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Linear Algebraic Equations, Matrices, and Eigenvalues. Matrix Theory. Scalar ODEs I: Homogeneous Problems. Scalar ODEs II: Nonhomogeneous Problems. Linear Systems of ODEs. Geometry, Calculus, and Other Tools. Integral Theorems, Multiple Integrals, and Applications. Numerical Methods I. Fourier Series. Partial Differential Equations Models. Separation of Variables for PDEs. Numerical Methods II. Optimization. Calculus of Variations. Functions of a Complex Variable. Conformal Mappings and the Laplace Equation. Integral Transform Methods. Nonlinear Ordinary Differential Equations. Key Terms. Reference. Appendices. Index. |