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Lecturer(s)
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Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
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Course content
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1. Complex numbers - arithmetic and conjugates, polar coordinates, rational powers 2. The complex plane. The topology of the complex plane 3. Open sets in the complex plane, complex functions. 4. Limits and continuity 5. Complex differentiation. Differentiable complex functions and the Cauchy-Riemann equations. 6. Analytic function, introduction to special functions 7. Curves in th complex plane 8. Integration. Integration along paths, the Fundamental Theorem of Calculus. 9. The estimation lemma, statement of Cauchy's Theorem. 10. Taylor and Laurent Series. Cauchy's Integral Formula and Taylor Series, Zeros and Poles, Laurent Series.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 28 hours per semester
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Learning outcomes
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The set of complex numbers, topology of the complex sphere. Basic analysis of complex functions, Cauchy-Riemann theorem. Complex series, Taylor series, definition of elementary functions. Laurent series.
Basic analysis of complex functions.
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Prerequisites
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Knowledge of mathematics at the hight school lavel.
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Assessment methods and criteria
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Oral exam
- understand the significance of differentiability for complex functions and be familiar with the Cauchy-Riemann equations; - evaluate integrals along a path in the complex plane and understand the statement of Cauchy's Theorem;
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Recommended literature
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Černý I.:. Základy analysy v komplexním oboru. Academia, Praha, 1967.
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