MATH 260 Differential Equations

This course consists of concepts generally encountered in a first course in differential equations including a comprehensive treatment of first-order differential equations employing a variety of solutions techniques. A study of higher-order equations, largely second-order, is included with emphasis on linear equations possessing constant coefficients as well as variable coefficients. Classical and contemporary applications are included throughout, coming from diverse fields such as mechanics, electrical circuits, and economics. MATLAB is used to provide an integrated environment for symbolic, graphic, and numeric investigations of routine solutions of differential equations and of modeling physical phenomena. The course concludes with a discussion of the Laplace transform and its application to linear equations with constant coefficients.

Credits

3

Prerequisite

MATH 182 or equivalent with a grade of C or higher

Hours Weekly

3 hours weekly

Course Objectives

1. 1. State and use basic definitions and theorems, correctly use standard symbolism, and
   accurately and quickly perform required computations both manually and with the support of
   MATLAB software.
2. 2. Build, solve and analyze mathematical models.
   
3. 3. Translate the basic ideas of ordinary differential equations between their analytic and their
   graphic representations.
4. 4. Solve routine application problems for first and second order ordinary differential equations.
5. 5. Solve simple non-routine problems so as to extend the scope of a topic to solve problems
   amid slightly altered conditions.
   
6. 6. Follow mathematical reasoning as provided in elementary proofs, develop logical arguments,
   and identify mathematical patterns.

Course Objectives

1. 1. State and use basic definitions and theorems, correctly use standard symbolism, and
   accurately and quickly perform required computations both manually and with the support of
   MATLAB software.
2. 2. Build, solve and analyze mathematical models.
   
3. 3. Translate the basic ideas of ordinary differential equations between their analytic and their
   graphic representations.
4. 4. Solve routine application problems for first and second order ordinary differential equations.
5. 5. Solve simple non-routine problems so as to extend the scope of a topic to solve problems
   amid slightly altered conditions.
   
6. 6. Follow mathematical reasoning as provided in elementary proofs, develop logical arguments,
   and identify mathematical patterns.