## Department of Mathematics

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Math 245: Elementary Differential Equations & Linear Algebra

#### Course Objectives

The principal aim of Elementary Differential Equations & Linear Algebra is for students to learn the elements of first order differential equations , second order linear differential equations; and systems of linear first order differential equations. Students also learn how to solve linear 2nd order initial value problems. Students will also learn the elements of matrix algebra including solving systems of linear algebraic equations and the use of eigenvalues and eigenvectors. Students who successfully complete Elementary Differential Equations & Linear Algebra will be capable of:

• Solving or approximating the solutions of first order linear and non-linear equations.
• Solving 2nd order linear differential equations and initial value problems.
• Solving non-homogeneous 2nd order linear differential equations by means of the Laplace transform.
• Using Gaussian elimination to solve systems of linear algebraic equations.
• Determining the transpose, inverse and determinants of matrices.
• Transforming a higher order linear differential equation into a system of first order equations. Use the resulting eigenvalues and eigenvectors of the system to determine solutions of the higher order equation.

#### Evaluation of Students

Students will be graded on their ability to solve a variety of problems involving first order and second order differential equations and matrix equations. While instructors may design their own methods of evaluation student performance, these methods must include in-class examinations, graded homework assignments and a final exam.

#### Course Outline

 Topics Number of Weeks First Order Differential Equations 3 Second Order Linear Differential Equations 3 Laplace Transforms. 2 Systems of Linear Equations 2 Matrix Algebra 2 Eigenvalues and Eigenvectors and Systems of First Order Linear Differential Equations 2

#### Textbooks & Software

William E. Boyce, Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, ISBN 0471319996

J. Polking, A. Boggess & D. Arnold, Differential Equations, ISBN 0130911062

Submitted by: David Ellis
Date: May 5th, 2003