Solutions to Applied Partial Differential Equations 5e
by Richard Haberman
115 of 765 listed exercises currently have solution PDFs.
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
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
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
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Section 4.2: Derivation of a Vertically Vibrating String
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Section 4.3: Boundary Conditions
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Section 4.4: Vibrating String with Fixed Ends
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Section 4.5: Vibrating Membrane
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Section 4.6: Reflection and Refraction of Electromagnetic and Acoustic Waves
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Section 5.3: Sturm-Liouville Eigenvalue Problems
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Section 5.4: Heat Flow in a Nonuniform Rod without Sources
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Section 5.5: Self-Adjoint Operators
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Section 5.5A: Self-Adjoint Operators Appendix
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Section 5.6: Rayleigh Quotient
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Section 5.7: Vibrations of a Nonuniform String
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Section 5.8: Boundary Conditions of the Third Kind
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Section 5.9: Large Eigenvalues (Asymptotic Behavior)
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Section 5.10: Approximation Properties
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Section 6.2: Finite Differences and Truncated Taylor Series
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Section 6.3: Heat Equation
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Section 6.4: Two-Dimensional Heat Equation
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Section 6.5: Wave Equation
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Section 6.6: Laplace's Equation
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Section 6.7: Finite Element Method
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Section 7.2: Separation of the Time Variable
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Section 7.3: Vibrating Rectangular Membrane
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Section 7.4: Statements and Illustrations of Theorems for the Eigenvalue Problem
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Section 7.5: Green's Formula, Self-Adjoint Operators, and Multidimensional Eigenvalue Problems
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Section 7.6: Rayleigh Quotient and Laplace's Equation
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Section 7.7: Vibrating Circular Membrane and Bessel Functions
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Section 7.8: More on Bessel Functions
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Section 7.9: Laplace's Equation in a Circular Cylinder
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Section 7.10: Spherical Problems and Legendre Polynomials
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Section 8.2: Heat Flow with Sources and Nonhomogeneous Boundary Conditions
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Section 8.3: Method of Eigenfunction Expansion with Homogeneous Boundary Conditions (Differentiating Series of Eigenfunctions)
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Section 8.4: Method of Eigenfunction Expansion Using Green's Formula (With or Without Homogeneous Boundary Conditions)
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Section 8.5: Forced Vibrating Membranes and Resonance
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Section 8.6: Poisson's Equation
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Section 9.2: One-Dimensional Heat Equation
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Section 9.3: Green's Functions for Boundary Value Problems for Ordinary Differential Equations
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Section 9.4: Fredholm Alternative and Generalized Green's Functions
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Section 9.5: Green's Functions for Poisson's Equation
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Section 9.6: Perturbed Eigenvalue Problems
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Section 10.2: Heat Equation on an Infinite Domain
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Section 10.3: Fourier Transform Pair
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Section 10.4: Fourier Transform and the Heat Equation
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Section 10.5: Fourier Sine and Cosine Transform: The Heat Equation on Semi-Infinite Intervals
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Section 10.6: Worked Examples Using Transforms
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Section 10.7: Scattering and Inverse Scattering
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Section 11.2: Green's Functions for the Wave Equation
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Section 11.3: Green's Functions for the Heat Equation
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Section 12.2: Characteristics for First-Order Wave Equations
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Section 12.3: Method of Characteristics for the One-Dimensional Wave Equation
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Section 12.4: Semi-Infinite Strings and Reflections
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Section 12.5: Method of Characteristics for a Vibrating String of Fixed Length
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Section 12.6: The Method of Characteristics for Quasilinear Partial Differential Equations
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Section 12.7: First-Order Nonlinear Partial Differential Equations
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Section 13.2: Properties of the Laplace Transform
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Section 13.3: Green's Functions for Initial Value Problems for Ordinary Differential Equations
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Section 13.4: A Signal Problem for the Wave Equation
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Section 13.5: A Signal Problem for a Vibrating String of Finite Length
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Section 13.6: The Wave Equation and Its Green's Function
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Section 13.7: Inversion of Laplace Transforms Using Contour Integrals in the Complex Plane
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Section 13.8: Solving the Wave Equation Using Laplace Transforms (with Complex Variables)
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Section 14.2: Dispersive Waves and Group Velocity
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Section 14.3: Wave Guides
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Section 14.4: Fiber Optics
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Section 14.5: Group Velocity II and the Method of Stationary Phase
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Section 14.6: Slowly Varying Dispersive Waves (Group Velocity and Caustics)
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Section 14.7: Wave Envelope Equations (Concentrated Wave Number)
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Section 14.8: Stability and Instability
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Section 14.9: Singular Perturbation Methods: Multiple Scales
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Section 14.10: Singular Perturbation Methods: Boundary Layers Method of Matched Asymptotic Expansions
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