Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH208
Module Title: Numerical Analysis
Module Level: Level 2
Module Credits: 5.00
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims To provide an understanding of the basis of numerical computation and its connection to other subjects. To provide an introduction to the main topics of Numerical Analysis with the central theme on the solution of linear algebraic equations.
 Learning outcomes A. Apply numerical methods in a number of different contexts.B. Solve systems of linear and nonlinear algebraic equations to specified precision.C. Compute eigenvalues and eigenvectors by the power method.D. Solve boundary value and initial problems to finite precision.E. Develop quadrature methods for numerical integration.
 Method of teaching and learning This module will be delivered by a combination of formal lectures and tutorials.
 Syllabus (a)Solution of non-linear equations in one variable and multi-variables, Newton-Raphson, Jacobian Matrix and error behaviour. (b)Norms, Spectral Radius, Gauss elimination and LU factorization. Partial pivoting. (c)Iterative methods(Gauss Seidel, Jacobi, SOR), convergence of linear iterative methods. (d)The eigenvalue problem: the power method and inverse power method (e)Ordinary and partial differential equations, multi-step methods, finite difference methods. (f)Lagrange interpolation and quadrature methods: trapezoidal rule, Simpsonâ€™s rule, Gaussian quadrature; numerical solution of initial value problems and Fredholm integral equations.
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark
 Module Catalogue generated from SITS CUT-OFF: 12/16/2019 7:42:00 AM