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     MA 501 Advanced Mathematics for Engineers and Scientists I
 

Survey of mathematical methods for engineers and scientists. Ordinary differential equations, series solutions, and the method of Frobenius; Fourier series, Fourier integral, and Fourier transforms; special functions, Strum-Louville theory, and eigenfunctions; partial differential equations and separation of variables. Applications to engineering and science. 3 credit hours. Not for credit by mathematics majors.

  
     

Prerequisite
  

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.

 
Course Objectives  

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.

 
Course Outline  

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
8) Legendre polynomials and Bessel functions
TAKE HOME MIDTERM TEST OVER a WEEKEND THROUGH 15.6. MA 501-651 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


Textbook  

O'Neil, Peter V., Advanced Engineering Mathematics, Sixth Edition, Thompson Books/Cole. ISBN: 0-534-55208-0


Course Requirements   A detailed schedule for assignments will be found in the syllabus.

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.

 
Computer and Internet Requirements  

NCSU has recommended minimum specifications for computers that are generally used for courses. Those specifications can be found here: http://www.ncsu.edu/it/compspecs/

Engineering Online recommends that your computer meets or exceeds the following minimum specifications below. A computer with greater capability (processor speed, RAM, internet bandwidth, disk capacity) will be more likely to properly display the video content of Engineering Online courses.

Windows:

  • Microsoft Windows XP, Windows 2003, or Windows Vista
  • Intel-compatible 1 GHz processor
  • 512 MB RAM
  • 60 GB hard drive with 1 GB free space available
  • Video display at 1024 x 768 or greater
  • Sound output and speakers
  • Microsoft Internet Explorer 6.0 SP1 or later, Firefox 2.0 or later, or Google Chrome 1.0
  • Windows Media Player 9.0 or later
  • Real One Player Basic (required for certain courses)
  • Adobe Acrobat Reader
  • Broadband Internet connection (256 Kbps or more)

Mac OS X:

  • Mac OS X 10.4.8 or later
  • G4 processor
  • 512 MB RAM
  • 60 GB hard drive with 1 GB free space available
  • Video display at 1024 x 768 or greater
  • Sound output and speakers
  • Safari 2.0.4 (or later) or Firefox 2.0 (or later)
  • Silverlight  (viewers may be prompted to install this when first viewing a presentation)
  • Real One Player Basic (required for certain courses)
  • Adobe Acrobat Reader
  • Broadband Internet connection (256 Kbps or more)
  • NOTE:  The Flip4Mac plug-in causes problems when viewing Mediasite presentations and should be disabled.

Linux:

  • Playback of Mediasite presentations on Linux is accomplished via the Moonlight Project, an open source implementation of Microsoft Silverlight. For more installation on the installation and configuration of Moonlight, please visit http://www.go-mono.com/moonlight/. The compatible operating systems and browsers are listed on this page.
  • Microsoft Media Pack for Moonlight
  • Adobe Reader for Unix
  • Broadband Internet connection (256 Kbps or more)

 
Instructor  

Dr. Harvey J. Charlton, Assistant Professor
North Carolina State University
Dept. of Mathematics
203 Harrelson Hall
Campus Box 8205
Raleigh, NC 27695-8205

Phone: (919) 513-2291
Fax: (919) 513-7336
E-Mail: charlton@math.ncsu.edu
Instructor's Website: http://www4.ncsu.edu/~charlton/