## Differential Equations - MTH 267 at Germanna Community College

https://courses.vccs.edu/colleges/gcc/courses/MTH267-DifferentialEquations

Effective: 2017-08-01

### Course Description

Introduces ordinary differential equations. Includes first order differential equations, second and higher order ordinary differential equations with applications and numerical methods.

Lecture 3 hours. Total 3 hours per week.

3 credits

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

The general purpose is to give the student a solid grasp of the methods solving and applying differential equations and to prepare the student for further coursework in mathematics, engineering, computer science and the sciences.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 264 or equivalent with a grade of C or better.

### Course Objectives

- First Order Differential Equations
- Classify a differential equation as linear or nonlinear.
- Understand and create a directional field for an arbitrary first-order differential equation.
- Determine the order, linearity or nonlinearity, of a differential equation.
- Solve first order linear differential equations.
- Solve Separable differential equations.
- Solve initial value problems.
- Numerical Approximations
- Use the Euler or tangent line method to find an approximate solution to a linear differential equation.
- Higher Order Differential Equations
- Solve second order homogenous linear differential equations with constant coefficients including those with complex roots and real roots.
- Determine the Fundamental solution set for a linear homogeneous equation.
- Calculate the Wronskian.
- Use the method of Reduction of order.
- Solve nonhomogeneous differential equations using the method of undetermined coefficients.
- Solve nonhomogeneous differential equations using the method of variation of parameters.
- Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
- Solve applications of differential equations as applied to Newton's Law of cooling, population dynamics, mixing problems, and radioactive decay. (1st order)
- Solve springs-mass-damper, electrical circuits, and/or mixing problems (2nd order)
- Solve application problems involving external inputs (non-homogenous problems).
- Laplace Transforms
- Use the definition of the Laplace transform to find transforms of simple functions
- Find Laplace transforms of derivatives of functions whose transforms are known
- Find inverse Laplace transforms of various functions.
- Use Laplace transforms to solve ODEs.

### Major Topics to be Included

- First Order Differential Equations
- Numerical Approximations
- Higher Order Differential Equations
- Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
- Laplace Transforms