An Introduction to Partial Differential Equations with MATLAB

摘要: Introduction What are Partial Differential Equations? PDEs We Can Already Solve Initial and Boundary Conditions Linear PDEs--Definitions PDEs--The Principle of Superposition Separation Variables for Linear, Homogeneous Eigenvalue Problems The Big Three Second-Order, with Constant Coefficients Heat Equation Diffusion Wave the Vibrating String Equations Laplace's Equation--The Potential Using to Fourier Series Properties Sine Cosine Series, Continued Series---Proof Pointwise Convergence Completeness Solving a Finite Rod on Rectangular Domain Nonhomogeneous Characteristicsfor First-Order Variable D'Alembert's Solution Infinite Characteristics Semi-Infinite General Second-Order Integral Transforms Laplace Transform Distributions, Dirac Delta Function Generalized Proof Formula Bessel Functions Orthogonal Polynomials Special Their Ordinary Points Power Solutions Chebyshev, Hermite Legendre Method Frobenius Laguerre Interlude: Gamma Recap: A List Sturm-Liouville Theory Regular Periodic Singular Self-Adjoint Mean-Square or L2 Norm in Mean Parseval's Equality Higher Dimensions Dimensions: Examples Derivations Rectangle Multiple Polar Coordinates Poisson's Spherical Postlude: Eigenvalues Eigenfunctions Operator Green's Identities Laplacian ODEs Elliptic (I): Two (II): Helmholtz Function's Evolution Numerical Methods Difference Approximations Spectral Element References Uniform Differentiation Integration Important Theorems: Limits, Derivatives, Integrals, Interchange Operations Existence Uniqueness Theorems Menagerie MATLAB Code Figures Exercises Answers Selected