BDP Ch. 10 review sheet

BDP Ch. 10 review sheet - Be able to solve Boundary Value...

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Boyce/9ed/Ch10 Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 9e 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 (p. 596) Important Skills:
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Unformatted text preview: Be able to solve Boundary Value Problems. (Ex. 1 - 4, p. 579 - 580) Know how to compute Fourier Series for functions. (Ex. 1 - 3, p. 588 - 591) Understand the convergence properties of Fourier Series and Gibbs Phenomenon. (Ex. 1, p. 597) Know the difference between even and odd functions and the ramifications on their Fourier Series. (Ex. 1 & 2, p. 605 - 607) Be able to use Separation of Variables to solve heat conduction problems, (Ex. 1, p.616; Ex. 1, p. 623, and Ex. 2, p. 626) as well as wave propagation problems. (Ex. 1, p. 635) Know the difference between Dirichlet and Neumann problems. (p. 647) Be able to apply Separation of Variables to solve Laplace's equation. (Ex. 1, p. 650) Relevant Applications: Acoustics, Scalar Electromagnetic Propagation, Chemical or Thermal Diffusion...
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