Spring 2023  MATH 232 D400
Applied Linear Algebra (3)
Class Number: 5303
Delivery Method: In Person
Overview

Course Times + Location:
Mo, We, Fr 1:30 PM – 2:20 PM
SRYC 5280, Surrey

Instructor:
Abraham Punnen
apunnen@sfu.ca
1 778 7827611

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. 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 may 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 nSpace
 Dot Product and Orthogonality
 Lines and Planes
 Row Reduction (Gaussian elimination) to Echelon form
 The Geometry of Linear Systems
 Applications in business, science and engineering
 Matrix operations
 Matrix inverse; and properties of matrices
 Elementary matrices and calculating matrix inverses
 Matrices with special forms.
 Matrices as transformations
 Geometry of Linear Transformations
 Kernel and range
 Composition and Invertibility
 Application to Computer Graphics (optional)
 Calculating determinants
 Properties of determinants
 Cramer's rule (optional)
 Arithmetic in Cartesian coordinates.
 The complex plane, complex conjugate, magnitude and argument (phase).
 Polar form, De Moivre's formula and Euler's formula.
 Roots of quadratic polynomials.
 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 and Linear Independence
 Basis and Dimension
 The Fundamental Spaces of a Matrix
 Rank
 Change of basis
 Projection
 Orthogonal bases and the Gram Schmidt process
 Orthogonal matrices (optional)
 Application to least squares approximation
Grading
 Assignments 20%
 Midterms (2, 15% each) 30%
 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.
REQUIREMENTS:
This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).
Materials
REQUIRED READING:
An Introduction to Linear Algebra
Daniel Norman and Dan Wolczuk
3rd Edition
Pearson
The SFU Bookstore will stock both the hardcopy and the electronic version of this textbook. Students are encouraged to obtain the hardcopy.
ISBN: 9870134682631
RECOMMENDED READING:
Stephen Boyd and Lieven Vandenberghe
ISBN: 9781316518960
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/coursematerials/mypersonalizedcoursematerials.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/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/s1001.html