| Professor: | Douglas Anderson, Ph.D. |
| Ivers 234 D | |
| 299-4453 | |
| andersod@cord.edu |
Office Hours: TTh 1:00-4:00, MWF by discovery.
Text: E.B. Saff and A.D. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science 3rd Edition, Prentice Hall, Upper Saddle River, 2003. ISBN 0-13-907874-6.
Prerequisites: Math 223 Calculus III. Math 210 Linear Algebra is also recommended.
Purpose: This course will introduce you to the complex number system, which can be visualized in rectangular and polar coordinates, and quickly build on that system with functions (maps) of a complex variable. The calculus of complex-valued functions will then be covered, including continuity, differentiability, analyticity, and integrability. Series representations, contour deformations, and Mobius transformations will also be discussed. The exercises are a mixture of calculations as in a typical calculus course, and rigorous proofs befitting an analysis course. This course is recommended for all mathematics students considering graduate school in mathematics. Math 330 Real Analysis is also recommended for students considering graduate school; these two analysis courses can be taken in either order.
Homework: Homework will be assigned each day for your practice in mastering the material, and will be due two class periods later. I will drop your four (4) lowest homework scores before calculating your overall homework grade. Homework that is turned in should be neat and organized. You will not only be graded on correct answers but also on the neatness, organization, steps used to derive your answers, and the use of correct grammar and complete sentences.
Exams: There will be three (3) unit exams, plus the final exam.
| Grading: | Points | Scale | |||
| Homework | 200 | A 90%--100% | |||
| Exams(3) | 300 | B 80%--89% | |||
| Final Exam | 200 | C 70%--79% | |||
| D 60%--69% | |||||
| F Below 60% |
| Date | Section | Exercises |
| Jan 5 | 1.1 Algebra of Complex Numbers | (4) 4,7,11,14,19,24,25*,26,30 |
| 7 | 1.2 Point Representation | (12) 6,7,8,10,14,15*,17* |
| 9 | 1.3 Vectors and Polar Forms | (22) 4,7,9,11*,12,13*,15*,22 |
| 12 | 1.4 Complex Exponential | (31) 3,4,8,11,12a,17,18 |
| 14 | 1.5 Powers and Roots | (37) 3,4,5abd,7bc*,11*,16,18 |
| 16 | 1.6 Planar Sets | (42) 2,3*,4,5*,6,7*,8,12 |
| 19 | 2.1 Functions of a Complex Variable | (56) 4,5,7*,8,9*,11* (label pts) |
| 21 | 2.2 Limits and Continuity | (63) 6,7,8,9*,11,12,14,16,17 |
| 23 | 2.3 Analyticity | (70) 4,5*: rule (7),7,9,10,11,13,16 |
| 26 | 2.4 Cauchy-Riemann Equations | (77) 1,2,3,7*,8,11*,12,13*,14 |
| 28 | Review | |
| 30 | Exam I | |
| Feb 2 | 2.5 Harmonic Functions | (84) 2,3ace,4,6,8,11-13 |
| 4 | 3.1 Polynomials & Rational Functions | (108) 4,7*,8,9*,10,11 |
| 6 | 3.2 Exp, Trig, & Hyperbolic Functions | (115) 1*,5,10,11*,15*,17,19*,20 |
| 9 | 3.3 Logarithmic Function | (123) 1,2,3,5,8,9,10,11,12,14 |
| 11 | 3.5 Complex Powers, Inverse Trig | (136) 1,3,4,5,8,9*,11*,15*ab |
| 13 | 4.1 Contours | (159) 1,3,4,7,8,10 |
| 16 | 4.2 Contour Integrals | (170) 1*,3,6,7,8,12,14(b),16,17 |
| 18 | 4.3 Independence of Path | (178) 1abceg,3*,4,5*,7,8,10 |
| 20 | 4.4a Cauchy's Integral Theorem | (199) 1,2,3,9,12,15*,18 |
| Mar 2 | 4.4a Cauchy's Integral Theorem | continued |
| 4 | 4.5 Cauchy's Integral Formula | (212) 1,3,4,7*,10,16 |
| 6 | 4.6 Bounds for Analytic Functions | (219) 2,4,5,6,10,14,18 |
| 9 | Review | |
| 11 | Exam II | |
| 13 | 5.1 Sequences and Series | (239) 1bdf,2bd,3*,4,6,8bc,12 |
| 16 | 5.2 Taylor Series | (249) 1ade,2ade,5*bce,6,16 |
| 18 | 5.3 Power Series | (258) 1*,2,3,8,9*,16 |
| 20 | 5.5 Laurent Series | (276) 1,3*,4,7a*,9* |
| 23 | Red River Flood '09 | No Class |
| 25 | Red River Flood '09 | No Class |
| 27 | Red River Flood '09 | No Class |
| 30 | Red River Flood '09 | No Class |
| Apr 1 | Red River Flood '09 | No Class |
| 3 | Red River Flood '09 | No Class |
| 6 | 5.6 Zeros and Singularities | (285) 1,3,5*,6,12,13* |
| 8 | 6.1 Residue Theorem | (313) 1bdfg,3*abc,4,6,7* |
| 10 | Good Friday | No Class |
| 13 | 6.2 Trigonometric Integrals | (317) 1*,2,4,8 |
| 15 | 6.3 Improper Integrals | (325) 2,4,6,11*, residue handout |
| 17 | 6.4 Jordan's Lemma | (336) 1*,3*,4,7*,9* |
| 20 | 7.2 Geometric Considerations | (382) 1,3,4,5,6,11,12,13,14 |
| 22 | 7.3 Mobius Transformations I | (392) 1,2,3,5,6,7,8 |
| 24 | 7.4 Mobius Transformations II | (404) 5,7,9,15,17,19 |
| 27 | Review | |
| May 1 | (Friday) Final Exam | 2:00 ~ 4:00 |