View Poll Results: For those who have used this book Strongly Recommend 1 100.00% Lightly Recommend 0 0% Lightly don't Recommend 0 0% Strongly don't Recommend 0 0% Voters: 1. You may not vote on this poll

Blog Entries: 5

## Basic Partial Differential Equations by D. Bleecker and G. Csordas

Code:
 Preface
Review and Introduction A Review of Ordinary Differential Equations
General Solutions and Elementary Techniques

First-Order PDEs First-Order Linear PDEs (Constant Coefficients)
Variable Coefficients
Higher Dimensions, Quasi-linearity, Applications
Supplement on General Nonlinear First-Order PDEs (Optional

The Heat Equation 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

Fourier Series and Sturm-Liouville Theory Orthogonality and the Definition of Fourier Series
Convergence Theorems for Fourier Series
Sine and Cosine Series and Applications
Sturm-Liouville Theory

The Wave Equation The Wave Equation - Derivation and Uniqueness
D'Alambert's Solution of Wave Problems
Other Boundary Conditions and Inhomogeneous Wave Equations

Laplace's Equation 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

Fourier Transforms 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

Numerical Solutions of PDEs - An Introduction 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)

PDEs in Higher Dimensions 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

Appendix The Classification Theorem
Fubini's Theorem
Leibniz's Rule
The Maximum/Minimum Theorem
A Table of Fourier Transforms
Bessel Functions

References