Yuba Community College District

Yuba College Course Outline

### Course Information

Course Number: MATH 2
Full Course Title: Ordinary Differential Equations
Short Title: Differential Equations
TOP Code: 1701.00 - Mathematics, General
Effective Term: Fall 2013

### Course Standards

Course Type: Credit - Degree Applicable
Units: 3.0
Total class hours: 162.0
Total contact hours in class: 54.0
Lecture hours: 54.0
Hours outside of class: 108.0
Repeatable: No

### Minimum Qualifications for Instructors

• Mathematics (Masters Required)

### Course Description

The course is an introduction to ordinary differential equations including both quantitative and qualitative methods as well as applications from a variety of disciplines. Introduces the theoretical aspects of differential equations, including establishing when solution(s) exist, and techniques for obtaining solutions, including, series solutions, Laplace transforms and linear systems.

### Conditions of Enrollment

Satisfactory completion of: MATH 1B

• Language - recommended eligibility for English 1A
• Mathematics - recommended eligibility for Math 52

### Content

Course Lecture Content
1. Solutions of ordinary differential equations
2. First order differential equations including separable, homogeneous, exact, and linear
3. Existence and uniqueness of solutions
4. Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields
5. Second order and higher order linear differential equations
6. Fundamental solutions, independence, and Wronskian
7. Nonhomogeneous equations
8. Qualitative analysis: phase portraits
9. Numerical approximation methods such as Euler's method
10. Applications of higher order differential equations such as the harmonic oscillator and circuits
11. Variation of parameters
12. Laplace Transforms
13. Series Solutions
14. Systems of Ordinary differential equations

### Objectives

1. Create and analyze mathematical models using ordinary differential equations.

2. Identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations.

3. Apply the existence and uniqueness theorems for ordinary differential equations. **Requires Critical Thinking**

4. Find power series solutions to ordinary differential equations.

5. Determine the Laplace Transform and inverse Laplace Transform of functions.

6. Solve Linear Systems of ordinary differential equations.

### Student Learning Outcomes

1. Computation – Solve nth-order linear differential equations.
2. Critical Thinking – Solve ordinary differential equations by applying an appropriate technique.

### Methods of Instruction

• Lecture/Discussion

### Assignments

Writing Assignments

### Methods of Evaluation

• Exams
• Homework
• Portfolio
• Problem Solving Exercises
• Quizzes
• Other
Group or individual projects.

### Course Materials

Textbooks:
1. William E. Boyce and Richard C. DiPrima. Elementary Differential Equations and Boundary Value Problems, 9th ed. John Wiley & Sons, Inc., 2009, ISBN: 978-0-470-38334-6
Equivalent text is acceptable