FYSS7301 Complex Analysis (5 cr)

• Complex numbers and elementary functions of complex variables

• Derivative and analyticity of a function of complex variables

• Contour integration in the complex plane

• Cauchy’s theorem and Cauchy’s integral formulae

• Taylor series and analytic continuation

• Laurent series, classification of singularities and calculation of residues

• Residue theorem, with various applications in contour integrals in the complex plane, summation of series and infinite products 

After this course, the student will

• knows how to deal with functions of complex variables

• understands the concept of analyticity of a function and can apply this especially in contour integrals in the complex plane

• knows the concept of analytical continuation

• be able to form Laurent series of functions of complex variables, understands the classification of singularities and is able to apply these in finding the residues

• knows what is the residue theorem and is able to apply this in contour integrals in the complex plane and also in summation of series 

• MATP211 Calculus 1

• MATA181-MATA182 Vektoricalculus 1 and 2 or similar.  

Lecture notes by Kari J. Eskola