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21-256 Multivariate Analysis and Approximation
Spring 2004

Instructor: Dr. Timothy Flaherty
Office: Wean Hall 6101
Phone: 412-268-2556
e-mail: tim@andrew.cmu.edu
Course Web Page: http://www.math.cmu.edu/~tim/256s04/256s04.html
Text: Calculus: Early Transcendentals, 5th edition, by James Stewart, and Introduction to Mathematical Programming, by Russell C. Walker
Lecture: Porter Hall 100, MWF 1:30-2:20.
Recitations:
Section A, Tues., Thurs., 12:30-1:20, DH 1217, David Korpi, dkorpi@andrew.cmu.edu
Section B, Tues., Thurs., 12:30-1:20, BH 235B, Juan Rivera, juanr@andrew.cmu.edu
Section C, Tues., Thurs., 12:30-1:20, WEH 6423, Aris Winger, awinger@andrew.cmu.edu
Section D, Tues., Thurs., 1:30-2:20, SH 220, Aris Winger, awinger@andrew.cmu.edu
Section E, Tues., Thurs., 2:30-3:20, WEH 6423, Juan Rivera, juanr@andrew.cmu.edu

Introduction: We will begin the course by focusing on representations of functions using power series. Taylors Theorem, which gives approximations to functions by polynomials, will be introduced next. We then take up the subject of linear algebra, and make use of vectors and matrices, to coordinate our efforts in studying multivariate problems. We will then take up the issue of multivariate analysis by first studying analytic geometry in three dimensions. Partial derivatives are introduced and we will use them later to examine various optimization problems. Several of the many possible applications which combine the forces of algebra and calculus are then examined, including extrema determination, least squares approximations, and constrained extrema problems.

Lectures: Lecture will be from 1:30 to 2:20 on Monday, Wednesday, and Friday of each week in Porter Hall, room 100. We will follow the university calendar for this term. Tardiness and absence from class is strongly discouraged. Students are encouraged to ask questions and participate in class. You are responsible for all of the material and announcements presented during lecture.

Recitations: Students will also have two periods a week of recitation supervised by a teaching assistant. The purpose of the recitation is to solve problems and ask questions related to the text or lecture.

Homework: Homework problems are posted on the course web page. You are expected to do every problem assigned. In addition, certain homework problems will be collected. You will submit your homework to the T.A. as scheduled. Late homework will generally not be accepted. Students must turn their homework in during the assinged recitation. You are encouraged to work together and seek whatever help you need in solving homework problems. Copying or permitting your work to be copied is considered cheating, and will be subject to the policies regarding cheating as stated in the student handbook. Your goal should be a complete and thorough understanding of the material as demonstrated by your ability to handle the homework problems with ease. To accomplish this, you may expect to spend a considerable amount of time working many problems, and seeking help for those problems which you can not do. Usually it will be necessary to work many problems that are not assigned to gain a thorough understanding.

Quizzes: We will have approximately 10 quizzes, given at various times during recitation or lecture. These will generally be unannounced.

Exams: There will be three tests and a final exam, scheduled as follows:
Test 1: February 11, 1:30-2:20, PH 100
Test 2: March 17, 1:30-2:20, PH 100
Test 3: April 7, 1:30-2:20, PH 100
Final Exam: Date, time, location will be announced.

Make-up Exams: Will not be provided unless the student documents an illness or emergency. Any conflict with a university sponsored event must be brought to the instructor before the exam date for a make-up to be considered. You may notify the instructor in person, by e-mail, by phone, or by leaving a message at the Mathematics Department office at 412-268-2545.

Academic Honesty: We will apply the university guidelines as stated in the student handbook to ensure academic honesty.

Calculators and Computers: Calculators and Computers are not permitted during any quiz or exam, unless otherwise announced. However, you are encouraged to properly use these tools in your study and homework to gain a further understanding of the material. Exams and quizzes will be designed so that extensive numerical calculations are unnecessary. You are expected to be able to perform routine algebraic, trigonometric, and geometric calculations.

Grading Philosophy: Our objective will be a complete and thorough understanding of the material. Your work should demonstrate clearly and convincingly that you understand the material and how to solve problems. Partial credit will only be given to work that demonstrates an understanding of the question and the method of solution. Avoid careless mistakes which will hurt your grade - it is strongly recommended that you review your algebra and calculus early and often if you need help in these areas.

Grades: Your grade will be determined by the quizzes and exams using the following weights:
Quizzes: 10 % (Drop the two lowest scores or missed quizzes.)
Homework: 10 % (Drop the two lowest scores or missed homeworks.)
Your best test score: 20 %
Your second best test score: 15 %
Your third best test score: 10 %
Your final exam score: 35 %

Course Grade: Your grade will be determined as follows. I do not ``curve". To get an ``A", you should expect to get 90% or above. Midterm grades will be assigned based on your performance at the time these grades are assigned. Midterm grades are to be used only as a communication between the instructor and the student of your status in the course at a particular time - they are not to be used for any other purpose.
90% - 100% : A
80% - 89% : B
70% - 79% : C
60% - 69% : D
0% - 59% : R

Lesson Schedule: You will be given a lesson schedule plan which will include the section to be covered on each lecture date. This schedule may be modified at any time, but we will try to follow it closely. You are encouraged to read the text material in advance to prepare for each lecture.




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Timothy J Flaherty 2004-01-14