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MATH 463 , Spring 2013: Schedule, Notes and Summary

Homeworks:

See the textbooks problems from sections covered in class.

Quizzes:

Quizzes are cumulative.

Lecture Date What was covered Notes Homeworks from textbook sections
1 Jan. 24 Addition and multiplication; the complex field - 1-3
2 Jan. 29 Modulus, Conjugate, Exponential Form - 4-6
3 Jan. 31 Products, Arguments, Roots Quiz 1 7-9, 97
4 Feb. 5 Examples, Topology on C - 9-11, 99
5 Feb. 7

Functions, Mappings, Exponential

 Quiz 2 12-14, 90-91
6 Feb.12 Limits - 15-17
7 Feb.14 Continuity, Derivatives - 18-19
8 Feb.19 CR Equations, Polar Coordinates Quiz 3 20-23
9 Feb.21 Analytic Functions - 23-25
10 Feb.26 Harmonic Functions; Analytic Continuations Quiz 4 26-28, 104
11 Feb.28 Elementary Functions: Expo, Log, Branches - 29-33, 97
12 Mar. 5 Trigonometric and Hyperbolic Functions Quiz 5 33-36
13 Mar. 7 Inverse Trigonometric, Integrals, Contours - 36-39
14 Mar.12 Contour integrals, examples Quiz 6 40-44
- Mar.13 Review Session Wednesday 3:00-4:30pm , MATH 0304
15 Mar.14 - Test 1 Chapters 1-3
- Mar.19 - Spring Break  
-  Mar.21 - Spring Break  
16 Mar.26 Antiderivatives and Cauchy-Goursat Theorem - 44-47
17 Mar.28 Cauchy Theorem on simple and multiple connected domains - 47-49
18 Apr. 2 Cauchy Integral Formula Quiz 7 50-51
19 Apr. 4 Consequences: Liouville's theorem, maximum modulus theorem - 52-54
20 Apr. 9 Series (Chapter 5), Singular points, residues Quiz 8 68-69
- April 10 Review Session Wednesday 3:00-5:00pm in MATH 0304
21 Apr.11 - Test 2  
22 Apr.16 Cauchy's residues theorem, Singularities, Residues - 70-73
23 Apr.18 Zeros, Poles - 74-76
24 Apr.23 Improper Integrals Quiz 9 78-79
25 Apr.25 Special Integrals - 80-81
26 Apr.30 Branch Cuts, Indented Paths Quiz 10 82-84
27 May 2 Trigonometric Integrals, Inverse Laplace Transform - 85,88,89
28 May 7 Argument Principle, Rouche'sTheorem, Quiz 11 86-87
29 May 9 Nyquist Stability Theorem. Review -