Mathematics: Complex Analysis 1

Education facts

Code: MATC21

<p>The course provides a solid introduction to the theory of analytic functions and provides concepts and methods from complex analysis that are important for further studies in mathematics and other areas of science.</p><p>The course treats basic theory of analytic functions:</p> <ul> <li>Elementary properties of analytic functions in one variable. Complex differentiability and Cauchy-Riemann equations. Calculation rules. Elementary examples of analytic functions: power series expansions, exponential functions, branches of logarithms, and functions defined by these calculation rules.</li> <li>Contour integrals in the complex plane. Cauchy’s integral theorem and integral formula. Existence of a primitive function and local power series expansion of analytic functions. Cauchy estimates, Liouville’s theorem, and the fundamental theorem of algebra.</li> <li>Theory of meromorphic functions: singular points, Laurent series expansion and the residue theorem. Residue calculus.</li> <li>Further elements of the theory of holomorphic functions such as argument principle, Rouché’s theorem, and open mapping property.</li> <li>Harmonic functions. Regularity, existence of harmonic conjugate, mean value property, maximum principle, Poisson integrals.</li> </ul>

Entry requirements

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.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Mathematics: Complex Analysis 1

  Lund University

  Start date: 2 November 2026

  End date: 17 January 2027

  Pace of study: 50 %