# Course Description:ENGRG 5030 Linear Algebra

 Course Number: ENGRG 5030 Course Name: Linear Algebra Course Description: This course is an on-line introductory course in linear algebra. This foundation course is designed to prepare a student for study in the Master' of Science in Engineering program. Matrices, systems of equations, determinants, eigenvalues, eigenvectors, vector spaces, linear transformations, and diagnolization. This course is not appropriate for students seeking a MS or MA degree in mathematics. P: MATH 2740 with a grade of "C" or better. Prerequisites: None Level: Graduate Credits: 3 Format: Online Semesters Offered: Spring 2013: NOSummer 2013: YESFall 2013: YESSpring 2014: NO Summer 2014: YES Fall 2014: YES Registration Instructions

Learning Outcomes

• To develop an understanding of the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
• To develop your ability to handle some abstract mathematics.

In regard to the second objective, this course may be unlike any mathematics course you have had before. This course will require you not only to solve problems (as you have done in previous math classes) but also to know definitions and theorems and to be able to justify mathematical conclusions with proof. The required answer may be not a number but rather an explanation. In this sense, you may be taking your first real math class.

Unit Descriptions

Unit 1
Section 1.1:  Systems of Linear Equations
Section 1.2:  Row Reduction and Echelon Forms
Section 1.3:  Vector Equations
Section 1.4:  The Matrix Equation
Section 1.5:  Solutions Sets of Linear Systems
Section 1.6:  Applications of Linear Systems
Section 1.8:  Introduction to Linear Transformations
Section 1.9:  The Matrix of a Linear Transformation
Section 2.1:  Matrix Operations
Section 2.2:  The Inverse of a Matrix
Section 2.3:  Characterizations of Invertible Matrices
Section 2.7:  Applications to Computer Graphics
Section 3.1:  Introduction to Determinants

Unit 2
Section 4.1:  Vector Spaces and Subspaces
Section 4.2:  Null Space, Column Spaces and Linear Transformations
Section 4.3:  Linearly Independent Sets; Bases
Section 4.4:  Coordinate Systems
Section 4.5:  Dimension of a Vector Space
Section 4.6:  Rank
Section 4.9:  Markov Chains
Section 5.1:  Eigenvectors and Eigenvalues
Section 5.2:  The Characteristic Equation
Section 5.3:  Diagonalization

Unit 3
Section 5.4:  Eigenvectors and Linear Transformations
Section 5.5:  Complex Eigenvalues
Section 6.1:  Inner Product, Length, and Orthogonality
Section 6.2:  Orthogonal Sets
Section 6.1:  Inner Product, Length, and Orthogonality
Section 6.2:  Orthogonal Sets
Section 6.3:  Orthogonal Projections
Section 6.4:  The Gram-Schmidt Process
Section 6.5:  Least-Squares Problems
Section 7.1:  Diagonalization and Symmetric Matrices
Section 7.3:  Constrained Optimization

Number of Exams

There are 4 exams for this course.

Number of Assignments

There are 10 assignments and 8 quizzes for this course.

Number of Projects

There are no group projects for this course.