electiveHQ

Most problems in Applied Mathematics are modelled using a set of equations that can be written down but cannot be solved analytically. In this module we examine numerical methods that can be used to solve such problems with a computer. Practical computer lab sessions will cover the implementation of these methods using mathematical software (Python). No previous knowledge of computing is assumed. Topics and techniques discussed include but are not limited to the following list: - The programming environment: installing and running Python, version control with Git - Introduction to programming: functions, loops, logical statements, arrays, floating-point arithmetic, data storage, debugging code, documentation - Visualising results and datasets: plotting using Matplotlib and other visualisation software - Interpolation: Lagrange polynomials, Newton's divided-difference. Linear least squares - Root-finding for single-variable functions: Bracketing and Bisection, Newton–Raphson method. Error and reliability analyses for the Newton–Raphson method. - Solving ordinary differential equations (ODEs): Euler Method, Runge–Kutta method. Shooting methods. Error analysis. - Numerical integration: Midpoint, Trapezoidal and Simpson methods. Error analysis. - Matrices: condition numbers, inversion