Lecturer(s)


ENGLIŠ Miroslav, prof. RNDr. DrSc.

Course content

1. Complex numbers, analytic functions  algebraic and goniometric form of a complex number; curves and domains in the complex plane; derivatives of functions of complex variable; analytic functions; CauchyRiemann equations; exponential and trigonometric functions; logarithm. 2. Conformal mapping  linear transformations, Moebius transformations, exponential function, logarithm. 3. Integration in the complex domain  integrals over curves, Cauchy theorem, Cauchy formula. 4. Power series in the complex domain  Taylor series, Laurent series, singularities and roots. 5. Integration using residue theorem  residues, residue theorem, evaluation of integrals.

Learning activities and teaching methods

unspecified

Recommended literature


E. Kreyszig. Advanced Engineering Mathematics. Wiley, New York, 1983.

J. Smítal, P. Šindelářová. Komplexní analýza. MÚ SU, Opava, 2002.

P. V. O'Neil. Advanced Engineering Mathematics. Wadsworth Publishing Company, Belmont, 1983.

R. V. Churchill, J. W. Brown, R. F. Verhey. Complex Variables and Applications. Mc GrawHill, New York, 1976.

W. Rudin. Analýza v reálném a komplexním oboru. Academia, Praha, 1987.
