DIFFERENTIAL EQUATIONS FOR ENGINEERS
MA
311
Catalogue
Description
This course is
more thorough than Math 310 and is designed for Pre-Engineering students.
4 credits. Prerequisite: Ma 292 Calculus and Analytic
Geometry III or equivalent.
Goals
A. To help students develop the skills needed to
solve Differential Equations of Order One and
Higher Degrees.
C. Computer Applications
Procedures
A. Lecture/Discussion
C. Assignments
Course
Content
A. Introduction
1. Definitions
2. Elimination
of Arbitrary Constants
3. Families
of Curves
1. General
solutions of Ordinary Differential Equations
2. Separation
of Variables
3. Equations
with Homogeneous Coefficients
4. Exact
Equations
5. The
Linear Equation of Order One
6. The
Determination of Integrating Factors
7. Bernoulli's
Equations
8. Substitution:
Coefficients Linear in 2 Variables
C. Orthogonal Trajectories
1. Rectangular
Coordinates
2. Polar
Coordinates
D. Linear Differential Equations
1. The
General Linear Equation
2. Linear
Independence
3. The
Wronskian
4. General
Solution of a Homogeneous Equation
5. General
Solution of a Non Homogeneous Equation
6. Differential
Operators
7. The
Fundamental Laws of Operation
E. Linear Equations with Constant Coefficients
1. The Auxiliary Equation; Distinct Roots
2. The
Auxiliary Equation; Repeated Roots
3. The
Auxiliary Equation; Imaginary Roots
4. Systems
of Equations
F. Equations of Order One and Higher Degree
1. Factoring
the Left Member
2. Singular
Solutions
3. The
c Discriminant Equation
4. The
p Discriminant Equation
5. Clairant's Equation
G. Miscellaneous Topics
1. Linear
Systems of Equations
2. Variation
of Parameters
3. Power
Series
H. Computer Applications
Evaluation Methods
1. (2)
- In-House Exams
2. (1)
- Take Home Exam
3. (5)
- Quizzes
4. Final
Exam
Bibliography
Required Text: Zill, Dennis G., A First Course in Differential
Equations, 6th Ed., PWS-Kent,
Boyce, William
E., and DiPrima, Richard C., Elementary
Differential Equations and Boundary Value Problems, 4th Ed., John Wiley
& Sons, New York,
1986. *
Rainville, Earl D. and Bedient,
Phillip E., Elementary Differential Equations, 7th Ed., MacMillan
Publishing Co., 1989.
Zill, Dennis G.,
A First Course in Differential Equations with Applications, Prindle, Weber & Schmidt.
Software
Phase
Portraits by Herman Gollwitzer, MacIntosh, available from Kinko's Academic Courseware
Exchange.
DE Graph by Henry C. Pinkham, MacIntosh,
available from Kinko's Academic Courseware Exchange.
Phaser by Huseyin Kocak,
* means in New Jersey City University Library