This note covers the following
topics: Fourier Analysis, Least Squares, Normwise Convergence, The Discrete
Fourier Transform, The Fast Fourier Transform, Taylor Series, Contour
integration, Laurent series, Chebyshev series, Signal smoothing and root
finding, Differentiation and integration, Spectral methods, Ultraspherical
spectral methods, Functional analysis, Spectrum, Infinite-dimensional linear
algebra, Linear partial differential equations, Laplace's equation,
Riemann–Hilbert problems, Matrix-valued Riemann–Hilbert.
This lecture note
explains the following topics: Computer Arithmetic, Numerical Solution of Scalar
Equations, Matrix Algebra, Gaussian Elimination, Inner Products and Norms,
Eigenvalues and Singular Values, Iterative Methods for Linear Systems, Numerical
Computation of Eigenvalues, Numerical Solution of Algebraic Systems, Numerical
Solution of Ordinary Differential Equations, Numerical Solution of the Heat and
Wave Equations, Approximation and Interpolation, The Finite Element Method.
This note covers the following topics: Approximation and
Interpolation, Numerical Quadrature, Direct Methods of Numerical Linear Algebra,
Numerical solution of nonlinear systems and optimization, Numerical Solution of
Ordinary Differential Equations, Numerical Solution of Partial Differential
Equations and e Iterative Methods of Numerical Linear Algebra.