MTH-230 Differential Equations
Instructor: Edward Bailey (ebailey@bcc.edu)
MW 09:00AM - 11:45AM, TEC 210
http://mathematikoi.blogspot.com
This first course in Differential Equations is equivalent to those offered at 4-year institutions. In the expectation that most, if not all, students enrolled in this course will be pursuing degrees in engineering, the topics covered will be geared toward engineering applications. This course should be readily transferrable to such institutions. Should any difficulty arise in securing transfer credit, the student should contact both the instructor and the BCC transfer coordinator.
Course Outline
Unit I: Basic definitions and principles.
1) Basic definitions
2) First order ordinary Differential Equations (DE’s)
a) Existence (and uniqueness) theorem
b) Solution methods
i) Separable variables
ii) Homogeneous DE’s
iii) Exact DE’s
iv) Solution by integrating factors of linear 1st order DE’s
v) Bernoulli Equation (optional)
Unit II: Second order linear DE’s
1) Preliminary theory
a) Initial value and boundary value problems
b) Linear dependence and independence
c) Solutions of linear equations
2) Variation of parameters
3) Constructing a second solution of a 2nd order homogeneous linear DE from a known solution
4) Homogeneous linear DE’s with constant coefficients
5) Undetermined coefficients and differential operators
6) Physical applications: mechanical vibration and analogous systems
Unit III: Laplace Transform and systems of DE’s
1) Laplace transform
2) Inverse transform
3) Translation theorems and derivatives of a transform
4) Transforms of derivatives, integrals, and periodic functions
5) Applications
6) Dirac delta function (optional)
7) Laplace transform method of solving systems of linear DE’s
Prerequisite: MTH-220 Calculus III
Text: Zill, D.
A First Course in Differential Equations, The Classic Fifth Edition. Brooks/Cole, 2001.
Grading: There will be three exams given, one corresponding to each unit. Where x is the average of your test grades, x ≥ 90% earns an A, x ≥ 80% earns a B, x ≥ 70% earns a C, and x ≥ 60% earns a D. Averages of at least 85% or 75% earn a B+ or C+, respectively.
Homework: It will be assigned at each class meeting and posted on the blog (see above). It will not be collected or graded. Bring it to class and be prepared to discuss it. Since you made it through Calculus III, you should be well aware that diligence in doing homework assignments is the key to success.
Calculators: Use of calculators on tests is neither necessary nor permitted.
Office Hours: I do not have an office. However, I can meet with students on campus on Mondays and Wednesdays after class. Email me and I’ll try to get back to you promptly. Email is the way for you to contact me outside of class. Use your BCC email account so your email is not mistaken for spam. Check my blog for announcements (see above).
