Wednesday, January 9, 2013

Farlow's Partial Differential Equations ToC

Table of Contents

The following is a table of contents for notes from Farlow's Partial Differential Equations for Scientists and Engineers.

  1. Introduction
  2. Diffusion Type Problems
  3. Diffusion Type Problems (Parabolic Equations)
  4. Boundary Conditions for Diffusion Type Problems
  5. Derivation of the Heat Equation
  6. Separation of Variables
  7. Transforming Nonhomogeneous BCs into Homogeneous BC
  8. Solving More Complicated Problems by Separation of Variables
  9. Transforming Hard Equations into Easier ones
  10. Solving Nonhomogenous PDEs (Eigenfunction Expansions)
  11. Integral Transforms (Sine and Cosine Transforms)
  12. The Fourier Series and Transform
  13. The Fourier Transform and its Applications to PDEs
  14. The Laplace Transform
  15. Duhamel's Principle
  16. The Convection Term in Diffusion Problems
  17. The One-Dimensional Wave Equation (Hyperbolic Equation)
  18. The D'Alembert Solution of the Wave Equation
  19. More on the D'Alembert Solution
  20. Boundary Conditions associated with the Wave Equation
  21. The Finite Vibrating String (Standing Waves)
  22. The Vibrating Beam (Fourth-Order PDE)
  23. Dimensionless Problems
  24. Classification of PDEs (Canonical Form of the Hyperbolic Equation)
  25. The Wave Equation in Two and Three Dimensions (Free space)
  26. The Finite Fourier Transforms (Sine and Cosine Transforms)
  27. Superposition
  28. First order Equations (Methods and Characteristics)
  29. Nonlinear First-Order Equations (Conservation Equations)

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