| Professor: | Douglas Anderson, Ph.D. |
| Ivers 234E | |
| 299-4453 | |
| andersod@cord.edu |
Office Hours: TTh 1:00-3:30, MWF by discovery.
Text: E.B. Saff and A.D. Snider, Fundamentals of Complex Analysis for Mathematics, Science, and Engineering 2nd Edition, Prentice Hall, Upper Saddle River, 1993.
Prerequisites: Math 223.
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 8 | 1.1 Algebra of Complex Numbers | (4) 4,7,11,14,19,24,25*,26,30 |
| 10 | 1.2 Point Representation | (11) 6,7,8,10,14,15*,17* |
| 13 | 1.3 Vectors and Polar Forms | (19) 4,7,9,11*,12,13*,15*,22 |
| 15 | 1.4 Complex Exponential | (25) 3,8,11,12a,14,17,18 |
| 17 | 1.5 Powers and Roots | (31) 3,4,5abd,7bc*,11*,16,18 |
| 20 | 1.6 Planar Sets | (35) 2,3*,4,5*,6,7*,8,12 |
| 22 | 2.1 Functions of a Complex Variable | (44) 4,5,7*,8,9*,11* (label pts) |
| 24 | 2.2 Limits and Continuity | (49) 4,5,6,7*,9,10,12,14,15 |
| 27 | 2.3 Analyticity | (56) 4,5*: rule (7),7,9,10,11,13,16 |
| 29 | 2.4 Cauchy-Riemann Equations | (62) 1,2,3,7*,8,11*,12,13*,14 |
| 31 | 2.5 Harmonic Functions | (68) 2,3ace,4,6,8,11-13 |
| Feb 3 | Review | |
| 5 | Exam I | |
| 7 | 3.1 Elementary Functions | (79) 1*,5,10,11*,15*,17,19*,20 |
| 10 | 3.2 Logarithmic Function | (86) 1,2,3,5,8,9,10,11,12,14 |
| 12 | 3.3 Complex Powers, Inverse Trig | (93) 1,3,4,5,8,9*,11*,15*ab |
| 14 | Nobel Peace Prize Forum | No Class |
| 17 | 4.1 Contours | (113) 1,3,4,7,8,10 |
| 19 | 4.2 Contour Integrals | (122) 1*,3,6,7,8,12,14(b),16,17 |
| 21 | 4.3 Independence of Path | (128) 1abceg,3*,4,5*,7,8,10 |
| 24 | 4.4a Cauchy's Integral Theorem | (148) 1,2,3,9,12,15*,18 |
| 26 | 4.4a Cauchy's Integral Theorem | continued |
| 28 | 4.5 Cauchy's Integral Formula | (160) 1,3,4,7*,10,16 |
| Mar 10 | 4.6 Bounds for Analytic Functions | (167) 2,4,5,6,10,14,18 |
| 12 | Review | |
| 14 | Exam II | |
| 17 | 5.1 Sequences and Series | (185) 1bdf,2bd,3*,4,6,8bc,12 |
| 19 | 5.2 Taylor Series | (195) 1ade,2ade,5*bce,6,16 |
| 21 | 5.3 Power Series | (203) 1*,2,3,8,9*,16 |
| 24 | 5.5 Laurent Series | (217) 1,3*,4,7a*,9* |
| 26 | 5.6 Zeros and Singularities | (225) 1,3,5*,6,12,13* |
| 28 | 6.1 Residue Theorem | (251) 1bdfg,3*abc,4,6,7* |
| 31 | 6.2 Trigonometric Integrals | (255) 1*,2,4,8 |
| Apr 2 | 6.3 Improper Integrals | (262) 2,4,6,11*, residue handout |
| 4 | 6.4 Jordan's Lemma | (271) 1*,3*,4,7*,9* |
| 7 | 6.5 Indented Contours | (279) 1,2,5*,6,12 |
| 9 | Review | |
| 11 | Exam III | |
| 14 | 6.6 Multiple-Valued Functions | (287) 1*,3*,4 |
| 16 | 7.2 Geometric Considerations | (314) 1,3,5,11 |
| 18 | Good Friday | No Class |
| 21 | Easter Monday | No Class |
| 23 | 7.3 Mobius Transformations I | (325) 1,3,5,7 |
| 25 | 7.4 Mobius Transformations II | (335) 5,7,9,15,17 |
| 28 | Review | |
| May 2 | (Friday) Final Exam | 2:00 ~ 4:00 |