Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title NUMERICAL METHODS
Code MATH266
Coordinator Dr I Thompson
Mathematical Sciences
Ian.Thompson@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2014-15 Level Two Second Semester 15

Aims

To provide an introduction to the main topics in Numerical Analysis and their relation to other branches of Mathematics


Learning Outcomes

After completing the module students should be able to:

• write simple mathematical computer programs in Maple,

• understand the consequences of using fixed-precision arithmetic,

• analyse the efficiency and convergence rate of simple numerical methods,

• develop and implement algorithms for solving nonlinear equations,

• develop quadrature methods for numerical integration,

• apply numerical methods to solve systems of linear equations and to calculate eigenvalues and eigenvectors,

• solve boundary and initial value problems using finite difference methods.


Syllabus
36 

• Elements of computer programming: variables, conditionals, loops, arrays and procedures.

• Rounding, error propagation and cancellation.

• Solving nonlinear equations; bisector, false position, secant and Newton-Raphson methods.

• Newton-Cotes and Gaussian quadrature.

• Numerical methods for linear systems: Gaussian elimination, LU factorisation and iterative methods.

• Norms and conditioning.

• Calculation of eigenvalues and eigenvectors via the power algorithm and the inverse power algorithm.

• Numerical solution of ordinary and partial differential equations by finite difference methods.

• Numerical solution of Fredholm integral equations.


Teaching and Learning Strategies

See http://www.liv.ac.uk/media/livacuk/maths/currentstudents/docs/LT.pdf


Teaching Schedule
  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 36

   12

       48
Timetable (if known)              
Private Study 102
TOTAL HOURS 150

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Answer all of Section A and THREE questions from Section B. The marks shown against questions, or parts of questions, indicate their relative weight. Section A carries 55% of the available marks.  2.5 hours  Second semester  90  Standard University Policy      
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homeworks    Second semester  10  None: exemption approved November 2007  University Policy applies - see Department/School handbook for details.  This work is not marked anonymously.  

Recommended Texts

W. Gautschi, Numerical Analysis, Birkhauser (2012).

R.L. Burden and J.D. Faires, Numerical Analysis, PWS-Kent.