This module builds upon the core numerical techniques students learned in Year 2.
It further develops theoretical foundations of practical algorithms for approximating functions and data (Lagrange and Hermite interpolation, adaptive approximation), for solving systems of nonlinear equations (Newton's method and its variants, fixed-point methods), for efficient evaluation of integrals (Romberg, Gaussian, and adaptive quadratures), and for numerical solution of ordinary differential equations (Taylor series method, Runge-Kutta methods, multistep methods). Theoretical and practical aspects of numerical algorithms will be illustrated with MATLAB examples, but no programming will be required.
Learning Outcomes
By the end of the module students should be able to:
Construct Lagrange and Hermite interpolants for given functions or data.
Implement a range of iterative techniques for solving systems of nonlinear equations.
Solve ordinary differential equations numerically using a range of methods.
Students taking the module at Level M will explore the subject beyond the taught syllabus.
Assessment
27686-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions
Assessment: 90% on one 1.5-hour examination; 10% from coursework and/or class tests.