Summer 2020 - MATH 232 D200
Applied Linear Algebra (3)
Class Number: 1242
Delivery Method: In Person
Course Times + Location:
Mo, We, Fr 2:30 PM – 3:20 PM
REMOTE LEARNING, Burnaby
Exam Times + Location:
Aug 14, 2020
3:30 PM – 6:30 PM
1 778 782-7530
Prerequisites:MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B.
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.
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.
- Vectors in Euclidean n-Space
- 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 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.
- 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
- Change of basis
- Orthogonal bases and the Gram Schmidt process
- Orthogonal matrices (optional)
- Application to least squares approximation
- Online Assignments (Möbius Assessment) 5%
- Quizzes 10%
- Midterm 1 17.5%
- Midterm 2 17.5%
- Final Exam 50%
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 + SUPPLIES:
Möbius Assessment account for online assignments (registration will be through Canvas using your SFU computing ID). If you purchased a licence within the past two semesters you will not need to purchase another one. Watch for registration details in Canvas.
Contemporary Linear Algebra
Howard Anton and Robert C. Busby
As an e-text available for purchase through Vitalsource (ISBN 9780471782834) here:
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TEACHING AT SFU IN SUMMER 2020Please note that all teaching at SFU in summer term 2020 will be conducted through remote methods. Enrollment in this course acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.
Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (email@example.com or 778-782-3112) as soon as possible to ensure that they are eligible and that approved accommodations and services are implemented in a timely fashion.