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Haberman Fifth Edition Partial Differential Equations 2.3.8 Solutions


On this webpage you will find my solutions to the fifth edition of "Appled Partial Differential Equations with Fourier Series and Boundary Value Problems" by Richard Haberman. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.

  • Chapter 1: Heat Equation
    • Section 1.2: Derivation of the Conduction of Heat in a One-Dimensional Rod
    • Section 1.3: Boundary Conditions
    • Section 1.4: Equilibrium Temperature Distribution
    • Section 1.5: Derivation of the Heat Equation in Two or Three Dimensions

  • Chapter 2: Method of Separation of Variables
    • Section 2.2: Linearity
    • Section 2.3: Heat Equation with Zero Temperatures at Finite Ends
    • Section 2.4: Worked Examples with the Heat Equation
    • Section 2.5: Laplace's Equation: Solutions and Qualitative Properties

  • Chapter 3: Fourier Series
    • Section 3.2: Statement of Convergence Theorem
    • Section 3.3: Fourier Cosine and Sine Series
    • Section 3.4: Term-by-Term Differentiation of Fourier Series
    • Section 3.5: Term-By-Term Integration of Fourier Series
    • Section 3.6: Complex Form of Fourier Series

  • Chapter 4: Wave Equation: Vibrating Strings and Membranes
    • Section 4.2: Derivation of a Vertically Vibrating String
    • Section 4.3: Boundary Conditions
    • Section 4.4: Vibrating String with Fixed Ends
    • Section 4.5: Vibrating Membrane
    • Section 4.6: Reflection and Refraction of Electromagnetic and Acoustic Waves

  • Chapter 5: Sturm-Liouville Eigenvalue Problems
    • Section 5.3: Sturm-Liouville Eigenvalue Problems
    • Section 5.4: Heat Flow in a Nonuniform Rod without Sources
    • Section 5.5: Self-Adjoint Operators
    • Section 5.6: Rayleigh Quotient
    • Section 5.7: Vibrations of a Nonuniform String
    • Section 5.8: Boundary Conditions of the Third Kind
    • Section 5.9: Large Eigenvalues (Asymptotic Behavior)
    • Section 5.10: Approximation Properties

  • Chapter 6: Finite Difference Numerical Methods
    • Section 6.2: Finite Differences and Truncated Taylor Series
    • Section 6.3: Heat Equation
    • Section 6.4: Two-Dimensional Heat Equation
    • Section 6.5: Wave Equation
    • Section 6.6: Laplace's Equation
    • Section 6.7: Finite Element Method
  • Chapter 7: Higher-Dimensional Partial Differential Equations
    • Section 7.2: Separation of the Time Variable
    • Section 7.3: Vibrating Rectangular Membrane
    • Section 7.4: Statements and Illustrations of Theorems for the Eigenvalue Problem
    • Section 7.5: Green's Formula, Self-Adjoint Operators, and Multidimensional Eigenvalue Problems
    • Section 7.6: Rayleigh Quotient and Laplace's Equation
    • Section 7.7: Vibrating Circular Membrane and Bessel Functions
    • Section 7.8: More on Bessel Functions
    • Section 7.9: Laplace's Equation in a Circular Cylinder
    • Section 7.10: Spherical Problems and Legendre Polynomials

  • Chapter 8: Nonhomogeneous Problems
    • Section 8.2: Heat Flow with Sources and Nonhomogeneous Boundary Conditions
    • Section 8.3: Method of Eigenfunction Expansion with Homogeneous Boundary Conditions (Differentiating Series of Eigenfunctions)
    • Section 8.4: Method of Eigenfunction Expansion Using Green's Formula (With or Without Homogeneous Boundary Conditions)
    • Section 8.5: Forced Vibrating Membranes and Resonance
    • Section 8.6: Poisson's Equation

  • Chapter 9: Green's Functions for Time-Independent Problems
    • Section 9.2: One-Dimensional Heat Equation
    • Section 9.3: Green's Functions for Boundary Value Problems for Ordinary Differential Equations
    • Section 9.4: Fredholm Alternative and Generalized Green's Functions
    • Section 9.5: Green's Functions for Poisson's Equation
    • Section 9.6: Perturbed Eigenvalue Problems

