MIA 501E - Engineering Mathematics

Course Objectives

1) Provide graduate students with the advanced analytical methods that will form the basis for their research areas.
2) To give a feel what an ODE is and what we mean by solving it.
3) To extend the concepts from first-order to second-order ODEs and to present the properties of linear ODEs.
4) Extension of the concepts and theory from second-order to higher order ODEs.
5) Solving linear ODEs by using series solutions technique.
6) An introduction to important special functions and their use in the solution of engineering problems.
7) To introduce the Laplace transform method for solving linear ODEs and corresponding initial value problems.
8) A sound understanding of linear algebra and systems of linear equations.
9) Theory and applications of Fourier analysis methods.
10) To give a feel to solve important Partial Differential Equations (PDEs).

Course Description

Ordinary Differential Equations (ODEs): First-Order ODEs, Second-Order Linear ODEs, Higher-Order Linear ODEs, Series Solutions of ODEs. Special Functions. Laplace Transforms. Linear Algebra: Matrices, Vectors, Determinants, Linear Systems, Matrix Eigenvalue Problems. Fourier Analysis: Series, Integrals, and Transforms. Partial Differential Equations (PDEs).