Spring 2023
Syllabus Statements
Weekly Plan
Homework
Exams
Weekly Plan (tentative) and Short Lecture Summaries
| Week | Topics |
|---|---|
| Jan 24, Jan 26 | Introduction, basic properties of complex numbers, Euler's formula (sections 1.1-1.11) |
| Jan 31, Feb 2 | Topology, functions and mappings, limits, continuity (sections 1.12-2.18) |
| Feb 7, Feb 9 | Derivatives, Cauchy-Riemann equations, analytic functions and examples (sections 2.19-2.26) |
| Feb 14, Feb 16 | Harmonic functions, uniquely determined analytic functions, the exponential and logarithm functions (sections 2.26-3.34) |
| Feb 21, Feb 23 | The power, sine, cosine functions, derivatives and integrals, contour integrals (sections 3.35-4.45) |
| Feb 28, Mar 2 | Contour integrals, antiderivatives (sections 4.46-4.49)
Midterm 1 on Mar 2 (Thursday) |
| Mar 7, Mar 9 | The Cauchy-Goursat theorem, the Cauchy integral formula (sections 4.50-4.57) |
| Mar 14, Mar 16 | Spring Break |
| Mar 21, Mar 23 | Liouville's theorem, Fundamental Theorem of Algebra, Taylor series (sections 4.58-4.65) |
| Mar 28, Series, Mar 30 | Laurent series, integration and differentiation of series (sections 5.66-5.73) |
| Apr 4, Apr 6 | The Cauchy Residue Theorem, poles, removable and essential singularities (sections 6.74- 6.81) |
| Apr 11, Apr 13 | Zeros and poles (sections 6.82-6.84)
Midterm 2 on Apr 11 (Tuesday) |
| Apr 18, Apr 20 | Riemann's theorem, Casorati-Weierstrass theorem, Improper integrals (sections 6.84-7.86) |
| Apr 25, Apr 27 | Jordan's lemma, The argument principle (sections 7.87-7.93) |
| May 2, May 4 | Rouché's Theorem, the square root, Riemann surfaces (sections 7.94-8.100, 8.107-8.110) |
|
May 9 (Tuesday) 2:15 PM - 5:00 PM |
Final Exam |