  • Chapter 10: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
    • Section 10.2: Heat Equation on an Infinite Domain
    • Section 10.3: Fourier Transform Pair
    • Section 10.4: Fourier Transform and the Heat Equation
    • Section 10.5: Fourier Sine and Cosine Transforms: The Heat Equation on Semi-Infinite Intervals
    • Section 10.6: Worked Examples Using Transforms
    • Section 10.7: Scattering and Inverse Scattering
  • Chapter 11: Green's Functions for Wave and Heat Equations
    • Section 11.2: Green's Functions for the Wave Equation
    • Section 11.3: Green's Functions for the Heat Equation

  • Chapter 12: The Method of Characteristics for Linear and Quasilinear Wave Equations
    • Section 12.2: Characteristics for First-Order Wave Equations
    • Section 12.3: Method of Characteristics for the One-Dimensional Wave Equation
    • Section 12.4: Semi-Infinite Strings and Reflections
    • Section 12.5: Method of Characteristics for a Vibrating String of Fixed Length
    • Section 12.6: The Method of Characteristics for Quasilinear Partial Differential Equations
    • Section 12.7: First-Order Nonlinear Partial Differential Equations

  • Chapter 13: Laplace Transform Solution of Partial Differential Equations
    • Section 13.2: Properties of the Laplace Transform
    • Section 13.3: Green's Functions for Initial Value Problems for Ordinary Differential Equations
    • Section 13.4: A Signal Problem for the Wave Equation
    • Section 13.5: A Signal Problem for a Vibrating String of Finite Length
    • Section 13.6: The Wave Equation and Its Green's Function
    • Section 13.7: Inversion of Laplace Transforms Using Contour Integrals in the Complex Plane
    • Section 13.8: Solving the Wave Equation Using Laplace Transforms (with Complex Variables)

