Undergraduate courses in differential equations and systems of differential equations; methods for solving ordinary differential equations including Laplace transforms; matrix techniques for systems of linear ordinary differential equations; or by consent of the instructor.
Introduce and train students in the skills of using mathematical methods for solving of engineering problems. Specifically we present mathematical methods for the solution of the Wave, Heat, and Laplace equations in various coordinate systems.
TOPICS
1) Review of differential equations
2) Review: power series solutions of differential equations, Frobenius method
3) Frobenius method, Fourier series of a function
4) Convergence of the Fourier series
5) Fourier sine and cosine series
6) Fourier integral and Fourier transform
7) Fourier cosine and sine transform and Fourier finite transforms
8) Legendre polynomials and Bessel functions
TAKE HOME MIDTERM TEST OVER a WEEKEND THROUGH 15.6. MA 501-601 STUDENTS SHOULD ARRANGE WITH ENGINEERING ONLINE TO TAKE THE TEST AS CLOSE TO the DATE in the syllabus AS POSSIBLE
9) Strum-Louiville theory and eigenfunction expansions
10) Fourier series solution of the wave equation
11) Wave motion along unbounded strings and d'Alembert's solution
12) Vibration of membranes and heat equation
13) Heat equation and conduction in infinite media
14) Heat conduction in cylinders and plates and the Dirchlet problem
15) Dirchlet problem for different geometries and the Neuman problem
In event there is extra time it will be used on elementary nonlinear examples
O'Neil, Peter V., Advanced Engineering Mathematics, Sixth Edition, Thompson Books/Cole. ISBN: 0-534-55208-0
Determination of grades: + and - system
Homework: 1/3
Examinations: 2/3
Software Requirements: None, but familiarity with Maple®, Mathematica®, and or MATLAB™ is strongly recommended. Software can be accessed through the Virtual Computing Lab if you have a high speed internet connection.
Projects: None
IMPORTANT NOTE: The course offered this summer was recorded during the 15-week semester at NC State University. The summer session, however, is 10 weeks in duration. Therefore, students will need to cover the course material at a considerably faster pace than during the regular semester. All course requirements must be completed during the 10-week summer session. This should be a consideration before registering for the course.
Engineering Online uses Real Media software to distribute the course lectures. To view the following sample lecture, you will need to download RealOne Player and have a Cable, DSL, T1 or faster connection to the Internet. If you have problems viewing a lecture, please contact the Engineering Online office at 1-877-254-0058. Click the link below to download RealOne Player.
8.22 MB
Note: If you are behind a firewall, there is a chance you will not be able to access the files.
Click link to view lecture: MA 501 - Lecture 1
To Download a video lecture file to your computer, click on the link below and choose "Save" to specify the location for the file to be saved.
Download lecture: MA 501 - Lecture 1
NCSU has recommended minimum specifications for computers used for classes. Depending on your computer needs, we recommend your computer meet or exceed the following minimum specifications below.
PCs must have an Intel-compatible 800 MHz processor, 256 MB RAM, 8 GB hard drive with 1 GB free space available, 256 Color Display, CD-ROM drive, 800x600 (min.) video adapter, sound card, and speakers. The operating system should be Windows 2000 or XP. Real One Player Basic (available free online) and high speed Internet connection such as cable, DSL, T1 or LAN will be required for EOL courses.
MAC users must have a G3 processor with firewire and USB factory built-in, 256 MB RAM, 10 GB with 1GB free space available, 256 Color Display, CD-ROM drive, 800x600 (min) video adapter, sound card, and speakers. The operating system must be MacOS 10.3 (minimum) along with the above RealOne and Internet specifications above .
For more detailed information on computer specifications and recommendations, please refer to our website at: http://engineeringonline.ncsu.edu/currentstudents/computeraccess.htm
Dr. Harvey J. Charlton, Assistant Professor
North Carolina State University
Dept. of Mathematics
203 Harrelson Hall
Campus Box 8205
Raleigh, NC 27695-8205
Fax: (919) 513-7336
E-Mail: charlton@math.ncsu.edu
Instructor's Website: http://www4.ncsu.edu/~charlton/