Undergraduate Programme and Module Handbook 2024-2025

# Module MATH2011: COMPLEX ANALYSIS II

## Department: Mathematical Sciences

### MATH2011: COMPLEX 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 1 (MATH1061) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra 1 (MATH1071) and Analysis 1 (MATH1051) [the latter may be co-requisite].

#### Corequisites

- Analysis 1 (MATH1051) unless taken before.

#### Excluded Combination of Modules

- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Mathematical Methods in Physics (PHYS2611)

#### Aims

- To introduce the student to the theory of complex analysis.

#### Content

- Complex differentiation.
- Conformal Mappings.
- Metric Spaces.
- Series, Uniform Convergence.
- Contour Integrals, Calculus of Residues.
- Applications.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve unseen problems in Complex Analysis.
- Reproduce theoretical mathematics in the field of Complex Analysis to a level appropriate to Level 2.
- Have a knowledge and understanding of this subject demonstrated through one or more of the following topic areas: Complex Differentiation.
- Conformal Mappings.
- Metric Spaces.
- Contour integrals, calculus of residues.
- Series, Uniform Convergence.
- Applications of Complex analysis.

Subject-specific Skills:

- In addition students will have enhanced mathematical skills in the following areas: Spatial awareness.

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.
- Fortnightly 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 | 52 | 2 or 3 lectures per week on an alternating basis throughout Michaelmas and Epiphany terms and two lectures in week 21 | 1 Hour | 52 | |

Tutorials | 10 | Fortnightly for 21 weeks | 1 Hour | 10 | ■ |

Problems Classes | 9 | Fortnightly for 20 weeks | 1 Hour | 9 | |

Preparation and Reading | 129 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 hours | 100% | Yes |

#### Formative Assessment:

One written or electronic 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