SUNY at Stony Brook MAT 342: Applied Complex Analysis
Spring 2020

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