Solving System of Linear Equations: Gaussian elimination, Jacobi and Gauss-Seidel iteration. Computing eigenvalues: power method, Jacobi’s method, LU algorithm. Polynomial interpolation: Lagrange interpolation, Hermite interpolation, least squares method. Numerical integration: Newton-Cotes formulae, composite formulae. Solution of equations by iteration: Simple iteration, Newton method.
Some least squares problems: fitting lines. rectangles, squares in the plane.
Fourier coefficients, Discrete Fourier transform (DFT), properties of the transform, the inverse of DFT. The Hadamard product, relation between the convolution product and the DFT. Trigonometric interpolation
Some applications of DFT, multiplication of polynomials, data smoothing, sound analysis, solving fourth-order boundary value problem of differential equation with DFT.
Algorithm and operating requirements of Fast Fourier transformation (FFT).
Gander, W., Hrebicek, J.: Solving Problems in Scientific Computing Using Maple and MATLAB. Springer, 1995.