Numerical Analysis - MAT00041H

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  • Department: Mathematics
  • Credit value: 20 credits
  • Credit level: H
  • Academic year of delivery: 2022-23

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

Pre-requisite modules:

Calculus (MAT00001C) and Algebra (MAT0010C), or

Mathematics for the Sciences I (MAT00007C) and Mathematics for the Sciences II (MAT00008C).

Plus Mathematical Skills II (MAT00027I), or sufficient programming skills obtained otherwise (e.g., through the Mathematics and Computer Science Combined programme)

Module will run

Occurrence Teaching period
A Autumn Term 2022-23 to Spring Term 2022-23

Module aims

  • To introduce numerical approximation techniques for solving standard problems in Mathematics, and explain when and why they work.
  • To derive some of these techniques rigorously from first principles.
  • To explain how (packaged) computer software is able to produce numerical solutions, and to enable a judgement of whether the results are reliable.
  • To provide opportunities for implementing numerical techniques on a computer.

Module learning outcomes

Subject content

  • Derive elementary numerical methods from first principles.
  • Apply the numerical methods discussed to simple examples, using pen and paper (i.e., without the help of a computer).
  • Implement numerical methods using computer software, and apply them in examples.
  • Compute error estimates for simple numerical methods.
  • Judge under which circumstances a given numerical method is reliable.

Academic and graduate skills

  • Understand some elements of computer programming
  • Understand the concept of computer algorithms

Module content

 

Syllabus

  • Numerical errors
  • Root finding for functions of one variable
  • Root finding for functions of several variables
  • Solving linear equation systems
  • Interpolation by polynomials
  • Numerical integration
  • Numerical differentiation
  • Initial value problems for ordinary differential equations
  • Boundary value problems for ordinary differential equations
  • Partial differential equations

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 60
Coursework - extensions not feasible/practicable 20
Essay/coursework 2.5
Essay/coursework 2.5
Essay/coursework 2.5
Essay/coursework 2.5
Essay/coursework 2.5
Essay/coursework 2.5
Essay/coursework 2.5
Essay/coursework 2.5

Special assessment rules

None

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

R L Burden and J D Faires, Numerical Analysis, Brooks/Cole