Course content

Differentiability of functions of complex variables, Cauchy-Riemann equations, analytical and harmonic functions, complex integration, Cauchy's integral theorem and formula, analytical functions such as power series, zero points and poles, essential singularities, Laurent series, residy calculus, Fourier series, Fourier techniques for partial differential equations, separation of variables, wave equation, heating equation, Laplace equation.

Learning outcome

1. Knowledge. The student has knowledge about basic concepts within complex function theory. The student knows about Fourier series and the use of these in the study of partial differential equations. The student knows basic theory of partial differential equations. The student has a solid foundation for further studies of complex analysis and differential equations. The student has knowledge of the requirements for stringency in mathematical analysis.
2. Skills. The student has basic technical computational skills that are important in complex analysis and differential equations. The student can understand mathematical reasoning that combines different concepts and results from the course content. The student is able to derive simple results that are based on the academic content of the course.

Learning methods and activities

Lectures and mandatory exercises.

Compulsory assignments

• Exercises

Recommended previous knowledge

MA1101, MA1102, MA1103, MA1201 and MA1202. Alternatively TMA4401, TMA4413 and MA1103.

Course materials

Will be announced at the start of the course.

Credit reductions