  • Chapter 14: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
    • Section 14.2: Dispersive Waves and Group Velocity
    • Section 14.3: Wave Guides
    • Section 14.4: Fiber Optics
    • Section 14.5: Group Velocity II and the Method of Stationary Phase
    • Section 14.6: Slowly Varying Dispersive Waves (Group Velocity and Caustics)
    • Section 14.7: Wave Envelope Equations (Concentrated Wave Number)
    • Section 14.8: Stability and Instability
    • Section 14.9: Singular Perturbation Methods: Multiple Scales
    • Section 14.10: Singular Perturbation Methods: Boundary Layers Method of Matched Asymptotic Expansions
Section 4.2 Section 4.3 Section 4.4 Section 4.5 Section 4.6
Exercise 4.2.1 Exercise 4.3.1 Exercise 4.4.1 Exercise 4.4.8 Exercise 4.5.1 Exercise 4.6.1
Exercise 4.2.2 Exercise 4.3.2 Exercise 4.4.2 Exercise 4.4.9 Exercise 4.5.2 Exercise 4.6.2
Exercise 4.2.3 Exercise 4.4.3 Exercise 4.4.10 Exercise 4.6.3
Exercise 4.2.4 Exercise 4.4.4 Exercise 4.4.11 Exercise 4.6.4
Exercise 4.2.5 Exercise 4.4.5 Exercise 4.4.12 Exercise 4.6.5
Exercise 4.4.6 Exercise 4.4.13
Exercise 4.4.7
Section 5.3 Section 5.4 Section 5.5 Section 5.5A
Exercise 5.3.1 Exercise 5.4.1 Exercise 5.5.1 Exercise 5.5.11 Exercise 5.5A.1
Exercise 5.3.2 Exercise 5.4.2 Exercise 5.5.2 Exercise 5.5.12 Exercise 5.5A.2
Exercise 5.3.3 Exercise 5.4.3 Exercise 5.5.3 Exercise 5.5.13 Exercise 5.5A.3
Exercise 5.3.4 Exercise 5.4.4 Exercise 5.5.4 Exercise 5.5.14 Exercise 5.5A.4
Exercise 5.3.5 Exercise 5.4.5 Exercise 5.5.5 Exercise 5.5.15 Exercise 5.5A.5
Exercise 5.3.6 Exercise 5.4.6 Exercise 5.5.6 Exercise 5.5.16 Exercise 5.5A.6
Exercise 5.3.7 Exercise 5.5.7 Exercise 5.5.17
Exercise 5.3.8 Exercise 5.5.8 Exercise 5.5.18
Exercise 5.3.9 Exercise 5.5.9
Exercise 5.3.10 Exercise 5.5.10
Section 5.6 Section 5.7 Section 5.8 Section 5.9 Section 5.10
Exercise 5.6.1 Exercise 5.7.1 Exercise 5.8.1 Exercise 5.8.9 Exercise 5.9.1 Exercise 5.10.1
Exercise 5.6.2 Exercise 5.7.2 Exercise 5.8.2 Exercise 5.8.10 Exercise 5.9.2 Exercise 5.10.2
Exercise 5.6.3 Exercise 5.7.3 Exercise 5.8.3 Exercise 5.8.11 Exercise 5.9.3 Exercise 5.10.3
Exercise 5.6.4 Exercise 5.8.4 Exercise 5.8.12 Exercise 5.10.4
Exercise 5.8.5 Exercise 5.8.13 Exercise 5.10.5
Exercise 5.8.6 Exercise 5.10.6
Exercise 5.8.7 Exercise 5.10.7
Exercise 5.8.8 Exercise 5.10.8
Section 6.2 Section 6.3 Section 6.4 Section 6.5 Section 6.6 Section 6.7
Exercise 6.2.1 Exercise 6.3.1 Exercise 6.3.10 Exercise 6.4.1 Exercise 6.5.1 Exercise 6.6.1 Exercise 6.7.1
Exercise 6.2.2 Exercise 6.3.2 Exercise 6.3.11 Exercise 6.4.2 Exercise 6.5.2 Exercise 6.6.2 Exercise 6.7.2
Exercise 6.2.3 Exercise 6.3.3 Exercise 6.3.12 Exercise 6.4.3 Exercise 6.5.3 Exercise 6.6.3 Exercise 6.7.3
Exercise 6.2.4 Exercise 6.3.4 Exercise 6.3.13 Exercise 6.4.4 Exercise 6.5.4 Exercise 6.6.4 Exercise 6.7.4
Exercise 6.2.5 Exercise 6.3.5 Exercise 6.3.14 Exercise 6.5.5 Exercise 6.6.5 Exercise 6.7.5
