Linear Algebra - Summer 2004

COURSE: MATH 2010-050 Call # 21107

TIME AND PLACE: 11:20-12:50 MTWRF in Room 212 of Gilbreath Hall

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: By appointment.

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.

MATH LAB: The Mathematics Laboratory is located in Rooms 308 and 309 of Warf-Pickle Hall. It is staffed by graduate students and upper level undergraduates. They are there to help you! Hours of operation are (tentatively) Monday-Friday 1:00-5:00. The phone number is 439-7611. The Math Hotline is 439-7887 (for short questions).

Sample Tests: Copies of old tests, along with solutions, are available through the reserve desk of the Sherrod Library. They can also be accessed over the internet. Go to the Voyager Library Catalog and click on "Simple Search." Then select "Course Reserve Search" and select my name from the "Instructor List." Perform the search, click on the title of the solution set of interest, and then you will be allowed access to a PDF copy of the document.

Supplemental "Text": Instructor's Solution Manual, J. Fraleigh and R. Beauregard (a copy will be on reserve in the library). You can download PDF versions of some of the sections of the solutions manual at:

http:www.etsu.edu/math/gardner/2010/manual1.pdf
http:www.etsu.edu/math/gardner/2010/manual2.pdf
http:www.etsu.edu/math/gardner/2010/manual3.pdf

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) as follows:

Average = (T1 + T2 + T3)/3.
Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned as appropriate.

Important Dates:
Sunday(?), July 18 = Last day for 75% refund.
Friday, July 23 = Test 1 (1.1-1.6, 2.1, 2.2).
Monday, July 19 = Last day to drop without grade of "W".
Sunday(?), July 25 = Last day for 25% refund.
Friday, July 30 = LAST DAY TO DROP without dean's approval. Verifiable extenuating circumstances required after this date.
Tuesday, August 3 = Test 2 (2.3-2.5, 3.1-3.5).
Wednesday, August 11 = Last day to withdraw from the university.
Friday, August 13 = Test 3 (4.1-4.3, 5.1, 5.2, 6.1-6.3).

We will follow this tentative outline. Changes to the original schedule are made in red.

DATE
AGENDA
HOMEWORK
MON 7/12
Introduction, 1.1 = Vectors in Euclidean Spaces
1.1 = 1-41 odd
TUE 7/13
1.2 = The Norm and the Dot Product
1.2 = 1-45 odd, 40
WED 7/14
1.3 = Matrices and Their Algebra
1.3 = 1-45 odd
THR 7/15
1.4 = Solving Systems of Linear Equations
1.4 = 1-51 odd
FRI 7/16
1.5 = Inverses of Square Matrices
1.5 = 1-37 odd
MON 7/19
1.6 = Homogeneous Systems, Subspaces, and Bases
1.6 = 1-47 odd
TUE 7/20
2.1 = Independence and Dimension
2.1 = 1-37 odd, 28
WED 7/21
2.2 = The Rank of a Matrix
2.2 = 1-23 odd
THR 7/22
Review, 2.3 = Linear Transformations of Euclidean Spaces
2.3 = 1-33 odd
FRI 7/23
Test 1 (1.1-1.6, 2.1, 2.2)
-
MON 7/26
2.4 = Linear Transformations of the Plane (in brief)
2.5 = Lines, Planes, and Other Flats
2.4 = 1-15 odd
2.5 = 1-13, 21-43 odd
TUE 7/27
3.1 = Vector Spaces
3.2 = Basic Concepts of Vector Spaces
3.1 = 1-29 odd, 18 3.2 = 1-47 odd, 26
TUE 7/27
2.5 = Lines, Planes, and Other Flats
2.5 = 1-13, 21-43 odd
WED 7/28
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd, 22
WED 7/28
3.1 = Vector Spaces
3.1 = 1-29 odd, 18
THR 7/29
3.4 = Linear Transformations
3.4 = 1-45 odd, 34
THR 7/29
3.2 = Basic Concepts of Vector Spaces
3.2 = 1-47 odd, 26
FRI 7/30
3.5 = Inner-Product Spaces
5.3 = 1-27 odd, 16
FRI 7/30
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd, 22
MON 8/2
Review, 4.1 = Areas, Volumes, and Cross Products
4.1 = 1-59 odd
MON 8/2
3.3 = Coordinatization of Vectors (cont.)
-
TUE 8/3
Test 2 (2.3-2.5, 3.1-3.5)
-
TUE 8/3
3.4 = Linear Transformations
3.4 = 1-45 odd, 34
WED 8/4
4.2 = The Determinant of a Square Matrix
4.2 = 1-35 odd
WED 8/4
Review, 4.1 = Areas, Volumes, and Cross Products
4.1 = 1-59 odd
THR 8/5
4.3 = Computation of Determinants and Cramer's Rule
4.3 = 1-39 odd
THR 8/5
4.2 = The Determinant of a Square Matrix
4.2 = 1-35 odd
FRI 8/6
5.1 = Eigenvalues and Eigenvectors
5.1 = 1-41 odd
FRI 8/6
Test 2 (2.3-2.5, 3.1-3.4)
-
MON 8/9
5.2 = Diagonalization
5.2 = 1-25 odd
MON 8/9
5.1 = Eigenvalues and Eigenvectors
5.2 = Diagonalization
5.1 = 1-41 odd
5.2 = 1-25 odd
TUE 8/10
6.1 = Projections
6.1 = 1-39 odd
TUE 8/10
5.2 (cont.), 6.1 = Projections
6.1 = 1-39 odd
WED 8/11
6.2 = The Gram-Schmidt Process
6.2 = 1-35 odd,
not 25g,h, 27
THR 8/12
Review, 6.3 = Orthogonal Projections
6.3 = 1-39 odd
THR 8/12
Review
-
FRI 8/13
Test 3 (4.1-4.3, 5.1, 5.2, 6.1-6.3)
-
FRI 8/13
Test 3 (4.1, 4.2, 5.1, 5.2, 6.1, 6.2)
-

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