Applied Partial Differential Equations (eBook)

Paul DuChateau, David Zachmann (Autoren)

eBook Download: EPUB

2012
Dover Publications (Verlag)
978-0-486-14187-9 (ISBN)

Infos

Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

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Superb introduction devotes almost half its pages to numerical methods for solving partial differential equations, while the heart of the book focuses on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included, with solutions for many at end of book. For students with little background in linear algebra, a useful appendix covers that subject briefly.

Inhalt

PrefaceChapter 1. Mathematical Modeling and Partial Differential Equations 1.1 Mathematical Modeling of Physical Systems 1.2 Equation of Heat Conduction 1.3 Steady-State Conduction of Heat 1.4 Transmission Line Equations 1.5 Well-Posed Problems 1.6 Classification of EquationsChapter 2. Fourier Series and Eigenfunction Expansions; Introduction 2.1 Fourier Series 2.2 Generalized Fourier Series 2.3 Sturm-Liouville Problems 2.4 Discrete Fourier Series 2.5 Function Space L superscript 2 2.6 Multiple Fourier Series 2.7 SummaryChapter 3. Boundary-Value Problems and Initial-Boundary-Value Problems on Spatially Bounded Domains 3.1 Boundary-Value Problems for Laplace and Poisson Equations 3.2 Evolution Equations: Initial-Boundary-Value Problems for Heat Equation 3.3 Evolution Equations: Initial-Boundary-Value Problems for Wave EquationChapter 4. Integral Transforms 4.1 Function Space L superscript 2 (a, b) When (a, b) Is Unbounded 4.2 The Fourier Transform 4.3 The Laplace TransformChapter 5. Boundary-Value Problems and Initial-boundary Value Problems on Unbounded Domains 5.1 Elementary Examples on (- infinity, infinity) 5.2 Examples on Semibounded Regions 5.3 Inhomogeneous Equations 5.4 Duhamel's PrincipleChapter 6. Uniqueness and Continuous Dependence on Data 6.1 Well-Posed Problems in Partial Differential Equations 6.2 Green's Identities and Energy Inequalities 6.3 Maximum-Minimum PrinciplesChapter 7. First-Order Equations 7.1 Constant-Coefficient Advection Equation 7.2 Linera and Quasi-linear Equations 7.3 Conservation Law Equations 7.4 Generalized Solutions 7.5 Applications of Scalar Conservation Laws 7.6 Systems of First-Order EquationsChapter 8. Finite-Difference Methods for Parabolic Equations 8.1 Difference Formulas 8.2 Finite-Difference Equations for u subscript t - a superscript 2 u subscript xx = S 8.3 Computational Methods 8.4 Fourier's Method for Difference Equations 8.5 Stability of Finite-Difference Methods 8.6 Difference Methods in Two Space Variables 8.7 Conservation Law Difference Equations 8.8 Material Balance Difference Equation in Two Space VariablesChapter 9. Numerical Solutions of Hyperbolic Equations 9.1 Difference Methods for a Scalar Initial-Value Problem 9.2 Difference Methods for a Scalar Initial-Boundary-Value Problem 9.3 Scalar Conservation Laws 9.4 Dispersion and Dissipation 9.5 Systems of Equations 9.6 Second-Order Equations 9.7 Method of CharacteristicsChapter 10. Finite-Difference Methods for Elliptic Equations 10.1 Difference Equations for Elliptic Equations 10.2 Direct Solution of Linear Equations 10.3 Fourier's Method 10.4 Iterative Methods 10.5 Convergence of Iterative MethodsAppendix Linear Algebra Solutions to Selected Exercises; Index

Produkt-Details

• Erscheint lt. Verlag: 30.10.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Gewicht: 839 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 0-486-14187-X / 048614187X
• ISBN-13: 978-0-486-14187-9 / 9780486141879