Overview

Description

CALENDAR DESCRIPTION:

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Students with credit for MATH 240 make not take this course for further credit. Quantitative.

COURSE DETAILS:

Topics Outline:  Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations.

Topic Details:

Vectors

• Vectors in Euclidean n-Space
• Dot Product and Orthogonality
• Lines and Planes

Systems of Linear Equations

• Row Reduction (Gaussian elimination) to Echelon form
• The Geometry of Linear Systems
• Applications in business, science and engineering

Matrices

• Matrix operations
• Matrix inverse; and properties of matrices
• Elementary matrices and calculating matrix inverses
• Matrices with special forms.

Linear Transformations

• Matrices as transformations
• Geometry of Linear Transformations
• Kernel and range
• Composition and Invertibility
• Application to Computer Graphics (optional)

Determinants

• Calculating determinants
• Properties of determinants
• Cramer's rule (optional)

Complex Numbers

• Arithmetic in Cartesian co-ordinates.
• The complex plane, complex conjugate, magnitude and argument (phase).
• Polar form, De Moivre's formula and Euler's formula.
• Roots of quadratic polynomials.

Eigenvalues and Eigenvectors

• Properties and geometry
• Complex eigenvalues and complex eigenvectors
• Dynamical Systems and Markov Chains
• Application to Economics: the Leontief model (optional)
• The Power Method; Application to Internet Search Engines
• Matrix Similarity and Diagonalization

Subspaces of R^n

• Subspaces and Linear Independence
• Basis and Dimension
• The Fundamental Spaces of a Matrix
• Rank
• Change of basis

Orthogonality

• Projection
• Orthogonal bases and the Gram Schmidt process
• Orthogonal matrices (optional)
• Application to least squares approximation

Homework Quizzes:
Student will keep a homework portfolio will not be directly graded. There will be 10 homework quizzes. These will occur at the start of each Wednesday class (except for Midterm weeks). Each quiz consists of 2 homework question, and is worth 1% of your course score.

Algebra Workshop:
The Algebra Workshop is a drop-in workshop, open at least 3 days per week, where students may come from assistance with problems and questions during its working hours.

Calculators:
These will be permitted on examination, provided they do not have graphing/linear algebra capabilities nor online access.
The bookstore caries the following models:
SHARP EL-510RTB http://www.sharp.ca/model.aspx?ID=1343&group=cal&type=consumer)
SHARP EL-531XGB-WH http://www.sharp.ca/model.aspx?ID=1913&group=cal&type=consumer)

Grading

Materials

MATERIALS + SUPPLIES:

Möbius Assessment account for online assignments (register through Canvas with SFU computing ID).

REQUIRED READING: