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Engineering Online

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.
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

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.

Created 4/15/2020