Mathematics 100 Spring 2005 Information

Instructor: J. Gehrmann
Office: Brighton Hall Room 146 (BRH 146)
Telephone: 278-7116
Email: jgehrmann@csus.edu
Office Hours: TR 10:30-11:30 a.m.,W 4-5:30 p.m., or by appointment

Course Objective: To introduce and investigate principles of linear algebra from an applications viewpoint.

Required Textbook: Elementary Linear Algebra with Applications (9th Edition) by Howard Anton and Chris Rorres

Homework and Quizzes: Homework is very important and should be completed as the topics are covered in class. In completing this material you will gain a better understanding of the ideas considered in class and in your textbook. To encourage you to do this homework, announced and unannounced quizzes comprised of problems like those on the homework assignments will be given approximately once each week of the semester. In addition, you may be asked to turn in some exercises. The quizzes and exercises will be graded and averaged, and will constitute 10% of your numerical score.

Examinations: Three midterm examinations will constitute between 35% and 55% of your numerical score, and the comprehensive final examination will constitute between 35% and 55% of your numerical score (55% given to the higher of the final examination and average of the midterm examination scores, whichever is higher, and 35% to the other score).

Final Examination Time: Thursday, May 19, 3-5 P.M.

Grading: Your final numerical score will be computed from quiz, hour examination, and final examination scores using the percentages mentioned above. Letter grades will be assigned as follows: for an A, your numerical score must be 90 or greater, for a B, it must be between 80 and 89, for a C, between 65 and 79, and for a D, between 55 and 64.

Tentative Schedule by Topic:

Professor Gilbert Strang of MIT has made his Linear Algebra Lectures from Fall 1999 available on the Internet at URL: http://web.mit.edu/18.06/www/Video/video-fall-99-new.html

Even though Strang's MIT course covered much more material and in a somewhat different order and with different emphases, many of these lectures are appropriate for our applied linear algebra class, they are highly instructive and very clear and well-done. As we proceed through the semester, portions of these lectures may be shown in class, and I'll try to point you to other portions that may be useful to you.

Another useful resource is the Linear Algebra Toolkit by P. Bogacki

Math 100 Webpage--This includes links to information about problems discussed in class, announcements of exams and homework, and other class-related information. This page will be updated after each class.

Linear Equations (1 Week)

Introduction
Gaussian Elimination
Matrices
Elementary Matrices and a Method for Finding the Inverse of a Matrix
Further Results and Special Matrices

Determinants (1 Week)

Definition
Evaluating Determinants by Row Operations
Properties of Determinants

Vectors (2 Weeks)

Introduction
Norms and Vector Arithmetic
Dot Products and Projections
Cross Products
Lines and Planes in 3-Space

Vector Spaces (3 Weeks)

Euclidean n-Space
Linear Transformations from n-Space to m-Space and their Properties
Real Vector Spaces
Subspaces
Linear Dependence and Independence
Basis and Dimension
Row Space, Column Space, and Nullspace
Rank and Nullity

Inner Product Spaces (2 Weeks)

Inner Products
Angle and Orthogonality
Orthonormal Bases and the Gram-Schmidt Process
Least Squares Approximation
Orthogonal Matrices and Change of Basis

Eigenvalues and Eigenvectors (2 Weeks)

Definition
Diagonalization
Orthogonal Diagonalization

Linear Transformations (2 Weeks)

General Linear Transformations
Kernel and Range
Inverse Linear Transformations
Matrices of General Linear Transformations
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