On this webpage you will find my solutions to "Partial Differential Equations for Scientists and Engineers" by Stanley Farlow. 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: Introduction
- Lesson 1: Introduction to Partial Differential Equations
- Chapter 2: Diffusion-Type Problems
- Lesson 2: Diffusion-Type Problems (Parabolic Equations)
- Lesson 3: Boundary Conditions for Diffusion-Type Problems
- Lesson 4: Derivation of the Heat Equation
- Lesson 5: Separation of Variables
- Lesson 6: Transforming Nonhomogeneous BCs into Homogeneous Ones
- Lesson 7: Solving More Complicated Problems by Separation of Variables
- Lesson 8: Transforming Hard Equations into Easier Ones
- Lesson 9: Solving Nonhomogeneous PDEs (Eigenfunction Expansions)
- Lesson 10: Integral Transforms (Sine and Cosine Transforms)
- Lesson 11: The Fourier Series and Transform
- Lesson 12: The Fourier Transform and its Application to PDEs
- Lesson 13: The Laplace Transform
- Lesson 14: Duhamel's Principle
- Lesson 15: The Convection Term ux in Diffusion Problems
- Chapter 3: Hyperbolic-Type Problems
- Lesson 16: The One-Dimensional Wave Equation (Hyperbolic Equations)
- Lesson 17: The D'Alembert Solution of the Wave Equation
- Lesson 18: More on the D'Alembert Solution
- Lesson 19: Boundary Conditions Associated with the Wave Equation
- Lesson 20: The Finite Vibrating String (Standing Waves)
- Lesson 21: The Vibrating Beam (Fourth-Order PDE)
- Lesson 22: Dimensionless Problems
- Lesson 23: Classification of PDEs (Canonical Form of the Hyperbolic Equation)
- Lesson 24: The Wave Equation in Two and Three Dimensions (Free Space)
- Lesson 25: The Finite Fourier Transforms (Sine and Cosine Transforms)
- Lesson 26: Superposition (The Backbone of Linear Systems)
- Lesson 27: First-Order Equations (Method of Characteristics)
- Lesson 28: Nonlinear First-Order Equations (Conservation Equations)
- Lesson 29: Systems of PDEs
- Lesson 30: The Vibrating Drumhead (Wave Equation in Polar Coordinates)
- Chapter 4: Elliptic-Type Problems
- Lesson 31: The Laplacian (an intuitive description)
- Lesson 32: General Nature of Boundary-Value Problems
- Lesson 33: Interior Dirichlet Problem for a Circle
- Lesson 34: The Dirichlet Problem in an Annulus
- Lesson 35: Laplace's Equation in Spherical Coordinates (Spherical Harmonics)
- Lesson 36: A Nonhomogeneous Dirichlet Problem (Green's Functions)
- Chapter 5: Numerical and Approximate Methods
- Lesson 37: Numerical Solutions (Elliptic Problems)
- Lesson 38: An Explicit Finite-Difference Method
- Lesson 39: An Implicit Finite-Difference Method (Crank-Nicolson Method)
- Lesson 40: Analytic versus Numerical Solutions
- Lesson 41: Classification of PDEs (Parabolic and Elliptic Equations)
- Lesson 42: Monte Carlo Methods (An Introduction)
- Lesson 43: Monte Carlo Solutions of Partial Differential Equations
- Lesson 44: Calculus of Variations (Euler-Lagrange Equations)
- Lesson 45: Variational Methods for Solving PDEs (Method of Ritz)
- Lesson 46: Perturbation Method for Solving PDEs
- Lesson 47: Conformal-Mapping Solution of PDEs
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Lesson 5 |
Lesson 6 |
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| Lesson 7 |
Lesson 8 |
Lesson 9 |
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| Lesson 10 |
Lesson 11 |
Lesson 12 |
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| Lesson 13 |
Lesson 14 |
Lesson 15 |
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| Lesson 16 |
Lesson 17 |
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Lesson 19 |
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Problem 4 |
| Lesson 20 |
Lesson 21 |
Lesson 22 |
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Lesson 24 |
Lesson 25 |
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| Lesson 26 |
Lesson 27 |
Lesson 28 |
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| Lesson 29 |
Lesson 30 |
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Problem 6 |
| Lesson 31 |
Lesson 32 |
Lesson 33 |
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| Lesson 34 |
Lesson 35 |
Lesson 36 |
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| Lesson 37 |
Lesson 38 |
Lesson 39 |
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| Lesson 40 |
Lesson 41 |
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| Lesson 42 |
Lesson 43 |
Lesson 44 |
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| Lesson 45 |
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Lesson 47 |
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