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Durham University

Faculty Handbook Archive

Archive Module Description

This page is for the academic year 2019-20. The current handbook year is 2020-21

Department: Mathematical Sciences

MATH2051: NUMERICAL ANALYSIS II

Type Open Level 2 Credits 20 Availability Available in 2019/20 Module Cap Location Durham

Prerequisites

  • Calculus and Probability I (MATH1061) and Linear Algebra I (MATH1071) and Analysis I (MATH1051) and (Programming and Dynamics I (MATH1041) or Discovery Skills in Physics (PHYS1101) or Introduction to Programming (COMP1011) or Computational Thinking (COMP1051)); Analysis I (MATH1051) may be taken as a co-requisite.

Corequisites

  • Analysis I (MATH1051) unless taken before.

Excluded Combination of Modules

  • Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571)

Aims

  • Numerical analysis has the twin aims of producing efficient algorithms for approximation, and the analysis of the accuracy of these algorithms.
  • The purpose of this module is to introduce the basic framework of the subject, enabling the student to solve a variety of problems and laying the foundation for further investigation of particular areas in the Levels 3 and 4.

Content

  • Introduction: The need for numerical methods.
  • Statement of some problems which can be solved by techniques described in this module.
  • What is Numerical Analysis? Non-linear equations.
  • Errors.
  • Polynomial interpolation.
  • Least squares approximation.
  • Numerical differentiation.
  • Numerical integration.
  • Linear equations.
  • Practical sessions.

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Number Analysis.
  • have an awareness of the abstract concepts of theoretical mathematics in the field of Numerical Analysis.
  • have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Non-linear equations.
  • Errors.
  • Polynomial interpolation.
  • Least squares approximation.
  • Numerical differentiation and integration.
  • Matrix equations.
Subject-specific Skills:
  • In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling, Computation.
Key Skills:

    Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

    • Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
    • Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
    • Tutorials provide active engagement and feedback to the learning process.
    • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

    Teaching Methods and Learning Hours

    Activity Number Frequency Duration Total/Hours
    Lectures 42 2 per week for 21 weeks 1 Hour 42
    Tutorials 10 Fortnightly for 21 weeks 1 Hour 10
    Problems Classes 9 Fortnightly for 20 weeks 1 Hour 9
    Computer Practicals 20 Weekly for 20 weeks 1 Hour 20
    Preparation and Reading 119
    Total 200

    Summative Assessment

    Component: Examination Component Weighting: 90%
    Element Length / duration Element Weighting Resit Opportunity
    Written examination 3 hours 100% yes
    Component: Continuous assessment Component Weighting: 10%
    Element Length / duration Element Weighting Resit Opportunity
    A computer based assessment every three weeks one week 100% yes

    Formative Assessment:

    One written assignment to be handed in every third lecture in the first 2 terms. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment.


    Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University