Exercise 6.2.6 Exercise 6.3.6 Exercise 6.3.15 Exercise 6.5.6 Exercise 6.6.6 Exercise 6.7.6
Exercise 6.2.7 Exercise 6.3.7 Exercise 6.3.16 Exercise 6.5.7 Exercise 6.6.7 Exercise 6.7.7
Exercise 6.3.8 Exercise 6.3.17 Exercise 6.6.8
Exercise 6.3.9
Section 7.2 Section 7.3 Section 7.4 Section 7.5
Exercise 7.2.1 Exercise 7.3.1 Exercise 7.4.1 Exercise 7.5.1 Exercise 7.5.8
Exercise 7.2.2 Exercise 7.3.2 Exercise 7.4.2 Exercise 7.5.2 Exercise 7.5.9
Exercise 7.2.3 Exercise 7.3.3 Exercise 7.4.3 Exercise 7.5.3 Exercise 7.5.10
Exercise 7.3.4 Exercise 7.4.4 Exercise 7.5.4 Exercise 7.5.11
Exercise 7.3.5 Exercise 7.5.5 Exercise 7.5.12
Exercise 7.3.6 Exercise 7.5.6
Exercise 7.3.7 Exercise 7.5.7
Section 7.6 Section 7.7 Section 7.8 Section 7.9 Section 7.10
Exercise 7.6.1 Exercise 7.7.1 Exercise 7.8.1 Exercise 7.9.1 Exercise 7.10.1
Exercise 7.6.2 Exercise 7.7.2 Exercise 7.8.2 Exercise 7.9.2 Exercise 7.10.2
Exercise 7.6.3 Exercise 7.7.3 Exercise 7.8.3 Exercise 7.9.3 Exercise 7.10.3
Exercise 7.6.4 Exercise 7.7.4 Exercise 7.8.4 Exercise 7.9.4 Exercise 7.10.4
Exercise 7.6.5 Exercise 7.7.5 Exercise 7.8.5 Exercise 7.9.5 Exercise 7.10.5
Exercise 7.7.6 Exercise 7.8.6 Exercise 7.9.6 Exercise 7.10.6
Exercise 7.7.7 Exercise 7.8.7 Exercise 7.10.7
Exercise 7.7.8 Exercise 7.8.8 Exercise 7.10.8
Exercise 7.7.9 Exercise 7.8.9 Exercise 7.10.9
Exercise 7.7.10 Exercise 7.8.10 Exercise 7.10.10
Exercise 7.7.11 Exercise 7.8.11 Exercise 7.10.11
Exercise 7.7.12 Exercise 7.8.12 Exercise 7.10.12
Exercise 7.7.13 Exercise 7.8.13 Exercise 7.10.13
Exercise 7.7.14 Exercise 7.10.14
Exercise 7.7.15 Exercise 7.10.15
Exercise 7.7.16
Section 8.2 Section 8.3 Section 8.4 Section 8.5 Section 8.6
Exercise 8.2.1 Exercise 8.3.1 Exercise 8.4.1 Exercise 8.5.1 Exercise 8.6.1
Exercise 8.2.2 Exercise 8.3.2 Exercise 8.4.2 Exercise 8.5.2 Exercise 8.6.2
Exercise 8.2.3 Exercise 8.3.3 Exercise 8.4.3 Exercise 8.5.3 Exercise 8.6.3
Exercise 8.2.4 Exercise 8.3.4 Exercise 8.4.4 Exercise 8.5.4 Exercise 8.6.4
Exercise 8.2.5 Exercise 8.3.5 Exercise 8.5.5 Exercise 8.6.5
Exercise 8.2.6 Exercise 8.3.6 Exercise 8.5.6 Exercise 8.6.6
Exercise 8.3.7 Exercise 8.6.7
Exercise 8.6.8
Exercise 8.6.9
Exercise 8.6.10
Section 9.2 Section 9.3 Section 9.4 Section 9.5 Section 9.6
Exercise 9.2.1 Exercise 9.3.1 Exercise 9.3.14 Exercise 9.4.1 Exercise 9.5.1 Exercise 9.5.14 Exercise 9.6.1
Exercise 9.2.2 Exercise 9.3.2 Exercise 9.3.15 Exercise 9.4.2 Exercise 9.5.2 Exercise 9.5.15 Exercise 9.6.2
Exercise 9.2.3 Exercise 9.3.3 Exercise 9.3.16 Exercise 9.4.3 Exercise 9.5.3 Exercise 9.5.16 Exercise 9.6.3
Exercise 9.2.4 Exercise 9.3.4 Exercise 9.3.17 Exercise 9.4.4 Exercise 9.5.4 Exercise 9.5.17 Exercise 9.6.4
Exercise 9.3.5 Exercise 9.3.18 Exercise 9.4.5 Exercise 9.5.5 Exercise 9.5.18 Exercise 9.6.5
Exercise 9.3.6 Exercise 9.3.19 Exercise 9.4.6 Exercise 9.5.6 Exercise 9.5.19 Exercise 9.6.6
