| Week | Dates | Monday | T | Wednesday | R | Friday |
|---|---|---|---|---|---|---|
| 1 | Feb. 9-13 | Introduction
1-3: Complex #s Fields |
Proofs
4-5: Moduli, conjugates |
6-8: Exponential form, powers, roots | ||
| 2 | Feb. 16-20 | 9: Examples
10: Regions |
Quiz | 11-12: Functions/mappings | ||
| 3 | Feb. 23-27 | 13-15: ez, limits | 16-18: z --> infinity, continuity, derivatives | 19-21: Derivative rules, Cauchy-Riemann equations | ||
| 4 | Mar. 1-5 | 22-24: Polar coordinates, analytic functions | 25-27: Harmonic functions, uniqueness, reflection principle | Ch. 3: Elementary Functions
28-30: Exponential & logarithm functions |
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| 5 | Mar. 8-12 | 30-33: Branches, log identities, complex exponents, trig functions | 33-35: Trig & hyperbolic functions and their inverses | Review | ||
| 6 | Mar. 15-19 | Exam 1 | 36-37: Complex functions of a real variable
38: Contours |
39-40: Contour integrals | ||
| 7 | Mar. 22-26 | 40: Examples
41: |integral| upper bounds |
42-43: Antiderivatives | 44-46: Cauchy-Goursat theorem | ||
| 8 | Mar. 29-Apr.2 | 47: Cauchy integral formula; 48: Derivatives of all orders! 49: Liouville's Theorem, Fund.Thm. of Algebra | 50: Maximum modulus principle
Review |
Exam 2 | ||
| Break | Apr. 3-12 | Spring | & Easter | Break | ||
| 9 | Apr. 13-16 | Easter Monday | 51-52: Sequences & series | 12:10-12:50
53-54: Taylor series |
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| 10 | Apr. 19-23 | 55-56: Laurent series | 57-59: Absolute & uniform convergence; continuity, integration & differentiation | 60: Uniqueness
61: Multiplication & division of power series |
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| 11 | Apr. 26-30 | 62-64: Cauchy's residue theorem | 65: Types of singularities 66: Poles 12:50-1:20 | 67: Examples
68: Zeros |
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| 12 | May 3-7 | 69: Zeros & poles
70: Behavior near poles |
Review
Exam 3 given out |
Exam 3 due
Begin topics. |
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| 13 | May 10-14 | Review exam.
Organize projects. |
Work on ... | ... projects. | ||
| 14 | May 17-19, 21-22 | Jason & Andy
Cory and Alan |
Brian & Josh
Nate & Pete |
Finals ... | ||
| 15 | May 24-25 | ...Finals... | Final Exam 3:30- |