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Complex Analysis
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Section 1. Analytic Functions
(Notes: pp. 1 - 15)
- Complex-Valued Functions. Limits and Continuity
- Analiticity. The Cauchy-Riemann Equations
- Elementary Functions
- Section 2. Complex Integration
(Notes: pp. 16 - 32)
- Contour Integration
- Cauchy's Integral Theorem
- Cauchy's Integral Formula
- Bounds for Analytic Functions
- Section 3. Series Representations
(Notes: pp. 33 - 41)
- Tayloer Series and Power Series
- Laurent Series
- Zeros and Singularities
- Section 4. Residue Theory
(Notes: pp. 42 - 53)
- The Residue Theorem
- Techniques of Integration
- Section 5. Conformal Mapping
(Notes: pp. 54 - 67)
- Concepts. Riemann Mapping Theorem
- Mobius Transformations
- The Schwarz-Christoffel Transformations
Ordinary Differential Equations and Dynamical Systems
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