MTH 256 Applied Differential Equations

Lecture Hours: 4
Credits: 4

Covers solutions of linear and first-order non-linear differential equations. Includes Laplace transforms and convolutions.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and completion of MTH 254 or MTH 255, or equivalent course as determined by instructor; or consent of instructor. (All prerequisite courses must be completed with a grade of C or better.)
Student Learning Outcomes:

Create mathematical models of abstract and real-world situations using linear and first-order non-linear differential equations.
Use inductive reasoning to develop mathematical conjectures involving linear and first-order non-linear differential equations. Use deductive reasoning to verify and apply mathematical arguments involving these topics.
Use mathematical problem-solving techniques involving linear and first-order non-linear differential equations, including: IVP’s and BVP’s, separable equations, equations involving homogeneous functions, exact equations, linear independence, Cauchy differential equations, Laplace transforms, and convolution integrals.
Make mathematical connections and solve problems from other disciplines involving linear and first-order non-linear differential equations.
Use oral and written skills to individually and collaboratively communicate about linear and first-order non-linear differential equations.
Use appropriate technology to enhance mathematical thinking and understanding; to sketch direction fields and orthogonal trajectories, and to solve mathematical problems involving linear and first-order non-linear differential equations.
Do projects that encourage independent, nontrivial exploration of linear and first-order non-linear differential equations, and of some of the proofs at the heart of those topics.

Statewide General Education Outcomes:

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.

Content Outline

General Theory
- Classifications
- Initial and boundary value problems
- Existence and uniqueness theorems
- Direction fields
- Euler approximations
First-Order Equations
- Separable
- Homogeneous
- Exact
- Integrating factors
- Linear
- High order, variable missing
Linear Differential Equations
- Linear independence
- Linear operators
- Undetermined coefficients
- Variation of parameters
Laplace Transforms
- Definition
- Properties
- Inverse transforms
- Convolutions