Catalog Course Search Details

 Department:    MATH

 Course #:    238

 Credits:    5

 Variable:     No

 IUs:    5

 CIP:    270101

 EPC:    n/a

 REV:    2018

 Course Description  

An introductory course in differential equations including first order equations, second order and higher order equations, applications to physical and other systems.

 Prerequisite  

Prerequisite: MATH& 153 with a grade of C or better.

Contact Hours (based on 11 week quarter)

Lecture: 55

Lab: 0

Other: 0

Systems: 0

Clinical: 0

Intent: Distribution Requirement(s) Status:  

Academic Elective  

Equivalencies At Other Institutions

Learning Outcomes

After completing this course, the student will be able to:

1. Solve first and second order linear differential equations
2. Solver separable and exact equations
3. Solve ODEs using reduction of order, method of undetermined coefficients, and the method of variation of parameters.
4. Use ODEs to analyze physical applications and other systems.
5. Graphically and numerically solve ODEs using computer programs and calculators.
6. Apply alternative mathematical techniques, from a historical perspective where appropriate.
7. Understand how mathematics is used in other fields and occupations.
8. Understand the use of mathematics cross-culturally.

General Education Learning Values & Outcomes

Revised August 2008 and affects outlines for 2008 year 1 and later.

1. Information Literacy

Definition: Recognizing when information is needed and have the ability to locate, evaluate, and use effectively the needed information.

Outcomes: Students will be able to . . .
1.1 Determine the extent of information needed.

2. Critical Thinking

Definition: The ability to think critically about the nature of knowledge within a discipline and about the ways in which that knowledge is constructed and validated and to be sensitive to the ways these processes often vary among disciplines.

Outcomes: Students will be able to . . .
2.1 Identify and express concepts, terms, and facts related to a specific discipline.
2.3 Identify, interpret, and evaluate pertinent data and previous experience to reach conclusions.
2.7 Identify and evaluate connections and relationships among disciplines.
2.9 Apply and/or create problem-solving strategies to successfully adapt to unpredictable and/or changing environments.

8. Mathematical Reasoning

Definition: Understanding and applying concepts of mathematics and logical reasoning in a variety of contexts, both academic and non-academic.

Outcomes: Students will be able to . . .
8.1 Analyze problems to determine what mathematical principles apply.
8.2 Correctly apply logical reasoning and mathematical principles to solve problems.
8.3 Interpret information and reasoning expressed mathematically (for example in spreadsheets, diagrams, charts, formulas, etc.).
8.4 Communicate mathematical information effectively.

9. Scientific Literacy

Definition: Understanding scientific principles, and analyzing and applying scientific information in a variety of contexts.

Outcomes: Students will be able to . . .
9.1 Demonstrate an understanding of fundamental scientific concepts.

10. Technology

Definition: Understanding the role of technology in society and using technology appropriately and effectively.

Outcomes: Students will be able to . . .
10.3 Use technology appropriate to the context and task to effectively retrieve and manage information, solve problems, and facilitate communication.

Course Contents

1. First order linear and non-linear equations
2. Separable equations
3. Exact equations
4. Integrating factors
5. Fundamental solutions of the homogneous equation
6. Solutions to non-homogenous equations
7. Methods of undetermined coefficients
8. Method of variation of parameter
9. Homogenous equations with constant coefficients
10. Initial value problems
11. Applications to elementary mechanics, population dynamics, vibration, and other physical systems
12. Laplace transforms (optional)