COURSE SYLLABUS

Course Number: MATH2660

Course Title: TOPICS IN LINEAR ALGEBRA

Credit Hours: 3

Prerequisites: MATH1620

Corequisite:

Bulletin Description:

TOPICS IN LINEAR ALGEBRA (3). Pr., MATH1620. Vector spaces, linear transformations, matrices, determinants, linear equations, bases and dimension, eigenvalues, inner product spaces, diagonalization of symmetric matrices.

Objectives:

To present to the student an understanding of elements of linear algebra. To present to the student an understanding of the concept of higher dimensional spaces, matrices and matrix algebra, eigenvalues, and the application of these concepts to physical world problems.

Course Content: (Instructors have the freedom to alter the ordering of this material.)

 

Euclidean n-space as a Linear Space, Vector spaces, Linear Transformations;

Subspaces, Kernels and Dimension. [4 days]

Linear Equations: Matrices and Gauss-Jordan Elimination, Systems of Linear Equations. [5 days]

Basis and Linear Independence, Basis change Matrix. [6 days]

Inner Product Spaces; Orthogonality, Gramm-Schmidt Process. [3 days]

Matrix Algebra, Matrix inversion. [3 days]

Eigenvalue problems for matrices, Eigenvalues and Eigenvectors, Determinants. [7 days]

Diagonalization of Symmetric Matrices. [2 days]

Applications to physical world problems: [6 days]

Applications such as: Markov chains, circuits, network flow, ordinary differential equations.

Use of Matrix specific software. [3-4 days]

The syllabus leaves 5-6 days open for tests and for review or additional topics (such as quadratic forms).