Mathematics 252

Course Outline

LENGTH OF COURSE: One Semester (14 weeks)
 
CLASSROOM HOURS PER WEEK: 4 hours of lectures
 
NUMBER OF UNITS OF CREDIT: 3 credit hours
    Simon Fraser University - 3 credit hours
    University of British Columbia - 1.5 units
    University of Victoria - 1.5 units
PRESENT TRANSFERABILITY
    University of British Columbia - Mathematics 152 (1.5) (precludes credit for Mathematics 221
PREREQUISITE: Columbia College Mathematics 113 and 114 as co-requisite or the equivalent. 
 
AUDIENCE: This course is intended for seriousstudents of science and engineering.
 
CALENDAR DESCRIPTION
An introduction to linear and matrix algebra including theory and application of ector spaces, linear transformaions and matrices, eigenvectors and eigenvalues, linear differential equations and applications.
 
COURSE OUTLINE
1) Matrices and Gaussian Elimination (3 weeks)
Geometry of linear equations, Gaussian elimination, matrix notation and multiplication, row operations and triangular factors, inverees and transposes, applications.
 
2) Vector Spaces and Linear Equations(3 weeks)
Vector spaces and subspaces, m equations in n variables, linear independence, basis, dimension, fundamental subspaces, linear transformations
 
3) Orthogonality (2 weeks)
Perpendicular vectors and orthogonal subspaces, inner products and projections onto lines, projections and least squares approximations, orthogonal bases, Gram-Schmidt orthonormalization.
 
4) Determinants (2 weeks)
Properties of the determinant, formulas for the determinant applications.
5) Eigenvalues and Eigenvectors (3 weeks)
Properties The diagonal form of a matrix; differential equations and the powers of a matrix A; complex matrices: symmetric, Hermitian. orthogonal, unitary, similarity transformations, Fourier series
 
TEXTBOOK
    Howard Anton, Elementary Linear Algebrs, Seventh Edition, John Wiley and sons,1994
    Sections of the textbook relevant to the above topics: 1) Chapters 1 - 8, 2) Chapter : 9.1, 9.3, 9.4, 9.9 3) Chapter 10: 10.6
COURSE EVALUATION
    Quizzes and/or Assignments 10%
    Three One-Hour Tests 40%
    Comprehensive Final Exam 50%
INSTRUCTORS
    Kim Peu Chew, B.Sc. (Nanyang), M.A., Ph.D. (British Columbia)
    Sam Ekambaram, B.Sc. (Madras), Ph.D. (Simon Fraser)
    Peter Hurthig, B.Sc., M.Sc. (Briitsh Columbia)
    David Medalen, B.A. (St.Olaf), M.Sc. (British Columbia)