Partial Differential Equations through Examples and Exercises
by Pap, Endre
This book examines the complicated subject of Partial Differential Equations (PDEs). It involves the reader throughout by presenting theory, examples and exercises together. Both the classical and abstract aspects of the theory are dealt with, so that, for example, classical and generalised solutions in Sobolev and distribution spaces are treated. Most of the work is devoted to second or higher order PDEs; part of the distribution theory is included, covering Dirac's delta distribution delta fu…
Read More ↓Title Statements
- Full title :Partial Differential Equations through Examples and Exercises / by Endre Pap, Arpad Takači, Djurdjica Takači.
Summary
This book examines the complicated subject of Partial Differential Equations (PDEs). It involves the reader throughout by presenting theory, examples and exercises together. Both the classical and abstract aspects of the theory are dealt with, so that, for example, classical and generalised solutions in Sobolev and distribution spaces are treated. Most of the work is devoted to second or higher order PDEs; part of the distribution theory is included, covering Dirac's delta distribution delta function. Many practical tools are offered for solving important problems with the basic three PDEs, namely the wave equation, the Laplace equation, the heat equation and their generalisations. The majority of the problems are mathematical in character, though often physical interpretations are given. Audience: This volume is intended for undergraduate and graduate students in mathematics, physics technology and economics interested in PDEs for modelling complex systems.
Read More ↓Edition Statements
- Publication Date:1997.
Publication Statements
- Publisher(s):Springer Netherlands
- Place of Publication:Dordrecht
- Language:eng
- Publication Date:1997.
The Physical Object
- Description:1 online resource (xii, 404 pages)
Edition Identifiers
- ISBN:9789401155748, 9401155747
- DOI:10.1007/978-94-011-5574-8
- oclc:ocn851368396
- LC Classification:QA370-380
- Dewey Decimal:515.353
Table of Contents
1 Introduction -- 1.1 Basic Notions -- 1.2 The Cauchy-Kowalevskaya Theorem -- 1.3 Equations of Mathematical Physics -- 2 First Order PDEs -- 2.1 Quasi-linear PDEs -- 2.2 Pfaff's Equations -- 2.3 Nonlinear First Order PDEs -- 3 Classification of the Second Order PDEs -- 3.1 Two Independent Variables -- 3.2 n Independent Variables -- 3.3 Wave, Potential and Heat Equation -- 4 Hyperbolic Equations -- 4.1 Cauchy Problem for the One-dimensional Wave Equation -- 4.2 Cauchy Problem for the n-dimensional Wave Equation -- 4.3 The Fourier Method of Separation Variables -- 4.4 The Sturm -- Liouville Problem -- 4.5 Miscellaneous Problems -- 4.6 The Vibrating String -- 5 Elliptic Equations -- 5.1 Dirichlet Problem -- 5.2 The Maximum Principle -- 5.3 The Green Function -- 5.4 The Harmonic Functions -- 5.5 Gravitational Potential -- 6 Parabolic Equations -- 6.1 Cauchy Problem -- 6.2 Mixed Type Problem -- 6.3 Heat conduction -- 7 Numerical Methods -- 7.0.1 Preliminaries -- 7.0.2 Examples and Exercises -- 8 Lebesgue's Integral, Fourier Transform -- 8.1 Lebesgue's Integral and the L2(Q) Space -- 8.2 Delta Nets -- 8.3 The Surface Integrals -- 8.4 The Fourier Transform -- 9 Generalized Derivative and…
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