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, Sturm-Liouville theory, and eigenfunction expansion; 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

After completing this course the student should be able to use mathematical methods to solve engineering problems. In particular, the student will be able to

  • Solve a variety of second order differential equations, selecting from several techniques covered in the syllabus.
  • Apply mathematical methods to solve important boundary value problems – heat, wave, Laplace, and Poisson equations.
  • Identify specific types of equations and decide on appropriate mathematical methods to find the solution.
  • Use various theoretical mathematical ideas and results in this course to analyze certain physical problems.

• Course Outline


  1. Review of differential equations

  2. Power series solutions of differential equations; the method of Frobenius

  3. Fourier Analysis

    • Fourier series of a function
    • Convergence of the Fourier series
    • Fourier sine and cosine series
    • Fourier integral and Fourier transform
    • Fourier cosine and sine transform
    • Sturm-Liouville theory and eigenfunction expansion
    • Special functions: Legendre polynomials and Bessel functions

  4. Partial Differential Equations

    • The heat equation
    • The wave equation
    • The potential (Laplace) equation

• Course Requirements

A detailed schedule for assignments will be found in the syllabus.
Determination of grades: Your final grade in this course will be determined by grades earned:

Homework = 30%
2 Tests = 40%
Final Exam = 30%

Software Requirements: None, but familiarity with Maple®, Mathematica®, and or MATLAB™ is recommended. Software can be accessed through the Virtual Computing Lab if you have a high speed Internet connection.

Projects: None

• Textbook

O'Neil, Peter V., Advanced Engineering Mathematics, 7th Edition, Thompson Books/Cole. ISBN-13: 978-1-111-42741-2

• Computer and Internet Requirements

NCSU and Engineering Online have recommended minimum specifications for computers. For details, click here.

• Instructor
  Dr. Elisabeth Brown, Lecturer
SAS Hall 3278
NCSU Campus
Raleigh, NC 27695