# Complex Analysis Syllabus - Spring 2003

1/151.1Complex Numbers4, 7, 9, 11, 14, 18, 22, 23, 26
171.2Absolute Value and Conjugates4, 6-10, 14, 15
221.3Polar Form2-4, 7, 8, 11-13, 15, 16, 22
241.4Exponential Function1, 3, 5, 7-14
271.5Powers and Roots1, 4, 5, 10, 12, 18
29 Quiz #1
312.1Complex Functions1-3, 5, 7-10
2/32.2Limits and Continuity6, 7, 9-14, 16
52.3Analytic Functions4, 7, 9, 10, 13, 16
72.4Cauchy-Riemann Equations1-3, 6-8, 10-12, 15
102.5Harmonic Functions1, 3-6, 8, 10, 14, 18
12 Review
14 Test #1
173.1Trigonometric Functions5-8, 12, 13, 15, 18, 20, 21
193.2Logarithm Function1-5, 8, 9, 15
243.3Complex Powers1-6, 9, 13
264.1Contours1-3, 5, 7-11
28 Quiz #2
3/104.2Contour Integration3, 6-8, 10, 11, 14, 15
124.3Independence of Path1, 2, 4, 5, 7, 8, 11
144.4aCauchy's Integral Theorem1, 3, 9, 11, 13-15
174.5Cauchy's Integral Formula 1, 2, 3abc, 8a
194.5Integral Formula Consequences3def, 4, 6, 7, 10
214.6More Consequences1-3, 5, 6, 8, 13, 14, 21
24 Review
26 Test #2
285.2Taylor Series1ab, 2, 3, 5, 8ab, 9, 11ab, 13--15
315.5Laurent Series1, 3, 4, 6, 9
4/25.6Singularities and Poles1abdh, 3, 5, 6
46.1Residue Theorem1abcd, 2, 3abc, 4
76.2Trig Integrals1--5
11 Quiz #3
116.3Improper Integrals2-6, 11
146.4Improper Trig Integrals1, 3, 5, 7
167.3Möbius Transformations3-8
217.6Applications1, 2, 3, 6
237.6More Applicationsworksheet
25 Review
28 Test #3
30 Review for Final
5/2-7 Oral Final Exams