Linear Algebra - Fall 2001

COURSE: MATH 2010 Call # 33204

TIME AND PLACE: 12:45--2:05 TR in Room 314 of Gilbreath Hall

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: 10:15-11:10 MWF

OFFICE: Room 308G of Gilbreath Hall

PHONE: 439-6977 (308G Gilbreath), Math Department Office 439-4349

E-MAIL: gardnerr@etsu.edu
HOMEPAGE: www.etsu.edu/math/gardner/gardner.htm (see my homepage for a copy of this course syllabus and updates for the course).

TEXT: Linear Algebra, 3rd Edition, by J. Fraleigh and R. Beauregard.

Supplemental "Text": Instructor's Solution Manual J. Fraleigh and R. Beauregard (a copy will be on reserve in the library).

Class Notes: We will use overheads for the bulk of the in-class lectures. Copies of the overheads are available on the web in both PostScript and PDF formats. For details see:

www.etsu.edu/math/gardner/2010/notes.htm.

Prerequisite: A knowledge of differential calculus (such as provided by Calculus 1 or Technical Calculus 1). You will also need to know how to evaluate elementary definite integrals.

Note. Linear Algebra (or "Matrix Theory") is one of the most useful areas of mathematics. It is applicable in mathematics itself in areas ranging from Calculus and Discrete Math to Functional Analysis. It is applicable in statistics (least-squares methods and transition matrices), biology (population distributions and genetics), physics (theoretical and applied), computer science (in coding theory and cryptography) and almost any other area that uses numbers! We will illustrate some of these applications in this class. We will depend somewhat on technology (such as the TI-89 calculator) for rote computational work (though we will make sure to do several examples of each type of computation by hand, before relying on the technology). A users guide to the TI-89 for linear algebra computations will be given out in class and made available on the web at:

www.etsu.edu/math/gardner/2010/ti89la.pdf and www.etsu.edu/math/gardner/2010/ti89la.ps.
This will allow us to concentrate more on the concepts (i.e. the definitions, theorems, and ideas underlying the material).

Grading: Your grade will be determined by averaging your scores on three tests (T1 - T3) and the final (F) as follows:

Average = (T1 + T2 + T3 + 2F)/5.
Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned as appropriate.

Syllabus Attachment: You can find an on-line version of the university's syllabus attachment (which contains general information concerning advisement, honor codes, dropping, etc.) at

www.etsu.edu/reg/syllabus.htm and www.etsu.edu/reg/syllabus.pdf.

Important Dates:
Friday, September 7 = Last day for 75% refund.
Thursday September 20 = Test 1 (1.1-1.6).
Monday, September 24 = Last day to drop without grade of "W".
Monday, September 24 = Last day for 25% refund.
Monday, October 22 = LAST DAY TO DROP without dean's approval. Verifiable extenuating circumstances required after this date.
Thursday, October 25 = Test 2 (2.1-2.5, 3.1-3.5).
Thursday, November 29 = Test 3 (4.1-4.3, 5.1, 5.2, 6.1-6.3).
Wednesday, December 5 = Last day to withdraw from the university.
Thursday, December 13 = Comprehensive final, 1:20-3:20.

We will follow this tentative outline.

DATE
AGENDA
HOMEWORK
TUE 8/28
Introduction, 1.1 = Vectors in Euclidean Spaces
1.1 = 1-41 odd
THR 8/30
1.2 = The Norm and the Dot Product
1.2 = 1-45 odd, 40
TUE 9/4
1.3 = Matrices and Their Algebra
1.3 = 1-45 odd
THR 9/6
1.4 = Solving Systems of Linear Equations
1.4 = 1-51 odd
TUE 9/11
September 11, 2001
-
TUE 9/13
1.5 = Inverses of Square Matrices
1.5 = 1-37 odd
TUE 9/18
1.6 = Homogeneous Systems, Subspaces, and Bases
1.6 = 1-47 odd
THR 9/20
Catch up!
-
TUE 9/25
Review, 2.1 = Independence and Dimension
2.1 = 1-37 odd, 28
THR 9/27
Test 1 (1.1-1.6)
-
TUE 10/2
2.2 = The Rank of a Matrix
2.2 = 1-23 odd
THR 10/4
2.3 = Linear Transformations of Euclidean Spaces
3.1 = Vector Spaces
2.3 = 1-33 odd
3.1 = 1-29 odd, 18
TUE 10/9
3.2 = Basic Concepts of Vector Spaces
3.2 = 1-47 odd, 26
THR 10/11
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd, 22
TUE 10/16
3.4 = Linear Transformations
3.4 = 1-45 odd, 34
THR 10/18
3.5 = Inner-Product Spaces
5.3 = 1-27 odd, 16
TUE 10/23
 4.1 = Areas, Volumes, and Cross Products, Review
4.1 = 1-59 odd
THR 10/25
Test 2 (2.1-2.3, 3.1-3.5)
-
TUE 10/30
4.2 = The Determinant of a Square Matrix
4.2 = 1-35 odd
THR 11/1
4.3 = Computation of Determinants and Cramer's Rule
4.3 = 1-39 odd
TUE 11/6
5.1 = Eigenvalues and Eigenvectors
5.1 = 1-41 odd
THR 11/8
5.2 = Diagonalization
5.2 = 1-25 odd
TUE 11/13
6.1 = Projections
6.1 = 1-39 odd
THR 11/15
6.1 (continued)
-
TUE 11/20
6.2 = The Gram-Schmidt Process
6.2 = 1-35 odd, not 25g,h, 27
THR 11/22
Thanksgiving Holiday
-
TUE 11/27
Review
-
THR 11/29
Test 3 (4.1-4.3, 5.1, 5.2, 6.1-6.2)
-
TUE 12/4
6.3 = Orthogonal Projections
6.3 = 1--39 odd
THR 12/6
Review
-
THR 12/13
Comprehensive Final (1:20--3:20)
-

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