Online Course Catalog

This course covers:

• Systems of linear equations and matrices, eigenvalues, eigenvectors and diagonalization of matrices with applications to differential equations, least squares methods and numerical methods in linear algebra.
• Solution methods for systems of linear differential equations; the stability and qualitative behavior of solutions of nonlinear differential equations and systems.
• The solution of second order linear differential equations including the Legendre and Bessel equations.
• Orthogonal functions, inner product spaces, Fourier series, Bessel series, and other orthogonal series and discrete Fourier transforms with applications to signal processing and the solution of boundary value problems in mechanical vibrations, heat flow and steady-state temperature distributions.

Course Objectives: The primary objective of this course is to provide an introduction to a variety of methods in applied mathematics that are useful in engineering and science by using a problem solving approach. The content objectives include the following general topic areas: applied linear algebra and systems of linear and non-linear differential equations; orthogonal series methods including Fourier and Bessel series; the separation of variables method for boundary value problems involving partial differential equations; and discrete and continuous Fourier transform methods.

4 Hours

Engineering calculus, elementary applied differential equations, and some familiarity with matrices.

• Mathematics for Engineers