I. COURSE INFORMATION

• Meeting Time & Place: CE 115, Tuesday and Thursday, 6-8:30 PM, June 05 to July 25.
• Instructor: Dr. George D. Tintera
• Office: Seabreeze 211
• Office Hours: 2 to 6 PM, Tuesday and Thursday, 2 to 4 PM, Wednesday
  Appointments also available. Office hours subject to meetings related to other duties on campus. They may change during the first week or so of the semester.
• Phone: (361) 825-6028, FAX: (361) 825-5848
• Internet: tintera@falcon.tamucc.edu
• Class Website: http://www.tamucc.edu/~tintera/su00/5333/5333.html

II. COURSE DESCRIPTION

A continuation of MTH 3311, Linear Algebra. Abstract vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, canonical forms, and selected applications.

III.PREREQUISITES

MATH 3311 (Undergraduate Linear Algebra)

IV.TEXT AND OTHER SUPLIES REQUIRED

Linear Algebra with Applications, John T. Scheick, McGraw-Hill

V.COURSE OBJECTIVES

After completing the course, a student should be able to

• Understand the role of vector spaces in the solution of linear systems of equations,
• Understand the role of bases and changes of bases in the solutions of linear systems of equations,
• Interpret a matrix as a linear operator and make relevant calculations,
• Use inner products to calculate orthogonal bases, solve approximation problems and find QR decomposition of matrices,
• Calculate Eigenvalues and Eigenspaces of transformations and diagonalize transformations by a change of basis,
• Apply factorizations of matrices to special forms and solutions of equations,
• Apply the methods of linear algebra to differential equations.

VI. INSTRUCTIONAL METHODS AND ACTIVITIES

The class uses lecture format. Students are expected to read the text before class as directed and be prepared to participate in the class by calculating and evaluating models. A significant portion of the class time will be available for students to present their solutions of homework assignments.

VIII. EVALUATION AND GRADE ASSIGNMENT

Grades: Students will demonstrate their knowledge and use of definitions, relationships and theorems in both written assignments (homework sets) and in-class presentations. The presentations will be over homework sets and on two separate content presentations.

• A grade of A will be assigned to students who use definitions, ideas, terminology and symbols effectively to create solutions of non-routine problems and to give clear and coherent explanations of the reasoning that underlies such solutions.
• A grade of B will be assigned to students who can demonstrate understanding of basic definitions, ideas and relationships in the solving of problems, and can supply relevant reasons and calculations without prompting. Explanations may not always be clear and correct, but are substantially so.
• A grade of C will be assigned to students who can demonstrate knowledge of basic definitions, ideas and relationships and use them to start solutions to problems or complete solutions to problems whose outlines are given. Substantial gaps in reasoning may be present.
• A grade of D will be given to students who present incoherent, incomprehensible solutions and meaningless and incorrect calculations of most work.

Homework: The homework exercises will be listed in the course schedule (below). It is due the Tuesday after it is assigned. Completion of most problems should give students a chance to demonstrate their accomplishment consistent with earning an A. At least one problem in every section should give a chance for a student to demonstrate his/her accomplishment consistent with earning a C.

Presentations: The first presentation will be with one or more classmates on one portion of Section 3.4 from the text. The presentations will be July 11. The second presentation will be be on July 25 (the last day of class). The subject of the presentations are up to the students, but should be confirmed in advance with the instructor. They may be (but are not limited to) on material from the book not covered in class.

VIII. TENTATIVE COURSE SCHEDULE

(with homework problems in parentheses)

Week	Tuesday	Thursday
1 (June 6,8)	Systems of Equations 0.1 (1,2),0.2(1a,b,c,g,h,2,3,4),0.3 (1a,3,4,6,9)	Algebra and Solutions 0.4(1,2,7,9),0.5(1,3,4,14,15,16,20,21),0.6(handout in class-ComplexHW.pdf)
2 (June 13,15)	Chapter 1 1.1 (1.a,d,2), 1.2 (1a,b,i,p,2,5a,c,6a,b,12) 1.3(1b,d,2a,g,3,8,10,17,23)	More Chapter 1 1.4 (1a,b,2a,b,3a,b,8,15,17,24,25), 1.5 (1,3,4,11,15)
3 (June 20, 22)	Chapter 2	More Chapter 2
4 (June 27, 29)	Inner Products and Orthogonal Sets 3.1 (1,5a,b,d,6,b,c,9,13) 3.2 (2,4,a,b,5a,6,a,b,12)	Approximation and Orthogonal Projections 3.3 (2,6,10,13)
5 (July 4, 6)	4th of July--No Class Meeting	Complements and the Gram Matrix 3.5 (1a,2.10) 3.6 (4,7,8,)
6 (July 11,13)	First Presentations	More Chapter 4
7 (July 18, 20)	Spectral Theorem Quadratic Forms	Diagonalization Canonical Forms
8 (July 25)	Final Presentations

IX. CLASS POLICIES

Attendance: I will expect all students to attend all class meetings and I will take attendance. If you miss any class meetings without an excused absence, you must submit a written claim (e-mail is OK) to that effect. Do not assume that I have acknowledged your excuse until you have your claim returned with my approval.

Late Homework: In general, I accept homework after deadlines without penalty until such time as I have graded the homework of your classmates. After that time, I will continue to accept late homework, but with an increasing penalty as its lateness increases. Homework turned in more than 1 week after the due date will receive no credit. I also reserve the right to enforce exact deadlines on particular assignments if I feel it is important.

Registration: You are the only person responsible for your registration in this class. If for some reason you decide not to continue with the course, you will need to see your advisor or the registrar to drop the course. If you quit coming to class and do not drop, I will be forced to assign you a grade based on the work you have completed, usually an F. Please don't make me do that.

Last Revised June 8, 2000