Linear Algebra

Course Number: ENGRG 5030
Course Name: Linear Algebra (Online)
Course Description:    This course provides you with fundamental concepts in linear algebra. Topics include solving systems of linear equations, vector spaces, inner products, determinants, eigenvalues, similarity of matrices, and Jordan Canonical Form.
Prerequisites:    None
Level: Graduate
Credits: 3
Format: Online
Program: Master of Science in Engineering

Registration Instructions

NOTE: The information below is representative of the course and is subject to change.  The specific details of the course will be available in the Desire2Learn course instance for the course in which a student registers.

Additional Information

Learning Outcomes
Upon completion of this course, you should be able to

  • Develop an understanding of the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
  • 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 7.2:  Quadratic Forms
Section 7.3:  Constrained Optimization

Reading Assignments
The course is broken into three units. For each unit covered in this class, you will first read the unit materials carefully.

Self-Study Assignments
After you've read the unit materials, you are asked to look at and work the practice problems at the end of each assigned section in the text. The full solutions to these practice problems can be found immediately after the exercises.

You are then asked to work a number of exercises at the end of each section of the text. After completing these exercises, you should have a good working knowledge of the terms listed in Important Topics/Ideas.

These are the kind of problems that you will be asked and required to work on the exams and the quizzes. Remember, practice makes perfect!

Quizzes and Exams
There is a total of eight short quizzes (one quiz after [about] every third section of material covered). Each quiz is worth 15 points.

A 120-point exam follows each of the three units. The final exam is worth 200 points and is comprehensive.

Grading Scale
A 90% - 100%
B 80% - 89%
C 70% - 79%
D 60% - 69%
F 0% - 59%


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