springer Undergraduate Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Height
0.3 in
Item Weight
34.6 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-035689
Dewey Edition
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515/.353
Table Of Content
1. Mathematical Preliminaries.- 1.1 Introduction.- 1.2 Characteristics and Classification.- 1.3 Orthogonal Functions.- 1.4 Sturm-Liouville Boundary Value Problems.- 1.5 Legendre Polynomials.- 1.6 Bessel Functions.- 1.7 Results from Complex Analysis.- 1.8 Generalised Functions and the Delta Function.- 2. Separation of the Variables.- 2.1 Introduction.- 2.2 The Wave Equation.- 2.3 The Heat Equation.- 2.4 Laplace's Equation.- 2.5 Homogeneous and Non-homogeneous Boundary Conditions.- 2.6 Separation of variables in other coordinate systems.- 3. First-order Equations and Hyperbolic Second-order Equations.- 3.1 Introduction.- 3.2 First-order equations.- 3.3 Introduction to d'Alembert's Method.- 3.4 d'Alembert's General Solution.- 3.5 Characteristics.- 3.6 Semi-infinite Strings.- 4. Integral Transforms.- 4.1 Introduction.- 4.2 Fourier Integrals.- 4.3 Application to the Heat Equation.- 4.4 Fourier Sine and Cosine Transforms.- 4.5 General Fourier Transforms.- 4.6 Laplace transform.- 4.7 Inverting Laplace Transforms.- 4.8 Standard Transforms.- 4.9 Use of Laplace Transforms to Solve Partial Differential Equations.- 5. Green's Functions.- 5.1 Introduction.- 5.2 Green's Functions for the Time-independent Wave Equation.- 5.3 Green's Function Solution to the Three-dimensional Inhomogeneous Wave Equation.- 5.4 Green's Function Solutions to the Inhomogeneous Helmholtz and Schrödinger Equations: An Introduction to Scattering Theory.- 5.5 Green's Function Solution to Maxwell's Equations and Time-dependent Problems.- 5.6 Green's Functions and Optics: Kirchhoff Diffraction Theory.- 5.7 Approximation Methods and the Born Series.- 5.8 Green's Function Solution to the Diffusion Equation.- 5.9 Green's Function Solution to the Laplace and Poisson Equations.- 5.10Discussion.- A. Solutions of Exercises.
Synopsis
The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics., This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series., The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab- lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics., Partial differential equations fall into several areas of mathematics: many of the greatest advances in modern science have been based on discovering the underlying PDE for the process in question. In this book, the emphasis is on the practical solution of problems rather than the theoretical background. An introductory chapter recaps the mathematical preliminaries required and exercises with solutions are provided. With its companion volume, Analytic Methods for Partial Differential Equations, it provides a complete introduction to the subject.
LC Classification Number
QA299.6-433
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