This course is an introduction to complex analysis in one variable. The topics of the course include complex numbers and topology in the complex plane, analytic and harmonic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral formula, power series and Laurent series, roots and singularities, residue theory and Cauchy's residue theorem, the argument principle and conformal mappings – in particular Möbius mappings. The course also treats application of the presented theory.
The course requires courses in Mathematics minimum 60 ECTS or least two years of university studies and in both cases a course in multivariable calculus, minimum 7,5 ECTS or equivalent. Proficiency in English equivalent to the level required for basic eligibility for higher studies. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.
Please note: This application round is intended only for applicants within the EU/EEA and Switzerland.
Online application service in Swedish will open 15 September 2023 at 13:00 CET.
Application deadline is
16 October 2023. How to apply
Application and tuition fees
As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.