Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (Classic Version) 5th Edition Richard Haberman-Test Bank

Chapter 1: Heat Equation
1.1 Introduction
1.2 Deriving Heat Conduction in a One-Dimensional Rod
1.3 Boundary Conditions
1.4 Equilibrium Temperature Distribution
1.5 Deriving the Heat Equation in Two or Three Dimensions
Chapter 2: Separation of Variables Method
2.1 Introduction
2.2 Linearity
2.3 Heat Equation with Zero Temperatures at Finite Ends
2.4 Examples with the Heat Equation: Different Boundary Value Problems
2.5 Laplace’s Equation: Solutions and Qualitative Properties
Chapter 3: Fourier Series
3.1 Introduction
3.2 Convergence Theorem Statement
3.3 Fourier Cosine and Sine Series
3.4 Differentiation of Fourier Series Term by Term
3.5 Integration of Fourier Series Term by Term
3.6 Complex Form of Fourier Series
Chapter 4: Wave Equation: Vibrating Strings and Membranes
4.1 Introduction
4.2 Deriving 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
Chapter 5: Sturm-Liouville Eigenvalue Problems
5.1 Introduction
5.2 Examples
5.3 Sturm-Liouville Eigenvalue Problems
5.4 Example: Heat Flow in a Nonuniform Rod without Sources
5.5 Self-Adjoint Operators and Sturm-Liouville Eigenvalue Problems
5.6 Rayleigh Quotient
5.7 Example: Vibrations of a Nonuniform String
5.8 Boundary Conditions of the Third Kind
5.9 Large Eigenvalues (Asymptotic Behavior)
5.10 Approximation Properties
Chapter 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 Two-Dimensional Heat Equation
6.5 Wave Equation
6.6 Laplace’s Equation
6.7 Finite Element Method
Chapter 7: Higher Dimensional Partial Differential Equations
7.1 Introduction
7.2 Separation of the Time Variable
7.3 Vibrating Rectangular Membrane
7.4 Theorems for the Eigenvalue Problem ∇2φ + λφ = 0
7.5 Green’s Formula, Self-Adjoint 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
Chapter 8: Nonhomogeneous Problems
8.1 Introduction
8.2 Heat Flow with Sources and Nonhomogeneous Boundary Conditions
8.3 Eigenfunction Expansion with Homogeneous Boundary Conditions
8.4 Eigenfunction Expansion Using Green’s Formula
8.5 Forced Vibrating Membranes and Resonance
8.6 Poisson’s Equation
Chapter 9: Green’s Functions for Time-Independent Problems
9.1 Introduction
9.2 One-dimensional 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
Chapter 10: Infinite Domain Problems
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
10.6 Examples Using Transforms
10.7 Scattering and Inverse Scattering
Chapter 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
Chapter 12: The Method of Characteristics for Linear and Quasilinear Wave Equations
12.1 Introduction
12.2 Characteristics for First-Order Wave Equations
12.3 Method of Characteristics for the One-Dimensional Wave Equation
12.4 Semi-Infinite Strings and Reflections
12.5 Method of Characteristics for a Vibrating String of Fixed Length
12.6 Method of Characteristics for Quasilinear Partial Differential Equations
12.7 First-Order Nonlinear Partial Differential Equations
Chapter 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 Signal Problems for the Wave Equation
13.5 Signal Problems 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
Chapter 14: Dispersive Waves
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