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Course: Selected Lessons in Mathem. Analysis

Department/Abbreviation: OPT/VKMN

Year: 2020

Guarantee: 'doc. Mgr. Ladislav Mišta, Ph.D.'

Annotation: Algebra of complex numbers.

Course review:
1. Algebra of complex numbers. 2. Sequences and series. Power series. Convergence in the Gauss plane. 3. Functions of a complex variable. 4. Limit, continuity, derivative, Cauchy-Riemann condition. 5. Analytical functions. 6. Line integrals. 7. Cauchy integral theorem, consequences. 8. Residual theorem and applications. 9. Integral transforms. 10. Laplace transform. Inverse Laplace transform, rational functions. Application of the Laplace transform to the differential equation solution. 11. Fourier series. Fourier integral. Fourier transform and application. 12. Further similar integral transforms.