MAT 4725 Numerical Analysis

MAT 4725Numerical Analysis

Winter 2016

http://myhome.spu.edu/lauw

Dr. Wai W. Lau Dr. Lau

Wai

Dr. Wai W. Lau Dr. Lau

Wai =

Dr. Wai W. Lau Dr. Lau

Wai = =

Course Web Page

http://myhome.spu.edu/lauw Link to this document and other course

information

Office Hours See course web page By Appointment

Prerequisites MAT 2401 and 3237 or permission of the instructor

This course is Unique

• Mathematics• Programming (Maple Implementation of

numerical algorithms) Challenging

• Calculus• Analysis• Individual works

TextBurden and Faires, Numerical Analysis , 10th Edition            

TextRutschman and Zeng,Scientific Computing with Maple Programming (Section1.1-2.1)

Expectations - Handouts You are expected to print and bring your

handout to class. Fail to have your HO repeatedly will

negatively impact your grade.

Motivations Most real life problems cannot be solved

exactly.  Numerical analysis is the study of methods that approximate solutions numerically.

Probability

212

( , )

1( )2

xb

a

X N

P a X b e dx

a b

Population Model

0

( ) ( )

( ) ( 1)t t

dN t N t vdt

vN t N e e

= size of a population = birth rate = immigration per year (constant)

Population Model

435,0001,564,000 1,000,000 ( 1)e e

= 1,000,000, = 1,564,000 = ??? = 435,000

Exams 2 Mid-term Exams and a Final Exam.

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.  

Homework Group HW Individual HW

Group Homework You are required to work together in a

group of 2 (or 3 if approved).

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

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.

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 presentation of the class notes in the case that they are different from the textbook and supplemental materials.

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

Equation Editor

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 along the way, instead of spending 15 straight hours the night before exam;

• Prepare for the next class.

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.

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.

Modeling Contests Each group will enter into one of the following modeling contests (1/28-2/1):

• MCM: The Mathematical Contest in Modeling • ICM: The Interdisciplinary Contest in Modeling

Modeling Contests Case Studies are selected from past

contest problems Registration Fee: $100 per team Part of the mid-term exam

Modeling Contests A “N” grade will be given at the end of

the quarter. Grades for the MCM will be assigned as

followsResults Points (/60)

Unsuccessful 0

Successful

Honorable Mention

Meritorious Winner

Points DistributionExam 1 70 points

MCM/ICM 60 points

Final 120 Points

Homework 60 Points

Quizzes 80 Points

Class Participation 20 Points

Final Class Grade

90% A Range80% B Range70% C Range60% D Range

Below 60% E

Incomplete Policy No incomplete will be given if you do not

already have a passing grade (70%) at the time of the request.

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*.

Make-Up Policies NO makeups for classworks.

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. 

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.

Help!! Talk to me. I am available during office

hours and other times.

Maple Computer algebraic system Maple 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??????).

Working knowledge of Maple is assumed Review

Maple Essential Tutorials 1-6 Quiz next class

Homework Read Zeng 1.1, 1.2

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.

MCM Sample Problems

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.

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.

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.

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.

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.

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.

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.

2007 MCM problem BThe Airplane Seating Problem

Apart from consideration of the passengers’ wait time, from the airline’s point of view, time is money, and boarding time is best minimized. The plane makes money for the airline only when it is in motion, and long boarding times limit the number of trips that a plane can make in a day.

2007 MCM problem BThe Airplane Seating Problem

Devise and compare procedures for boarding and deboarding planes with varying numbers of passengers: small (85–210), midsize (210–330), and large (450–800). Prepare an executive summary, not to exceed two single-spaced pages, in which you set out your conclusions to an audience of airline executives, gate agents, and flight crews.

New This Year! MCM Problem A (continuous) MCM Problem B (discrete) MCM Problem C (data insights) ICM Problem D (operations

research/network science) ICM Problem E (environmental science) ICM Problem F (policy)