Throughout the course examples of real world problems will be mathematically modeled and computationally solved.
Linear Equations Some real world applications and motivations, Systems of linear equations and LU factorization, Sensitivity and Conditioning, Overdetermined systems, Linear Least Squares, methods for QR factorisation, Linear Regression, Data Fitting and Interpolation, Eigenvalue Problems, methods for Eigen and SVD factorizations.
Nonlinear Equations and Optimization Basic 1D search methods with and without derivatives. Convergence rates and stopping criteria, Multidimensional root finding, Newton and Gauss-Newtons methods. Conditions for extrema, local and global min and max. Unconstrained optimization.
Numerical Quadrature (Integration) and Differentiation Numerical Quadrature, Numerical Differentiation, Richardson Extrapolation.
Numerical solution of Differential Equations Initial value problems, boundary value problems, partial differential equations.