Syllabus and Weekly Plan (tentative)
Week 
Topics 
Jan 28, Jan 30 
Introduction, basic properties of complex numbers, Euler's formula (sections 1.11.11) 
Feb 4, Feb 6 
Topology, functions and mappings, limits, continuity (sections 1.122.18) 
Feb 11, Feb 13 
Derivatives, CauchyRiemann equations, analytic functions and examples (sections 2.192.26)

Feb 18, Feb 20 
Harmonic functions, uniquely determined analytic functions, the exponential and logarithm functions (sections 2.263.34)

Feb 25, Feb 27 
The power, sine, cosine functions, derivatives and integrals, contour integrals (sections 3.354.45) 
Mar 3, Mar 5

Contour integrals, antiderivatives (sections 4.464.49)
Midterm 1 on Mar 5 (Thursday) 
Mar 10, Mar 12 
The CauchyGoursat theorem, the Cauchy integral formula (sections 4.504.57)

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 4.584.65) 
Apr 7, Apr 9 
Laurent series, integration and differentiation of series (sections 5.665.73)

Apr 14, Apr 16 
The Cauchy Residue Theorem, poles, removable and essential singularities (sections 6.74 6.81)
Takehome Midterm 2 from Apr 16 till Apr 19

Apr 21, Apr 23 
Zeros and poles, Riemann's theorem, CasoratiWeierstrass theorem (sections 6.827.86) 
Apr 28, Apr 30 
Jordan's lemma, The argument principle (sections 7.877.93)

May 5, May 7 
Rouché's Theorem, the square root, Riemann surfaces (sections 7.948.100, 8.1078.110)

May 19 (Tuesday) 2:15 PM  5:00 PM

Final Exam