Exercise 9.3.7 Exercise 9.3.20 Exercise 9.4.7 Exercise 9.5.7 Exercise 9.5.20 Exercise 9.6.7
Exercise 9.3.8 Exercise 9.3.21 Exercise 9.4.8 Exercise 9.5.8 Exercise 9.5.21 Exercise 9.6.8
Exercise 9.3.9 Exercise 9.3.22 Exercise 9.4.9 Exercise 9.5.9 Exercise 9.5.22 Exercise 9.6.9
Exercise 9.3.10 Exercise 9.3.23 Exercise 9.4.10 Exercise 9.5.10 Exercise 9.5.23
Exercise 9.3.11 Exercise 9.3.24 Exercise 9.4.11 Exercise 9.5.11 Exercise 9.5.24
Exercise 9.3.12 Exercise 9.3.25 Exercise 9.4.12 Exercise 9.5.12
Exercise 9.3.13 Exercise 9.3.26 Exercise 9.4.13 Exercise 9.5.13
Section 10.2 Section 10.3 Section 10.4 Section 10.5 Section 10.6 Section 10.7
Exercise 10.2.1 Exercise 10.3.1 Exercise 10.4.1 Exercise 10.5.1 Exercise 10.6.1 Exercise 10.7.1
Exercise 10.2.2 Exercise 10.3.2 Exercise 10.4.2 Exercise 10.5.2 Exercise 10.6.2 Exercise 10.7.2
Exercise 10.3.3 Exercise 10.4.3 Exercise 10.5.3 Exercise 10.6.3 Exercise 10.7.3
Exercise 10.3.4 Exercise 10.4.4 Exercise 10.5.4 Exercise 10.6.4 Exercise 10.7.4
Exercise 10.3.5 Exercise 10.4.5 Exercise 10.5.5 Exercise 10.6.5 Exercise 10.7.5
Exercise 10.3.6 Exercise 10.4.6 Exercise 10.5.6 Exercise 10.6.6 Exercise 10.7.6
Exercise 10.3.7 Exercise 10.4.7 Exercise 10.5.7 Exercise 10.6.7
Exercise 10.3.8 Exercise 10.4.8 Exercise 10.5.8 Exercise 10.6.8
Exercise 10.3.9 Exercise 10.4.9 Exercise 10.5.9 Exercise 10.6.9
Exercise 10.3.10 Exercise 10.4.10 Exercise 10.5.10 Exercise 10.6.10
Exercise 10.3.11 Exercise 10.4.11 Exercise 10.5.11 Exercise 10.6.11
Exercise 10.3.12 Exercise 10.4.12 Exercise 10.5.12 Exercise 10.6.12
Exercise 10.3.13 Exercise 10.5.13 Exercise 10.6.13
Exercise 10.3.14 Exercise 10.5.14 Exercise 10.6.14
Exercise 10.3.15 Exercise 10.5.15 Exercise 10.6.15
Exercise 10.3.16 Exercise 10.5.16 Exercise 10.6.16
Exercise 10.3.17 Exercise 10.5.17 Exercise 10.6.17
Exercise 10.3.18 Exercise 10.5.18 Exercise 10.6.18
Exercise 10.5.19 Exercise 10.6.19
Exercise 10.5.20 Exercise 10.6.20
Exercise 10.6.21
Exercise 10.6.22
Section 11.2 Section 11.3 Section 12.2 Section 12.3
Exercise 11.2.1 Exercise 11.3.1 Exercise 12.2.1 Exercise 12.3.1
Exercise 11.2.2 Exercise 11.3.2 Exercise 12.2.2 Exercise 12.3.2
Exercise 11.2.3 Exercise 11.3.3 Exercise 12.2.3 Exercise 12.3.3
Exercise 11.2.4 Exercise 11.3.4 Exercise 12.2.4 Exercise 12.3.4
Exercise 11.2.5 Exercise 11.3.5 Exercise 12.2.5 Exercise 12.3.5
Exercise 11.2.6 Exercise 11.3.6 Exercise 12.2.6 Exercise 12.3.6
Exercise 11.2.7 Exercise 11.3.7 Exercise 12.2.7
Exercise 11.2.8 Exercise 11.3.8 Exercise 12.2.8
Exercise 11.2.9 Exercise 12.2.9
Exercise 11.2.10 Exercise 12.2.10
Exercise 11.2.11 Exercise 12.2.11
Exercise 11.2.12
Exercise 11.2.13
Exercise 11.2.14
Exercise 11.2.15
Section 12.4 Section 12.5 Section 12.6 Section 12.7
Exercise 12.4.1 Exercise 12.5.1 Exercise 12.6.1 Exercise 12.6.9 Exercise 12.6.17 Exercise 12.7.1
