Visual Complex Analysis Tristan Needham Oxford University Press, c2002.
Coursework: There will be a weekly problem set due at the beginning of class on Fridays. I expect you to write a complete solution to every assigned problem. If you get stuck on a problem, or if you are not confident in your solution, please confer with fellow students, a tutor, or come ask me in office hours. Late homework will be accepted with a 30% penalty compounded weekly. For example, an assignment that is late less than 1 week will yield 70% of its on-time value, between 1 and 2 weeks late yields 49% of on-time value, between 2 and 3 weeks late yields 34% of on-time value, and so forth. Missing homework will receive a score of zero. Exams: There will be two midterms and a final. Midterm 2 will cover the material after midterm 1. The final exam will be cumulative with an emphasis on the material after midterm 2. Missing an exam will result in an exam score of zero being assigned. Grades: Course grades are based on problem sets and exams. The weight each component shall receive is as follows: 34% problem set average, 22% Midterm 1, 22% Midterm 2, 22% Final Exam. When the final exam score exceeds the lesser of the two midterm scores, the final exam score will replace the lesser of the two midterm scores. The following distribution will be used to assign course grades: 100-93% = A, 92-90% = A-, 89-86% = B+, 85-83% = B, 82-80% = B-, 79-76% = C+, 75-73% = C, 72-70% = C-, 69-66% = D+, 65-63% = D, 62-60% = D-, Below 60% = F. Calculators: Calculators are always permitted. Tutoring: The Student Math Center is open every Sunday and Monday from 5-8pm in Galileo 201. Additional tutoring may be requested from the Academic Support Center in Sichel 105. Academic Honesty: The Saint Mary's policies regarding academic honesty detailed in the student handbook apply to this course. I encourage you to work with other students on coursework, but your write-ups should be in your own voice, and consist largely of your own work. Where your argument depends heavily on another's work, say so. Course Calendar: The course calendar details the schedule of coursework, exams and breaks.
Homework and Announcements
Assignment 12 due Wed Dec 6. Assignment 11 due Wed Nov 22.
An animation of stereographic projection of the Riemann sphere. Assignment 10 due Wed Nov 15. Assignment 9 due Fri Nov 3. Assignment 8 due Fri Oct 27. Assignment 7 due Fri Oct 20. Assignment 6 due Wed Oct 11. Assignment 5 due Wed Oct 4
p.185 #1, 3, 5, 10, 12 Assignment 4 due Wed Sep 27
p.117 #24, 25, 26. See the discussion of Section 2.VI.1, 2.VI.2 for the definitions of branch point and branch cut.
p.118 #27, 28
p.119 #34. See p.95 for a statement of the Binomial Theorem for a real exponent. Assignment 3 due Mon Sep 18
p.111 #5, 6(you may skip pt (v))
p.113 #12, 13, 14, 15
p.69 Read the first complete sentence (Sentence 1) on this page. (i) Show that Sentence 1 is equivalent to the divergence test from Math 28. (ii) Prove Sentence 1 by using the Cauchy criterion for convergence and setting m=n-1.(Using the divergence test itself would be cheating!) Assignment 2 due Fri Sep 8
1. Prove the Binomial Theorem which is stated on p.50 #32. There are many different proofs. You could supply the proof located at http://en.wikipedia.org/wiki/Binomial_theorem if you wish.
2. p.50 #32
3. p.51 #34
4. Sketch a moving particle illustration of the function f(z)=2eiπ/3z+(3+5i) Assignment 1 due Fri Sep 1
p.7 Prove the formulas in section 1.I.4 using the terminology established in the chart and diagram of p.6
p.45 #1,2
