Instructor

TBA

Mathematics

# MA 501 Advanced Mathematics for Engineers & Scientists I

3 Credit Hours

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. 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

TOPICS

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.

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

## Optional Recommended Textbook

O’Neil, Peter V., Advanced Engineering Mathematics, 7th Edition, Thompson Books/Cole. ISBN-13: 978-1-111-42741-2. NOTE: The 8th edition is acceptable as well.

## Computer and Software Requirements

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.

Please review minimum computer specifications recommended by NC State University and Engineering Online.

Created 4/15/2020