Numerical Methods

Full course description

Numerical methods are techniques for solving problems from continuous mathematics (calculus and linear algebra) 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 methods for core problems of continuous mathematics, namely the solution of algebraic equations and differential equations, interpolating data by polynomials, numerically estimating derivatives and integrals, approximating functions by polynomials and trigonometric 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.