Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: DTS104TC
Module Title: Numerical Methods
Module Level: Level 1
Module Credits: 2.50
Academic Year: 2020/21
Semester: SEM2
Originating Department: Shool of AI and Advanced Computing
Pre-requisites: N/A
   
Aims
To provide an understanding of the basis of numerical computation and its connection to other subjects.

To use numerical methods in solving mathematical problems
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 
In this module, we study the following numerical methods and how they may be applied in different contexts:-

(a)Solution of non-linear equations in one variable and multi-variables, Newton-Raphson, Jacobian Matrix and error behaviour and its consequences. (2 leactures)

(b)Norms, Spectral Radius, Gauss elimination and LU factorization for solving systems of equations. Partial pivoting. (2 lectures)

(c)Iterative methods(Gauss Seidel, Jacobi, SOR), convergence of linear iterative methods. (2 lectures)

(d)The eigenvalue problem: the power method and inverse power method (2 lectures)

(e)Ordinary and partial differential equations, multi-step methods, finite difference methods. (2 lectures)

(f)Lagrange interpolation and quadrature methods: trapezoidal rule, Simpson’s rule, Gaussian quadrature; numerical solution of initial value problems and Fredholm integral equations. (3 lectures)



The emphasis is to equip students with the knowledge to obtain numerical solutions to mathematical problems that otherwise may not be solved analytically
Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 13    13    49  98  75 

Assessment

Sequence Method % of Final Mark
1 Final Exam 80.00
2 Class Test 1 5.00
3 Class Test 2 5.00
4 Coursework 10.00

Module Catalogue generated from SITS CUT-OFF: 6/3/2020 1:31:59 AM