Yuba Community College District
Yuba College Course Outline
Course Information
Course Number:
MATH 2
Full Course Title:
Ordinary Differential Equations
Short Title:
Differential Equations
Effective Term:
Fall 2013
Course Standards
Lecture Hours:
54.000
Total Units:
3.000
Total Hours:
54.00
Repeatable:
No
Grading Method:
Letter Grade Only
Minimum Qualifications
 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
Completion with a C or better in: MATH 1B
Advisories

Language  recommended eligibility for English 1A

Mathematics  recommended eligibility for Math 52
Content
Course Lecture Content
 Solutions of ordinary differential equations
 First order differential equations including separable, homogeneous, exact, and linear
 Existence and uniqueness of solutions
 Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields
 Second order and higher order linear differential equations
 Fundamental solutions, independence, and Wronskian
 Nonhomogeneous equations
 Qualitative analysis: phase portraits
 Numerical approximation methods such as Euler's method
 Applications of higher order differential equations such as the harmonic oscillator and circuits
 Variation of parameters
 Laplace Transforms
 Series Solutions
 Systems of Ordinary differential equations
Objectives

Create and analyze mathematical models using ordinary differential equations.

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.

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

Find power series solutions to ordinary differential equations.

Determine the Laplace Transform and inverse Laplace Transform of functions.

Solve Linear Systems of ordinary differential equations.
Student Learning Outcomes
 Computation – Solve nthorder linear differential equations.
 Critical Thinking – Solve ordinary differential equations by applying an appropriate technique.
Methods of Instruction

Lecture/Discussion
Assignments
Hours per week on assignments outside of the class:
Reading Assignments
Writing Assignments
Methods of Evaluation
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes

OtherGroup or individual projects.
Course Materials
Textbooks:

William E. Boyce and Richard C. DiPrima. Elementary Differential Equations and Boundary Value Problems, 9th ed. John Wiley & Sons, Inc., 2009, ISBN: 9780470383346Equivalent text is acceptable