Mathematics: Complex Analysis 1

In this course, you will learn the basics of complex analysis – a central area of mathematics with many applications. You already have a firm background in the theory of differentiable functions in a real variable. Differentiable functions of a complex variable have many unexpected properties. For instance, if a function is differentiable one time in the complex sense, then it is differentiable any number of times.

Topics include

• Analytic functions and the Cauchy-Riemann equations
• Power series, exponential and logarithmic functions
• Contour integrals and Cauchy’s theorems
• Meromorphic functions and residue calculus
• Harmonic functions and the maximum principle

The course is an alternative-compulsory course in the Bachelor’s programme in Mathematics at Lund University. You can also take it as an elective in other science programmes, or as a stand-alone course.

You will learn through a mix of lectures and seminars. The seminars focus on selected exercises and require active participation and preparation.

Assessment includes a written exam and an oral exam at the end of the course. The oral exam is only available to students who pass the written exam. Re-examinations are offered shortly after the regular ones.

This course gives you powerful and versatile tools for further studies in mathematics, science, or engineering. Complex analysis is used in many fields – from physics and signal processing to fluid dynamics and data science. You will also develop skills in logical reasoning, problem-solving, and mathematical communication – valuable in both academic and professional settings.

Prerequisites

The course requires basic knowledge in analysis in one and several variables and linear algebra, corresponding to, for example: MATA31Analysis in One Variable, 15 credits MATA32 Algebra and Vector Geometry, 7,5 credits MATB21 Analysis in Several Variables, 7,5 credits MATB23 Analysis in Several Variables 2, 7,5 credits MATB32 Linear Algebra, 7,5 credits Additionally, knowledge equivalent to MATB33 Mathematics: Introduction to Higher Analysis, 7.5 credits, or FYSB21 : Mathematical Methods for Vibrations, Waves and Diffusion, 7.5 credits, is required.

Selection criteria

Seats are allocated according to the following: The general average (GPA) of your higher secondary school leaving certificate: 34 %, The Swedish national university aptitude test: 34 %, number of previous ECTS at the application deadline (up to 165): 32 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.