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An Introduction to Partial Differential Equations

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Author(s): Daniel J. Arrigo, Steven G. Krantz
Series: Synthesis Lectures on Mathematics and Statistics
Publisher: Morgan & Claypool Publishers
Year: 2018

Language: English
Pages: 155

Preface
Acknowledgments
Introduction
Model Equations
Advection Equation
Diffusion Equation
Laplace's Equation
Wave Equation
PDEs Are Everywhere
Exercises
First-Order PDEs
Constant Coefficient Equations
Linear Equations
Method of Characteristics
Quasilinear Equations
Higher-Dimensional Equations
Fully Nonlinear First-Order Equations
Method of Characteristics
Charpit's Method
Exercises
Second-Order Linear PDEs
Introduction
Standard Forms
Parabolic Standard Form
Hyperbolic Standard Form
Modified Hyperbolic Form
Regular Hyperbolic Form
Elliptic Standard Form
The Wave Equation
Exercises
Fourier Series
Fourier Series
Fourier Series on [- ,]
Fourier Series on [- L ,L]
Odd and Even Extensions
Sine Series
Cosine Series
Exercises
Separation of Variables
The Heat Equation
Nonhomogeneous Boundary Conditions
Nonhomogeneous Equations
Equations with a Solution-Dependent Source Term
Equations with a Solution-Dependent Convective Term
Laplace's Equation
Laplace's Equation on an Arbitrary Rectangular Domain
The Wave Equation
Exercises
Fourier Transform
Fourier Transform
Fourier Sine and Cosine Transforms
Exercises
Solutions
Author's Biography
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