Spring 2020 - MATH 232 D200
Applied Linear Algebra (3)
Class Number: 3717
Delivery Method: In Person
Course Times + Location:
Mo, We, Fr 9:30 AM – 10:20 AM
SRYE 1002, Surrey
Exam Times + Location:
Apr 16, 2020
8:30 AM – 11:30 AM
SRYE 1002, Surrey
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 (register through Canvas with SFU computing ID).
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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