PACIFIC UNION COLLEGE SYLLABUS - Autumn 2003

MATH 265    ELEMENTARY LINEAR ALGEBRA

COURSE DESCRIPTION: Matrix algebra and determinants, applications to solving systems of linear equations, vector spaces, linear transformations, eigenvalues, and eigenvectors.

PREREQUISITE: MATH 131.

OBJECTIVES: To present the topics of linear algebra needed by mathematics and by other majors such as physics, engineering, business, and technology.

This class is primarily about matrices and linear transformations. These are major tools in many areas of mathematics, science, and engineering. This class is a nice blend of concrete and abstract, applied and theoretical. It gives a glimpse of higher mathematics because it uses some abstract definitions and often uses proofs to aid understanding.

TEXT AND CALCULATOR: David C. Lay, Linear Algebra and Its Applications, Addison Wesley, third edition. You will also need a mathematics computer such as the TI 89 or TI92.

INSTRUCTOR: Lloyd Best (lbest@puc.edu). Phone: office/965-6591; home/942-9680. Fax: office/965-7135.

OFFICE: CSH 238C.

OFFICE HOURS: Monday: 9-10 & 1-2; Tuesday: 11-12 & 1-4; Wednesday: 1-2 & 3-4; Thursday: 11-12 & 1-2. These hours change from time to time. I am happy to help you during my office hours and by appointment.

GRADING: The final grade will be based on Homework (20%) and Tests (80%).

A A- B+ B B- C+ C C- D+ D D-
92% 88% 84% 80% 75% 70% 65% 60% 57% 53% 50%

LEARNING DIFFERENCES: PUC strives to accommodate students with documented learning differences. If you have a learning disability, or think you might have one, please check with the Counseling Center. They can provide a diagnosis and will work with your professors to accommodate your situation.

ATTENDANCE: An attendance record for this class will be kept. Previous students have discovered that missing three or more class presentations makes it very difficult to pass the course. While class attendance is not directly figured into your grade, some topics and explanations are presented in lectures that are not in the text. In addition, announcements made during classes have the same force as statements in this syllabus.

HOMEWORK: Assignments will be announced in class. Assigned work is collected near the beginning of class on the due date. Late work is not accepted unless delayed by illness or other emergency. You must ask me to sign any late work to indicate to the reader that it is accepted.

Preparation for doing the homework problems will require more than careful attention and participation in class. Before working on the assignment you will need to carefully read the textbook and rework the textbook examples. Many students find it very useful to study with other classmates.

TESTS: Tests must be taken at the scheduled time (see schedule). Only tests which are missed due to illness or emergency circumstances may be made up. If you must miss a test, you are required to notify me in advance.

ACADEMIC INTEGRITY: You are encouraged to work with other students on assignments, but your work should reflect your own understanding. Homework which matches word-for-word the answers in the back of the book or the work of another student will be given no credit. All test work must be completely your own. A student involved in cheating (or assisting someone in cheating) on a test should expect to be dismissed from the course with a failing grade. See PUC's Code of Academic Integrity (page 229 of the General Catalog) for further details.

Class Schedule

[This schedule is subject to revision. Changes may be announced in class.]

Date Homework Due This Day Class Lecture/Discussion
Sep 23 None §1.1: Systems of Linear Equations
Sep 24 H1.1: 1,4,5,9,13,15,18,22-24,29-32 §1.2: Row Reduction and Echelon Forms
Sep 25 H1.2: 1,3,7,12,13,17,21,22,24,28,33 §1.3: Vector Equations
Sep 26 H1.3: §1.4: Matrix Equations Ax = b
Sep 30 H1.4: §1.5: Solutions of Linear Systems, §1.6: Apps.
Oct 1 H1.5&6: §1.7: Linear Independence
Oct 2 H1.7: §1.8: Introduction of Linear Transformations
Oct 3 H1.8: §1.9: Matrix of a Linear Transformation
Oct 7 H1.9: §2.1: Matrix Operations
Oct 8 H2.1: §2.2a: Inverse of a Matrix
Oct 9 H2.2a: §2.2b: Inverse of a Matrix, continued
Oct 10 H2.2b: §2.3: Characterization of Invertible Matrices
Oct 14 H2.3: Review
Oct 15 Review for the test TEST Chapters 1-2 [100 points]
Oct 16 Read ahead §3.1: Introduction to Determinants
Oct 17 H3.1: §3.2: Properties of Determinants
Oct 21 H3.2: §3.3: Cramer's Rule, Volume, Linear Trans.
Oct 22 H3.3: §4.1a: Vector Spaces and Subspaces
Oct 23 H4.1a: §4.1b: Vector Spaces & Subspaces, continued
Oct 24 H4.1b: §4.2: Null & Column Spaces, Linear Trans.
Oct 28 H4.2: §4.3: Linearly Independent Sets; Bases
Oct 29 H4.3: §4.4: Coordinate Systems
Oct 30 H4.4: §4.5: Dimension of a Vector Space
Oct 31 H4.5: §4.6: Rank
Nov 4 H4.6: §4.7: Change of Basis
Nov 5 H4.7: Review
Nov 6 Review for the test TEST Chapters 3-4 [100 points]
Nov 7 Read ahead §5.1: Eigenvectors and Eigenvalues
Nov 11 H5.1: §5.2: Characteristic Equation
Nov 12 H5.2: §5.3: Diagonalization
Nov 13 H5.3: §6.1: Inner Product, Length, & Orthogonality
Nov 14 H6.1: §6.2: Orthogonal Sets
Nov 18 H6.2: §6.3: Orthogonal Projections
Nov 19 H6.3: §6.4: Gram-Schmidt Process
Nov 20 H6.4: §6.5: Least-Squares Problems
Nov 21 H6.5: §6.6: Applications to Linear Models
Nov 25- Thanksgiving Recess Have Fun!
Dec 2 H6.6: §6.7a: Inner Product Spaces
Dec 3 H6.7a: §6.7b: Inner Product Spaces, continued
Dec 4 H6.7b: §6.8: Applications of Inner Product Spaces
Dec 5 H6.8: Review
Dec 10 Wednesday, 12:30 p.m. FINAL TEST Chapters 1-6 [150 points]