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 for Applied Mathematics
Code MATH226
Coordinator Dr I Thompson
Mathematical Sciences
Ian.Thompson@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2023-24 Level 5 FHEQ Second Semester 15

Aims

To provide an introduction to the main topics in numerical analysis and their relation to other branches of Mathematics.

To demonstrate how these ideas can be implemented using a high-level programming language, leading to accurate, efficient mathematical algorithms.

Learning Outcomes

(LO1) To strengthen students’ knowledge of scientific programming, building on the ideas introduced in MATH111.

(LO2) To provide an introduction to the foundations of numerical analysis and its relation to other branches of Mathematics.

(LO3) To introduce students to theoretical concepts that underpin numerical methods, including fixed point iteration, interpolation, orthogonal polynomials and error estimates based on Taylor series.

(LO4) To demonstrate how analysis can be combined with sound programming techniques to produce accurate, efficient programs for solving practical mathematical problems.

(S1) Numeracy

(S2) Problem solving skills

Syllabus
 

• Review of the main programming concepts needed for numerical methods: variables, conditionals, loops, arrays and procedures.
• Rounding, error propagation and cancellation.
• Root finding algorithms for nonlinear functions; bisector, false position, secant and Newton-Raphson methods.
• Interpolation by polynomials
• Lagrange and Newton formulae
• Chebyshev nodes
• Alternative interpolation schemes using cubic splines.
• Newton-Cotes and Gaussian quadrature.
• Implementation of numerical methods in a high-level programming language.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH101 Calculus I 2022-23; MATH102 CALCULUS II 2022-23; MATH103 Introduction to Linear Algebra 2022-23 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment open book and remote, on Möbius  60    20       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
class test open book and remote  0    10       
Group Project  0    20       
Individual Project  0    50