Summer 2021 - MATH 240 D100

Overview

• Course Times + Location:

Mo, We, Fr 11:30 AM – 12:20 PM
REMOTE LEARNING, Burnaby

• Exam Times + Location:

Aug 11, 2021
8:30 AM – 11:30 AM
REMOTE LEARNING, Burnaby

• Prerequisites:

MATH 150 or 151 or MACM 101, with a minimum grade of C-; or MATH 154 or 157, both with a grade of at least B.

Description

CALENDAR DESCRIPTION:

Linear equations, matrices, determinants. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphasis and includes proofs of the basic theorems. Students with credit for MATH 232 cannot take this course for further credit. Quantitative.

COURSE DETAILS:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Linear Equations

• Systems of Linear Equations, Row Reduction and Echelon Form
• Vectors, Vector Equations, Matrices
• The Matrix Equation Ax=b
• Solution Sets of Linear Systems
• Matrix Inverse
• Linear Independence, Rank and Dimension
• Introduction to Linear Transformations
• The Matrix of a Linear Transformation
Vector Spaces
• Vector Spaces and Subspaces
• Null Spaces, Column Spaces, and Linear Transformations
• Linearly Independent Sets; Bases for Subspaces
• Coordinate Systems
• The Dimension of a Vector Space
• Change of Basis
Determinants
• Determinants and their Properties
• Cramer's Rule
Complex Numbers
• Arithmetic in Cartesian Co-ordinates
• The Complex Plane,Complex Conjugate, and Magnitude
• Polar Form, De Moivre's Formula and Euler's Formula
Eigenvalues and Eigenvectors
• Complex Eigenvalues
• The Characteristic Equation
• Diagonalization
• Eigenvectors and Linear Transformations
• Application: The Leslie Age Distribution model
Orthogonality and Least Squares
• Inner Product, Length and Orthogonality
• Orthogonal Sets
• Orthogonal Projections
• The Gram-Schmidt Process
• Application: Least Squares Problems

Course Delivery

•  Lecture: asynchronous- lectures will not be held at fixed times, on-line; they will be prerecord and released at fixed time
•  Midterm(s): synchronous; date: TBA
•  Final exam: synchronous; date: TBA

• Homework / Quizzes 10%
• Hand-In Proofs 10%
• Midterm 1 20%
• Midterm 2 20%
• Final Exam 40%

REQUIREMENTS:

• Ability to scan clearly readable documents (phone app acceptable)

Materials

Linear Algebra and Its Applications
5/E
Lay, Steven R.; Lay, David C.; McDonald, Judith; McDonald, Judi J.
Pearson Education
ISBN: 9780321982384