Full course description
Numerical mathematics is the art of solving mathematical problems with the aid of a digital computer. In this course, we will cover the fundamental concepts of numerical mathematics, including the floating-point representation of real numbers, truncation and round off errors, iterative methods and convergence. We will study the simplest and most important algorithms for core problems of numerical mathematics, namely the solution of algebraic equations, interpolating data by polynomials and splines, numerically estimating derivatives and integrals, solving differential equations, approximating functions by polynomials and Fourier series, solving systems of linear algebraic equations and computing eigenvalues. There will be a strong practical component, with students being expected to write their own numerical code and test the performance and suitability of different methods on various problems.
Desired prior knowledge: calculus, linear algebra
Faires & Burden, "Numerical Methods".