Undergraduate Programme and Module Handbook 2024-2025

# Module MATH2051: NUMERICAL ANALYSIS II

## Department: Mathematical Sciences

### MATH2051: NUMERICAL ANALYSIS II

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071) and Analysis I (MATH1051) and (Programming I (MATH1587) and Dynamics I (MATH1607) 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