Syllabus and Weekly Plan (tentative)
Week |
Topics |
Jan 28, Jan 30 |
Introduction, basic properties of complex numbers, Euler's formula (sections 1.1-1.11) |
Feb 4, Feb 6 |
Topology, functions and mappings, limits, continuity (sections 1.12-2.18) |
Feb 11, Feb 13 |
Derivatives, Cauchy-Riemann equations, analytic functions and examples (sections 2.19-2.26)
|
Feb 18, Feb 20 |
Harmonic functions, uniquely determined analytic functions, the exponential and logarithm functions (sections 2.26-3.34)
|
Feb 25, Feb 27 |
The power, sine, cosine functions, derivatives and integrals, contour integrals (sections 3.35-4.45) |
Mar 3, Mar 5
|
Contour integrals, antiderivatives (sections 4.46-4.49)
Midterm 1 on Mar 5 (Thursday) |
Mar 10, Mar 12 |
The Cauchy-Goursat theorem, the Cauchy integral formula (sections 4.50-4.57)
|
Mar 17, Mar 19 |
Spring Break |
Mar 24, Mar 26 |
Spring Break |
Mar 31, Apr 2 |
Liouville's theorem, Fundamental Theorem of Algebra, Taylor series (sections 4.58-4.65) |
Apr 7, Apr 9 |
Laurent series, integration and differentiation of series (sections 5.66-5.73)
|
Apr 14, Apr 16 |
The Cauchy Residue Theorem, poles, removable and essential singularities (sections 6.74- 6.81)
Take-home Midterm 2 from Apr 16 till Apr 19
|
Apr 21, Apr 23 |
Zeros and poles, Riemann's theorem, Casorati-Weierstrass theorem (sections 6.82-7.86) |
Apr 28, Apr 30 |
Jordan's lemma, The argument principle (sections 7.87-7.93)
|
May 5, May 7 |
Rouché's Theorem, the square root, Riemann surfaces (sections 7.94-8.100, 8.107-8.110)
|
May 19 (Tuesday) 2:15 PM - 5:00 PM
|
Final Exam
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