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Contents
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| Week 1: |
Complex numbers, complex plane, metric and limit on complex plane. |
| Week 2: |
Domains on complex plane, concept of Riemann sheet, power function and its inverse. |
| Week 3: |
Exponential function and logarithm. |
| Week 4: |
Trigonometrical functions and their inverses, order of branch points. |
| Week 5: |
Continuity on complex plane, derivative of a function, analytic functions and Cauchy-Riemann equations. |
| Week 6: |
Harmonic property of real and imaginary parts, geometrical meaning of derivative on complex plane (Conformal mapping). |
| Week 7: |
Integral of a complex variable function on a contour, conditions for the integral to be independent of the path, Cauchy theorem. |
| Week 8: |
Fundemental formula of integral calculus, integral of a uniformly convergent series, limits of some integrals - Jordan theorem. |
| Week 9: |
Midterm examination. |
| Week 10: |
Cauchy formula for bounded and unbounded domains, derivatives of an analytical function. |
| Week 11: |
Removable singularities, Liouville theorem, bounded harmonical functions. |
| Week 12: |
Maximum modulus principle, mean value theorem. |
| Week 13: |
Uniformly convergent series and Weierstrass theorem. Discrete singular points and classification of functions. |
| Week 14: |
Taylor and Laurent series. |
| Week 15*: |
General review. |
| Week 16*: |
Final examination. |
| Textbooks and materials: |
Kompleks Değişkenli Fonksiyonlar Teorisi
Mithat İdemen, İTÜ Vakfı Yayınları, 2. Baskı.
Kompleks Değişkenli Fonksiyonlar Teorisi Çözümlü Problemleri
Gökhan Uzgören ve Gökhan Çınar İTÜ Vakfı Yayınları
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| Recommended readings: |
Complex variables and applications, James Ward Brown, Ruel V. Churchill, Mc. Graw-Hill Company,6th Edition
Complex Analysis, Lars V. Ahlfors, Mc. Graw-Hill Company, 3rd Edition |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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