Math 201-105-RE Linear Algebra - SLC Home Page

Math 201-105-RE Linear Algebra Credits: 2

Ponderation: 3-2-3

2

3

Fall 2012 Periods: 14-24-34-44-54

Instructor: Office:

Steve Hardy Room 334

Prerequisite:

Secondary V Mathematics: Technical and Scientific Option (064-506)   Secondary V Mathematics: Natural Science Option (065-506) 

Telephone: Email:

Johann Carl Friedrich Gauss Born: 30 April 1777 in Brunswick Died: 23 Feb 1855 in Göttingen

656-6921 (ext. 433) [email protected]

or their equivalent.

Recommended:

Differential Calculus, Math 201-103-RE (previously) Integral Calculus, Math 201-203-RE (previously or concurrently)

Textbook (optional):

Anton, Howard

Elementary Linear Algebra (Abridged Version), 10th Ed.

Additional References:

Coleman, DelGrande & al Koleman Lipschutz, Seymour Ayres, Frank Jr.

Calculator:

Only the Sharp EL531W will be permitted for test and examinations. It may be purchased at the bookstore.

Program Objectives:

In this course you will see some of the contributions of linear algebra to the understanding of the human phenomena, partially satisfying objectives 022R and 022S. The elements of this objective are: 1) To understand the development of linear algebra. 2) To know and understand the main facts, notions, concepts, theories, methods and other key components of linear algebra. 3) To demonstrate the relevance and scope of these components in the understanding of the human phenomena.

Course Objectives:

In this course you will use the methods of linear algebra and vector geometry to study the various phenomena of human activities, satisfying objective 022Z of the Social Science Programme. The elements of this objective are: 1) To situate the historical context of the development of linear algebra and vector geometry. 2) To use matrices to solve concrete problems. 3) To apply different methods of solving systems of linear equations. 4) To use vectors operations to solve concrete problems. 5) To establish connections between vector geometry and linear algebra. 6) To apply the methods of linear algebra and vector geometry. 7) To solve optimization problems using methods of solving systems of linear inequations with two or more variables.

Course Description:

The course will follow the lecture method with frequent problem solving interludes during which the teacher will be available for individual help.

John Wiley & Sons, Inc.

Algebra Elementary Linear Algebra, 7th Ed. Linear Algebra, Schaum’s Outline Series Matrices, Schaum’s Outline Series

Student should feel free and are welcome to ask questions at any point during the lecture.

Evaluation: Quizzes:

Regular (weekly, ~10 minutes) quizzes will be given during the semester on the topic(s) covered during the week. A student missing a quiz will automatically be given the result “0” for that quiz.

Tests:

 There will be 3 class test during the semester which are compulsory. Unless a student is absent due to College-authorized reason (see section 2.7 of the IPESA) then a “0” will be given for that test.  Students are responsible for knowing when a test will be given. Ignorance of a test date will not be considered a valid excuse.  In the event that the college closes or the teacher is absent on a scheduled test or quiz date, the test/quiz is moved to the next school day automatically.

Final Exam:

There will be a three hours comprehensive final examination scheduled by the college between May 7 and May 18. This exam is compulsory and no alternate exam will be given.

Grading Scheme:

The midterm and final grades will be calculated as follows:

Quizzes Tests Final Exam

Approximately 10 3

Final Grade 15% 45% 40%

Absences:

Attendance is mandatory and a maximum of 7 absences will be tolerated (explained and/or unexplained). More than the 7 absences may mean failure in the course (see section 5.2 of the Institutional Policy on the Evaluation of Student Achievement (IPESA) on the SLC web site http://www.slc.qc.ca/).

Rules & Regulations:

St. Lawrence has definite rules regarding cheating and plagiarism. Any students caught cheating may receive a zero. If a student is caught a second time, automatic failure in the course will result and disciplinary action may be taken. For more information, students can consult section 5.5 of the IPESA.

Course Content:

1. SYSTEMS OF LINEAR EQUATIONS: a) Intro. To Systems of Linear Equations b) Gaussian & Gauss-Jordan Elimination c) Homogeneous Systems of Linear Equations d) Matrices, Operations & Arithmetic Rules e) Elementary Matrices & finding A-1 f) Invertibility of Matrices 2. DETERMINANTS: a) The Determinant Function b) Evaluating Determinants (Row Reduction) c) Properties of Determinants d) Cofactor Expansion; Cramer’s Rule 3. GEOMETRIC VECTORS: a) Representations as line segments b) Addition, Subtraction & Scalar Multiplication c) Properties of Algebraic Operations d) Linear Dependence/Independence e) Geometric Theorems f) Navigation Problems 4. VECTORS IN Rn (Emphasis on R2 and R3): a) Vector Arithmetic; Norm of a Vector b) Dot Product; Projections c) Cross Product d) Linear Dependence/Independence e) Bases (Orthogonal, Orthonormal) and Dimensions * These topics will only be covered if time allows.

5. EQUATIONS OF HYPERPLANES: a) Vector Equations in R2 and R3 b) Parametric Equations in R2 and R3 c) Symmetric Equations in R2 and R3 d) Distances and Intersections of Hyperplanes 6. VECTOR SPACES: a) Euclidean n-space b) General Vector Spaces c) Subspaces d) Linear Independence, Basis and Dimension e) Row/Column Space of a Matrix f) Inner Product Spaces g) Length and Angle in Inner Product Spaces 7. EIGENVALUES, EIGENVECTORS *: a) Characteristic Polynomial (Cayley-Hamilton Thm) *

b) Eigenvalues and Eigenvectors * 8. APPLICATIONS: Miscellaneous Applications of Linear Algebra * a) Least Squares Fit b) Transportation/Assignment Problem c) Linear Programming d) Simplex Method e) Leontief Economic Models e) Genetics f) Population Growth g) Animal Harvest