- #1
- 19,546
- 10,286
- Author: David Bleecker (Author), George Csordas (Author)
- Title: Basic Partial Differential Equations
- Amazon Link: https://www.amazon.com/dp/1571460365/?tag=pfamazon01-20
- Prerequisities:
Table of Contents:
Code:
[LIST]
[*] Preface
[*] Review and Introduction
[LIST]
[*] A Review of Ordinary Differential Equations
[*] Generalities about PDEs
[*] General Solutions and Elementary Techniques
[/LIST]
[*] First-Order PDEs
[LIST]
[*] First-Order Linear PDEs (Constant Coefficients)
[*] Variable Coefficients
[*] Higher Dimensions, Quasi-linearity, Applications
[*] Supplement on General Nonlinear First-Order PDEs (Optional
[/LIST]
[*] The Heat Equation
[LIST]
[*] Derivation of the Heat Equation and Solutions of the Standard Initial/Boundary-Value Problems
[*] Uniqueness and the Maximum Principle
[*] Time-Independent Boundary Conditions
[*] Time-Dependent Boundary Conditions and Duhamel's Principle for Inhomogeneous Heat Equations
[/LIST]
[*] Fourier Series and Sturm-Liouville Theory
[LIST]
[*] Orthogonality and the Definition of Fourier Series
[*] Convergence Theorems for Fourier Series
[*] Sine and Cosine Series and Applications
[*] Sturm-Liouville Theory
[/LIST]
[*] The Wave Equation
[LIST]
[*] The Wave Equation - Derivation and Uniqueness
[*] D'Alambert's Solution of Wave Problems
[*] Other Boundary Conditions and Inhomogeneous Wave Equations
[/LIST]
[*] Laplace's Equation
[LIST]
[*] General Orientation
[*] The Dirichlet Problem for a Rectangle
[*] The Dirichlet Problem for Annuli and Disks
[*] The Maximum Principle and Uniqueness for the Dirichlet Problem
[*] Complex Variable Theory with Applications
[/LIST]
[*] Fourier Transforms
[LIST]
[*] Complex Fourier Series
[*] Basic Properties of Fourier Transforms
[*] The Inversion Theorem and Parseval's Equality
[*] Fourier Transform Methods for PDEs
[*] Applications to Problems on Finite and Semi-Finite Intervals
[/LIST]
[*] Numerical Solutions of PDEs - An Introduction
[LIST]
[*] The O Symbol and Approximations of Derivatives
[*] The Explicit Difference Method and the Heat Equation
[*] Difference Equations and Round-off Errors
[*] An Overview of Some Other Numerical Methods for PDEs (Optional)
[/LIST]
[*] PDEs in Higher Dimensions
[LIST]
[*] Higher-Dimensional PDEs - Rectangular Coordinates
[*] The Eigenfunction Viewpoint
[*] PDEs in Spherical Coordinates
[*] Spherical Harmonics, Laplace Series and Applications
[*] Special Functions and Applications
[*] Solving PDEs on Manifolds
[/LIST]
[*] Appendix
[LIST]
[*] The Classification Theorem
[*] Fubini's Theorem
[*] Leibniz's Rule
[*] The Maximum/Minimum Theorem
[*] A Table of Fourier Transforms
[*] Bessel Functions
[/LIST]
[*] References
[*] Selected Answers
[*] Index of Notation
[*] Notation
[/LIST]
Last edited: