## Course Content and Outcome Guide for MTH 256

- Course Number:
- MTH 256
- Course Title:
- Differential Equations
- Credit Hours:
- 5
- Lecture Hours:
- 50
- Lecture/Lab Hours:
- 0
- Lab Hours:
- 0
- Special Fee:

#### Course Description

Includes a variety of differential equations and their solutions, with emphasis on applied problems in engineering and physics. Differential equations software will be used. Students communicate results in oral and written form. Graphing calculator required. TI-89 Titanium or Casio Classpad 330 recommended. Audit Available.#### Addendum to Course Description

This is a one term introduction to ordinary differential equations with applications. Topics include classification of, and what is meant by the solution of a differential equation, first-order equations for which exact solutions are obtainable, explicit methods of solving higher-order linear differential equations, an introduction to systems of differential equations, and the Laplace transform. Applications of first-order linear differential equations and second-order linear differential equations with constant coefficients will be studied.

#### Intended Outcomes for the course

Upon successful completion students should be able to:

• Analyze real world scenarios to recognize when ordinary differential equations (ODEs) or systems of ODEs are appropriate, formulate problems about the scenarios, creatively model these scenarios (using technology, if appropriate) in order to solve the problems using multiple approaches, judge if the results are reasonable, and then interpret and clearly communicate the results.

• Appreciate ODE and system of ODEs concepts that are encountered in the real world, understand and be able to communicate the underlying mathematics involved to help another person gain insight into the situation.

• Work with ODEs and systems of ODEs in various situations and use correct mathematical terminology, notation, and symbolic processes in order to engage in work, study, and conversation on topics involving ODEs and systems of ODEs with colleagues in the field of mathematics, science or engineering.

• Enjoy a life enriched by exposure to Calculus.

#### Outcome Assessment Strategies

#### Course Content (Themes, Concepts, Issues and Skills)

__Context Specific Skills__

__Learning Process Skills__

**1.**

**DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS**

**FIRST ORDER EQUATIONS**

**SYSTEMS OF DIFFERENTIAL EQUATIONS**

**4.**

**HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS**

**5.**

**THE LAPLACE TRANSFORM**

**6.**

**APPLICATIONS OF DIFFERENTIAL EQUATIONS**