### General Information

Course Code | X_400386 |
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Credits | 6 EC |

Period | P4+5 |

Course Level | 300 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. O. Fabert |

Examiner | dr. O. Fabert |

Teaching Staff |
dr. O. Fabert |

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods | Seminar, Lecture |
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Target audiences

This course is also available as:

### Course Objective

- The student can decide whether a complex function is analytic (=differentiable in the complex sense) and knows the connection with the

Cauchy-Riemann equations.

- She can do computations with elementary functions such as

exp/log/sin/cos over the complex numberts.

- She can integrate analytic functions along a path on the complex

plane, using the theorem of Cauchy-Goursat and its corollaries.

- She can compute Laurent series and determine the type of singularities

of analytic functions.

- She can compute integrals of complex functions using the residue

theorem and knows how to use this to compute integrals of real

functions.

### Course Content

In complex analysis one generalizes the standard concepts of realanalysis such as differentiation and integration from the real line to

the complex plane. Although these generalizations arise very naturally

and all standard examples of functions are also differentiable in the

complex sense, the latter property surprisingly turns out to be much

stronger. As a consequence, complex differentiable functions immediately

obey very special properties which we are going to explore in this

course. In particular, they lead to completely new and efficient methods

for computing integrals of real functions.

During the lectures the following topics will be treated:

- complex differentiation and the Cauchy-Riemann equations

- complex integration and the theorem of Cauchy-Goursat

- elementary properties of complex differentiable functions

- singularities, Laurent series and the residue theorem

- application to integrals of real functions

### Teaching Methods

Lecture (2 hours) and tutorial class (2 hours)### Method of Assessment

Two written exams (40%+40%) and two hand-in homeworks (10%+10%). Theretake exam counts for 100% of the final grade.

### Literature

Churchill, R. V., & Brown, J. W.: Complex variables and applications.Ninth edition, 2014, McGraw-Hill Book Co., New York