This course will introduce the student to the solution elementary differential equations and standard applications of differential equations in science. It will include the solution of first order linear differential equations with applications to exponential growth and decay problems, mixture problems, orthogonal trajectories, etc., solutions to second order differential equations with applications to harmonic motion, and the LaPlace transform.

### Prerequisites

MATH& 163 or instructor permission

Quarters Offered

Spring

Course Outcomes

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

- Solve first order linear equations of all types
- Solve application problems using first order linear equations
- Solve higher order differential equations using various methods, such as variation of parameters, differential operators, etc.
- Apply the solution of higher order differential equations to harmonic motion problems
- Solve differential equations using Laplace Transforms
- Solve differential equations using series solutions

Institutional Outcomes

IO2

**Quantitative Reasoning:**Students will be able to reason mathematically.Course Content Outline

- Introduction to differential equations

Basic definitions and terminology

Origins of differential equations - First ordered differential equations

Preliminary theory

Separable equations

Homogeneous equations

Exact equations

Linear equations

Bernoulli equations - Applications of differential equations

Exponential growth and decay

Newton’s Law of Cooling

Mixture problems

Chemical reactions

Misc. Applications - Linear equations of higher order

Initial value and boundary value problems

Linear dependence and Independence

Solution to linear equations

Finding a second solution from a known solution

Homogeneous linear equations with constant coefficients

Undetermined coefficients

Differential operators

Solving non-homogenous equations

Variation of parameters - Applications of second order equations

Simple harmonic motion

Damped motion

Forced motion - Differential equations with variable coefficients

Cauchy Euler Equation

Power series solutions around ordinary points

Power series solutions around singular points

Regular singular points

Method of Frobenius - Laplace Transforms

The Laplace Transform

The inverse transform

Operational properties

Translation theorems and derivatives of a transform

Transforms of derivatives and integrals

Department Guidelines

In order to give the instructor the greatest flexibility in assigning a grade for the course, grades will be based on various instruments at the instructor’s discretion. However, to maintain instructional integrity there must be four class exams or three class exams and a project. A final exam will be given if there are less than four exams or a project may be substituted for the final exam if there are four in-class exams. At least 60% of the grade will be based on quantifiable work (exams, homework, quizzes, etc.). The remaining portion of the grade may be based on quantifiable work, attendance, projects, journal work, etc., at the instructor’s discretion. The following is a compilation of acceptable grading instruments: in class exams and a final, attendance, homework or quizzes, research paper, modeling projects on the calculator or computer. Other projects or assignments may be assigned as deemed appropriate at the instructor’s discretion.