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

Original price was: $55.00.$44.97Current price is: $44.97.

**Format: **Downloadable ZIP File

**Resource Type: **Test bank

**Duration: **Unlimited downloads

**Delivery: **Instant Download

**ISBN-13: 9780137549702**

**Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition**prioritizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. The coverage includes orthogonal functions, Fourier series, Green’s functions, boundary value problems, and transform methods. This book is suitable for students studying science, engineering, and applied mathematics.

**Table of Contents**

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

## User Reviews

### Be the first to review “Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (Classic Version) 5th Edition Richard Haberman-Test Bank”

Original price was: $55.00.$44.97Current price is: $44.97.

There are no reviews yet.