1. MAT 3730 Complex Variables Spring 2012 http://myhome.spu.edu/lauw

2. Dr. Wai W. Lau Dr. Lau Wai

3. Dr. Wai W. Lau Dr. Lau Wai =

4. Dr. Wai W. Lau Dr. Lau Wai = =

5. Course Web Page http://myhome.spu.edu/lauw Link to this document and other course information

6. Office Hours See course web page By Appointment

7. Prerequisites MAT 3238 or permission of the instructor

8. Text Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3/E ISBN: 0-13-907874-6

9. Exams 1 Mid-term Exams and a Final Exam.

10. Homework You can choose to do your HW individually or in a team of two

11. Team Approach You can work with at most one classmate on the HW. Turn in one paper for each team. Team paper need to be typed in MS WORD with proper format.

12. Team Approach You need to state clearly on the front page the percentage of contributions of each team member. This approach is intended for you to have discussions over the HW. Do not take turn to do HW.

13. Individual Approach Your homework must be neat and easy to read. Otherwise, no points will be given. Sloppy handwriting will not be tolerated. You will get bonus points at the end of the quarter if most of your papers are typed.

14. Homework You are not allowed to discuss your HW with anyone (except your team parnter and the instructor). Discussing or copying homework is considered as an act of academic dishonesty. Your only references are the textbook and lecture notes. Do not use other references such as books, WIKI, and other web resources.

15. Homework You must show all of your work − a correct answer with no justification will also be worth NO credit. When explanations are called for on the homework, you should respond in complete sentences with proper grammar, spelling, and punctuation.

16. Homework Staple your Homework. Points will be taken off if you fail to do so. Homework is due at the beginning of the class. Absolutely no late homework. Excuses such “the printer is not working” will not be accepted.

17. Reading Assignment You are required to read the textbook before class everyday. I will ask questions during the class period to check your reading progress.

18. Class Participation You are expected to come to class. There are classwork in some class sessions.

19. Class Participation At the end of the quarter, your grades on class participation will be determined by the above activities and other observations by the instructor.

20. Class Participation Please respect your instructor and classmates. Do not talk during the lecture. Disruptive and disturbing behavior will not be tolerated.

21. Class Participation No text messaging, web surfing, email sending,…… Turn off your phone before you enter the classroom***.

22. Class Participation Annoying behaviors will reduce the maximum participation points that you can get.

23. Points Distribution Exam 1110 points Final110 Points Homework60 Points Class Participation20 Points

24. Final Class Grade 90%A Range 80%B Range 70%C Range 60%D Range Below 60%E

25. Missing Classes You are responsible to catch up all the materials if you miss classes for whatever reasons ( sickness, family issues, family Hawaii vacation, alien abduction etc).

26. Missing Classes The instructor will not "re-teach" the lecture in any form including special appointments.

27. Make-Up Policies If a student has a documented conflict that will prevent him or her from taking an exam at the scheduled time, he/she must arrange IN ADVANCE with the instructor to take the exam early.

28. Make-Up Policies Makeups are NOT AUTOMATIC. Do NOT assume that because you miss an exam that you will get to make it up. A makeup exam must be APPROVED by me. Lying to avoid taking an exam is considered as an act of academic dishonesty.

29. Help!! Talk to me. I am available during office hours and other times.

30. MAT 3730 Complex Variables Section 0.1 Introduction http://myhome.spu.edu/lauw

31. Complex Variables and Differential Equations Complex analysis has a lot of applications We are going to look at one simple case in differential equations.

32. Homogeneous Linear Equations with Constant Coefficients

33. One type of possible solutions are exponential functions. If we can find all the unknown r, we solve the D.E.

34. Find the unknown parameter r If y is a solution, then it satisfy the D.E. Thus,

35. Auxiliary (characteristic) Equations It is a quadratic equation, it has 3 different types of roots for r.

36. 2 Distinct Real Roots r 1, r 2 A pair of linearly independent (L.I.) solutions General Solutions of the D.E. is

37. 1 Repeated Real Root r We can find the second L.I. solution by the reduction of order: General Solutions of the D.E. is

38. Conjugate Complex Roots A  Bi We get 2 “complex” solutions which do not have obvious “real” physical meanings

39. Example 1 (Pendulum) When the angle is small, the motion can be modeled by

40. Example 1 (Pendulum)

43. Conjugate Complex Roots A  Bi By using algebra of complex numbers, it can be shown that the following are 2 L.I. solutions; General Solutions of the D.E. is

44. Mathematical Induction You need to follow the exact format shown in the handout.handout If you do not know Induction, you need to learn it on your own (Talk to me!)

45. Proofs by “Equivalence” You show avoid using this type of proofs

46. Next Class Read section 1.1, 1.2 Mostly definitions and review of algebra