Fall 2017 - MATH 232 D200

Applied Linear Algebra (3)

Class Number: 1334

Delivery Method: In Person

Overview

  • Course Times + Location:

    Mo, We, Fr 3:30 PM – 4:20 PM
    SUR 3310, Surrey

  • Exam Times + Location:

    Dec 16, 2017
    8:30 AM – 11:30 AM
    SP 291, Surrey

  • Prerequisites:

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

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:

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 Rn
  • 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

Grading

  • Assignments 10%
  • Midterm 1 20%
  • Midterm 2 20%
  • Final exam 50%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

REQUIRED READING:

Contemporary Linear Algebra
Howard Anton and Robert C. Busby
Wiley
ISBN: 9780471163626

Registrar Notes:

SFU’s Academic Integrity web site http://students.sfu.ca/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS