MAT 4725 Numerical Analysis

1. MAT 4725Numerical Analysis Winter 2014 http://myhome.spu.edu/lauw

2. Dr. Wai W. Lau • Dr. Lau • Wai

3. Dr. Wai W. Lau • Dr. Lau • Wai = Y

4. Dr. Wai W. Lau • Dr. Lau • Wai = = Y Why?

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 2401 and 3237 or • permission of the instructor

8. This course is • Unique • Mathematics • Programming (Maple Implementation of numerical algorithms) • Challenging • Calculus • Analysis • Individual works

9. Text Burden and Faires, Numerical Analysis , 9th Edition            

10. Text Rutschman and Zeng, Scientific Computing with Maple Programming (Section1.1-2.1)

11. Expectations - Handouts • You are expected to print and bring your handout to class. • Fail to have your HO repeatedly will negatively impact your grade.

12. Motivations • Most real life problems cannot be solved exactly.  Numerical analysis is the study of methods that approximate solutions numerically.

13. Probability

14. Population Model • N(t) = size of a population •  = birth rate • v = immigration per year (constant)

15. Population Model • N0 = 1,000,000, N(1) = 1,564,000 •  = ??? • v = 435,000

16. Exams • 2 Mid-term Exams and a Final Exam.

17. Homework • Homework problem sets will be assigned. • All work must be typed. • The ONLY references you can use are the textbooks and the lecture note.  You cannot use any other resources such as other books, software, and the internet.  

18. Homework • Group HW • Individual HW

19. Group Homework • You are required to work together in a group of 2 (or 3 if approved).

20. Individual Homework • No discussion with any other person, except may be the instructor.  • Discussing or copying homework is considered as an act of academic dishonesty

21. 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.

22. Homework • Homework must be written with proper logical format. • Pay attention to the notations and format used in the lecture. You need to follow the notations and presenationof the class notes in the case that they are different from the textbook and supplemental materials.

23. Homework • *.doc Type with Equation Editor • *.docx Saved to.docx to type with MS Equation Editor

24. Quizzes • Daily Short Quizzes (5 -15 min.) • Cover the materials discussed in the last class session and reading assignment. • This is to encourage you to • study alone the way, instead of spending 15 straight hours the night before exam; • Prepare for the next class.

25. Class Participation: 1. There are reading assignments everyday.  I will ask questions during the class period to check your reading progress 2. There are classwork in some class sessions. 3. You are expected to print and bring the handouts. At the end of the quarter, your grades on class participation will be determined by the above activities and other observations by the instructor.

26. Classwork • You may have limited discussions with one group partner • Each one need to write up his/ her own solutions and Maple implementations • You are not learning if you constantly depends on someone else to finish you work. • You need to develop the ability to debug your program.

27. Modeling Contests Each group will enter into one of the following modeling contests (2/6-2/10): • MCM: The Mathematical Contest in Modeling • ICM: The Interdisciplinary Contest in Modeling

28. Modeling Contests • Case Studies are selected from past contest problems • Registration Fee: $100 per team • Part of the mid-term exam

29. Modeling Contests • A “N” grade will be given at the end of the quarter. • Grades for the MCM will be assigned as follows

30. Points Distribution

31. Final Class Grade

32. Incomplete Policy • No incomplete will be given if you do not already have a passing grade (70%) at the time of the request.

33. Attendance Policy • Coming to class is extremely important. • You are expected to be on time. • You will not get a course grade higher than C- if you do not have at least 90% of attendance*. • You will not get a course grade higher than D if you do not have at least 80% of attendance*.

34. Make-Up Policies • NO makeups for classworks.

35. Make-Up Policies • NO makeups for classworks. • 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. 

36. 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.

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

38. Maple • Computer algebraic system Maple (version 17) will be used in this course to implement numerical algorithms.   • Maple will be available for use on computers in labs throughout the campus.  • Copies of the software for use on your own computer will also be available for purchase at a substantial discount for students (Discount code: AP??????).

39. Working knowledge of Maple is assumed • Review Maple Essential Tutorials 1-6 • Quiz next class

40. Homework • Read Zeng 1.1, 1.2

41. Handouts • You need to print your handouts prior to the class time. • Do not use the printer in this room without the instructor’s approval. • Handouts will be finalized by 10 pm the night before.

42. MCM Sample Problems

43. 2002 MCM problem BAirline Overbooking • You are all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.

44. 2002 MCM problem BAirline Overbooking • Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. • Consequently, most airlines overbook—that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take bumped and thus unable to take the flight for which they had reservations.

45. 2002 MCM problem BAirline Overbooking • Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.

46. 2002 MCM problem BAirline Overbooking Consider the overbooking issue in light of the current situation: • fewer flights by airlines from point A to point B; • heightened security at and around airports, • passengers’ fear, and • loss of billions of dollars in revenue by airlines to date.

47. 2002 MCM problem BAirline Overbooking • Build a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company, in order to find an optimal overbooking strategy—that is, the number of people by which an airline should overbook a particular flight so that the company’s revenue is maximized.

48. 2002 MCM problem BAirline Overbooking • Ensure that your model reflects the issues above and consider alternatives for handling “bumped” passengers. • Additionally, write a short memorandum to the airline’s CEO summarizing your findings and analysis.

50. 2007 MCM problem BThe Airplane Seating Problem • Airlines are free to seat passengers waiting to board an aircraft in any order whatsoever. It has become customary to seat passengers with special needs first, followed by first-class passengers (who sit at the front of the plane). Then coach and business-class passengers are seated by groups of rows, beginning with the row at the back of the plane and proceeding forward.