ch10 - • Know how to compute Fourier Series for...

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Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 8e Chapter 10: Partial Differential Equations and Fourier Series Definitions: Boundary Conditions, Two-Point Boundary Value Problem (BVP) homogeneous, Nonhomogeneous Eigenvalues, Eigenfunctions Fourier Series; Periodic, Fundamental Period Inner Product, Orthogonal, Mutually Orthogonal Piecewise Continuous Even and Odd Function Fourier Sine Series and Fourier Cosine Series Heat or Diffusion Equation Thermal diffusivity Wave Equation; Natural Frequencies, Natural Mode, Wavelength Laplace's Equations (Potential Equation) Potential equation Dirichlet and Neumann Problems Theorems: Theorem 10.3.1: Convergence of Fourier Series Important Skills: Be able to solve Boundary Value Problems. (Examples 1-4, p.571)
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Unformatted text preview: • Know how to compute Fourier Series for functions. (Examples 1-3, p.580) • Understand the convergence properties of Fourier Series and Gibbs Phenomenon. (Example 1, p.589) • Know the difference between even and odd functions and the ramifications on their Fourier Series (Examples 1 & 2, p.597) • Be able to use Separation of Variables to solve heat conduction problems, (Example 1 & 2, p.608, and Example 1, p.515) as well as wave propagation problems. (Example 1, p.627) • Know the difference between Dirichlet and Neumann problems, p.639. • Be able to apply Separation of Variables to solve Laplace's equation. (Example 1, p.642) Relevant Applications: • Acoustics, Scalar Electromagnetic Propagation, Chemical or Thermal Diffusion...
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