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LINEAR ALGEBRA

Course Outcomes

1. Students develop the algebra skills necessary to solve linear algebraic systems and linear systems of differential equations. [A1, A2, A3]
2. Students develop the matrix algebra skills necessary to do computational linear algebra. [A1, A2, A3]
3. Students obtain an understanding of the linear algebra structure underlying the theories of differential equations , Fourier analysis, and other areas of
applied mathematics. [A1, A2, A3]

Linear Algebra and Matrices

1. Matrix operations
- addition
- multiplication
- transpose
- inverse
- determinants
2. Row reduction of matrices
- row-echelon normal form
- rank
3. Systems of linear equations
- solve using matrix methods
- augmented matrices
- Cramer’ s rule
- solution space
- solving
4. Matlab (integrated into all topics)

  Vector Spaces and Matrices

1. Vector spaces associated to a matrix
- row space
- column space
- null space
- rank and nullity
- solving
2. More on vector spaces
- subspaces
- linear combinations
- spanning sets
- linear independence and dependence
- basis and dimension
- solving in general

 

  Applications

1. Eigenvalue – Eigenvector problems
- complex numbers
- case of distinct eigenvalues
2. Systems of differential equations
- first order linear systems
- complex exponentials
- stability of solutions
- inhomogeneous problems and variation
of parameters
3. Least square methods
- inner products , transpose, and distance
- projections onto subspace
- orthogonal bases
- solving by least squares method
4. Orthogonal, unitary, symmetric, and
Hermitian matrices and spectral theory

 

REQUIRED COURSE OR ELECTIVE COURSE: Option for Required Course

TEXTBOOK/REQUIRED MATERIAL: B. Kolmand and D. Hill,
Elementary Linear Algebra, 8th ed., Prentice Hall, 2004.

COORDINATING FACULTY: S. K. Yeung, Chair, Calculus Committee

COURSE DESCRIPTION: Introduction to linear algebra. Systems of linear
equations, matrix algebra, vector spaces, determinants, eigenvalues and
eigenvectors, diagonalization of matrices, applications. Not open to students
with credit in MA 262, MA 272, MA 350 or MA 351.

ASSESSMENTS TOOLS:
1. Daily homework
2. Quizzes
3. Three one-hour exams
4. Comprehensive final exam.

PROFESSIONAL COMPONENT:
1. Mathematics – 3 credits (100%)

NATURE OF DESIGN CONTENT:
N/A

COMPUTER USAGE:
Matlab

COURSE STRUCTURE/SCHEDULE:
1. Lecture – 3 days per week at 50 minutes.

TERMS OFFERED: Fall, Spring, and Summer

PRE-REQUISITES:
MA 162 Plane Analytic Geometry and Calculus II, or
MA 166 Analytic Geometry and Calculus II, or
MA 173 Calculus and Analytic Geometry II

COURSE OUTCOMES:

1. Students develop the algebra skills necessary to solve linear algebraic
systems and linear systems of differential equations. [A1, A2, A3]
2. Students develop the matrix algebra skills necessary to do computational
linear algebra. [A1, A2, A3]
3. Students obtain an understanding of the linear algebra structure underlying
the theories of differential equations, Fourier analysis, and other areas of
applied mathematics. [A1, A2, A3]

RELATED ME PROGRAM OUTCOMES:
A1. Math and science
A2. Engineering fundamentals
A3. Analytical skills

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