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

[Greg Bernhardt]

• 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:

[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]

 

[jackmell]

I've tried to use many PDE books over the years but have found this intro book very accessible. It's a nice read, not too complicated, not too many proof, and works very well for an intro course. It goes over first orders briefly, then second orders (of two varables) in detail. It then briefly introduces the student to PDE of more than three variables, and then presents a very nice section on numerical methods.

I highly recommend this text as a secondary textbook for anyone just starting with PDEs.