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Unit information: Methods of Complex Functions in 2015/16

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Unit name Methods of Complex Functions
Unit code MATH20001
Credit points 10
Level of study I/5
Teaching block(s) Teaching Block 1B (weeks 7 - 12)
Unit director Dr. Wiesner
Open unit status Not open

Analysis 1, Linear Algebra & Geometry 1 & Calculus 1



School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims


The unit gives an overview over methods for differentiating and integrating complex-valued functions, introduces the underlying theoretical results, and shows how they can be applied to problems in complex and real analysis.


The unit introduces functions of a complex variable, with a focus on holomorphic functions. It extends elementary calculus to functions of a complex variable, showing similarities and differences between the properties of two-dimensional vector fields and functions of a complex variable. The emphasis is on basic ideas and methods; theorems will be stated rigorously and the theory will be carefully developed, tut the emphasis is on methods rather than proofs.

Further information is available at:

Intended Learning Outcomes

Be familiar with and able to use the elementary properties of holomorphic functions of a complex variable. Find power series expansions, integrate holomorphic and functions with and without singularities. Master residue calculus and apply it to real-valued integrals.

Teaching Information

Lectures, problem sessions, homework problems and solutions

Assessment Information

100% examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Functions of a complex variable: Jerrold E. Marsden & Michael J. Hoffman Basic Complex Analysis, Edition 3, W. H. Freeman & Company, 1999