Linear Equations Some real world applications and motivations, Gauss and Gauss-Jordan Elimination, LU factorization, Sensitivity and Conditioning, Overdetermined systems and 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. Conditions for extrema, local and global min and max. Unconstrained optimization, Broyden and CG methods. Constrained optimization, Comparison of root finding and optimization, Trust region methods, Homotopy methods and Embeddings.
Numerical Integration and Differentiation Numerical Quadrature, Numerical Differentiation, Richardson Extrapolation.
Mathematical Modeling of Real world problems Throughout the course examples of real world problems will be mathematically modeled and computationally solved.
A grade of "satisfactory" requires a working knowledge of how to apply numerical methods to solve real world mathematical problems. For higher grades additionally an understanding of the mathematical derivation of numerical methods and their properties will be required.
Heath provides a mathematically careful treatment of core topics.
A more hands on introduction to numerical computing in Matlab