Exercise 12.4.2 Exercise 12.5.2 Exercise 12.6.2 Exercise 12.6.10 Exercise 12.6.18 Exercise 12.7.2
Exercise 12.4.3 Exercise 12.5.3 Exercise 12.6.3 Exercise 12.6.11 Exercise 12.6.19
Exercise 12.4.4 Exercise 12.5.4 Exercise 12.6.4 Exercise 12.6.12 Exercise 12.6.20
Exercise 12.4.5 Exercise 12.6.5 Exercise 12.6.13 Exercise 12.6.21
Exercise 12.4.6 Exercise 12.6.6 Exercise 12.6.14 Exercise 12.6.22
Exercise 12.4.7 Exercise 12.6.7 Exercise 12.6.15 Exercise 12.6.23
Exercise 12.4.8 Exercise 12.6.8 Exercise 12.6.16
Section 13.2 Section 13.3 Section 13.4 Section 13.5
Exercise 13.2.1 Exercise 13.3.1 Exercise 13.4.1 Exercise 13.5.1
Exercise 13.2.2 Exercise 13.3.2 Exercise 13.4.2 Exercise 13.5.2
Exercise 13.2.3 Exercise 13.3.3 Exercise 13.4.3 Exercise 13.5.3
Exercise 13.2.4 Exercise 13.3.4 Exercise 13.4.4 Exercise 13.5.4
Exercise 13.2.5 Exercise 13.3.5 Exercise 13.4.5 Exercise 13.5.5
Exercise 13.2.6 Exercise 13.4.6 Exercise 13.5.6
Exercise 13.2.7
Exercise 13.2.8
Exercise 13.2.9
Section 13.6 Section 13.7 Section 13.8
Exercise 13.6.1 Exercise 13.7.1 Exercise 13.8.1
Exercise 13.6.2 Exercise 13.7.2 Exercise 13.8.2
Exercise 13.6.3 Exercise 13.7.3 Exercise 13.8.3
Exercise 13.6.4 Exercise 13.7.4 Exercise 13.8.4
Exercise 13.6.5
Exercise 13.6.6
Section 14.2 Section 14.3 Section 14.4 Section 14.5
Exercise 14.2.1 Exercise 14.3.1 Exercise 14.4.1 Exercise 14.5.1
Exercise 14.2.2 Exercise 14.3.2 Exercise 14.4.2 Exercise 14.5.2
Exercise 14.2.3 Exercise 14.3.3 Exercise 14.4.3 Exercise 14.5.3
Exercise 14.2.4 Exercise 14.3.4 Exercise 14.4.4 Exercise 14.5.4
Exercise 14.2.5 Exercise 14.3.5 Exercise 14.5.5
Exercise 14.2.6 Exercise 14.3.6 Exercise 14.5.6
Exercise 14.2.7 Exercise 14.3.7 Exercise 14.5.7
Exercise 14.2.8 Exercise 14.3.8 Exercise 14.5.8
Exercise 14.2.9 Exercise 14.3.9
Exercise 14.2.10
Exercise 14.2.11
Section 14.6 Section 14.7 Section 14.8 Section 14.9 Section 14.10
Exercise 14.6.1 Exercise 14.7.1 Exercise 14.8.1 Exercise 14.9.1 Exercise 14.10.1
Exercise 14.6.2 Exercise 14.7.2 Exercise 14.8.2 Exercise 14.9.2 Exercise 14.10.2
Exercise 14.6.3 Exercise 14.7.3 Exercise 14.8.3 Exercise 14.9.3 Exercise 14.10.3
Exercise 14.6.4 Exercise 14.7.4 Exercise 14.8.4 Exercise 14.9.4 Exercise 14.10.4
Exercise 14.6.5 Exercise 14.7.5 Exercise 14.8.5 Exercise 14.9.5 Exercise 14.10.5
Exercise 14.6.6 Exercise 14.7.6 Exercise 14.8.6 Exercise 14.9.6 Exercise 14.10.6
Exercise 14.7.7 Exercise 14.8.7 Exercise 14.9.7 Exercise 14.10.7
Exercise 14.7.8 Exercise 14.8.8 Exercise 14.9.8 Exercise 14.10.8
Exercise 14.7.9 Exercise 14.8.9 Exercise 14.9.9 Exercise 14.10.9
Exercise 14.7.10 Exercise 14.8.10 Exercise 14.9.10 Exercise 14.10.10
Exercise 14.7.11 Exercise 14.8.11 Exercise 14.9.11 Exercise 14.10.11
Exercise 14.7.12 Exercise 14.8.12

Haberman Fifth Edition Partial Differential Equations 2.3.8 Solutions

Source: https://stemjock.com/habermanpde5e.htm

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