Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (Classic Version), 5th edition
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Overview
Applied Partial Differential Equations with Fourier Series and Boundary Value Problems emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations.
Published by Pearson (July 14th 2021)  Copyright © 2019
ISBN13: 9780137549702
Subject: Advanced Math
Category: Partial Differential Equations
Table of contents
1. Heat Equation
 1.1 Introduction
 1.2 Derivation of the Conduction of Heat in a OneDimensional Rod
 1.3 Boundary Conditions
 1.4 Equilibrium Temperature Distribution
 1.5 Derivation of the Heat Equation in Two or Three Dimensions
2. Method of Separation of Variables
 2.1 Introduction
 2.2 Linearity
 2.3 Heat Equation with Zero Temperatures at Finite Ends
 2.4 Worked Examples with the Heat Equation: Other Boundary Value Problems
 2.5 Laplace’s Equation: Solutions and Qualitative Properties
3. Fourier Series
 3.1 Introduction
 3.2 Statement of Convergence Theorem
 3.3 Fourier Cosine and Sine Series
 3.4 TermbyTerm Differentiation of Fourier Series
 3.5 TermByTerm Integration of Fourier Series
 3.6 Complex Form of Fourier Series
4. Wave Equation: Vibrating Strings and Membranes
 4.1 Introduction
 4.2 Derivation of a Vertically Vibrating String
 4.3 Boundary Conditions
 4.4 Vibrating String with Fixed Ends
 4.5 Vibrating Membrane
 4.6 Reflection and Refraction of Electromagnetic (Light) and Acoustic (Sound) Waves
5. SturmLiouville Eigenvalue Problems
 5.1 Introduction
 5.2 Examples
 5.3 SturmLiouville Eigenvalue Problems
 5.4 Worked Example: Heat Flow in a Nonuniform Rod without Sources
 5.5 SelfAdjoint Operators and SturmLiouville Eigenvalue Problems
 5.6 Rayleigh Quotient
 5.7 Worked Example: Vibrations of a Nonuniform String
 5.8 Boundary Conditions of the Third Kind
 5.9 Large Eigenvalues (Asymptotic Behavior)
 5.10 Approximation Properties
6. Finite Difference Numerical Methods for Partial Differential Equations
 6.1 Introduction
 6.2 Finite Differences and Truncated Taylor Series
 6.3 Heat Equation
 6.4 TwoDimensional Heat Equation
 6.5 Wave Equation
 6.6 Laplace's Equation
 6.7 Finite Element Method
7. Higher Dimensional Partial Differential Equations
 7.1 Introduction
 7.2 Separation of the Time Variable
 7.3 Vibrating Rectangular Membrane
 7.4 Statements and Illustrations of Theorems for the Eigenvalue Problem ∇^{2}φ + λφ = 0
 7.5 Green's Formula, SelfAdjoint Operators and Multidimensional Eigenvalue Problems
 7.6 Rayleigh Quotient and Laplace's Equation
 7.7 Vibrating Circular Membrane and Bessel Functions
 7.8 More on Bessel Functions
 7.9 Laplace’s Equation in a Circular Cylinder
 7.10 Spherical Problems and Legendre Polynomials
8. Nonhomogeneous Problems
 8.1 Introduction
 8.2 Heat Flow with Sources and Nonhomogeneous Boundary Conditions
 8.3 Method of Eigenfunction Expansion with Homogeneous Boundary Conditions (Differentiating Series of Eigenfunctions)
 8.4 Method of Eigenfunction Expansion Using Green’s Formula (With or Without Homogeneous Boundary Conditions)
 8.5 Forced Vibrating Membranes and Resonance
 8.6 Poisson’s Equation
9. Green’s Functions for TimeIndependent Problems
 9.1 Introduction
 9.2 Onedimensional Heat Equation
 9.3 Green’s Functions for Boundary Value Problems for Ordinary Differential Equations
 9.4 Fredholm Alternative and Generalized Green’s Functions
 9.5 Green’s Functions for Poisson’s Equation
 9.6 Perturbed Eigenvalue Problems
 9.7 Summary
10. Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
 10.1 Introduction
 10.2 Heat Equation on an Infinite Domain
 10.3 Fourier Transform Pair
 10.4 Fourier Transform and the Heat Equation
 10.5 Fourier Sine and Cosine Transforms: The Heat Equation on SemiInfinite Intervals
 10.6 Worked Examples Using Transforms
 10.7 Scattering and Inverse Scattering
11. Green’s Functions for Wave and Heat Equations
 11.1 Introduction
 11.2 Green’s Functions for the Wave Equation
 11.3 Green’s Functions for the Heat Equation
12. The Method of Characteristics for Linear and Quasilinear Wave Equations
 12.1 Introduction
 12.2 Characteristics for FirstOrder Wave Equations
 12.3 Method of Characteristics for the OneDimensional Wave Equation
 12.4 SemiInfinite Strings and Reflections
 12.5 Method of Characteristics for a Vibrating String of Fixed Length
 12.6 The Method of Characteristics for Quasilinear Partial Differential Equations
 12.7 FirstOrder Nonlinear Partial Differential Equations
13. Laplace Transform Solution of Partial Differential Equations
 13.1 Introduction
 13.2 Properties of the Laplace Transform
 13.3 Green’s Functions for Initial Value Problems for Ordinary Differential Equations
 13.4 A Signal Problem for the Wave Equation
 13.5 A Signal Problem for a Vibrating String of Finite Length
 13.6 The Wave Equation and its Green’s Function
 13.7 Inversion of Laplace Transforms Using Contour Integrals in the Complex Plane
 13.8 Solving the Wave Equation Using Laplace Transforms (with Complex Variables)
14. Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
 14.1 Introduction
 14.2 Dispersive Waves and Group Velocity
 14.3 Wave Guides
 14.4 Fiber Optics
 14.5 Group Velocity II and the Method of Stationary Phase
 14.7 Wave Envelope Equations (Concentrated Wave Number)
 14.7.1 Schrödinger Equation
 14.8 Stability and Instability
 14.9 Singular Perturbation Methods: Multiple Scales
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