Electrical and Computer Engineering

ELEC-307.  Mathematical Methods.  Vector analysis.  Gradient operator, line, surface and volume integrals. Curl, divergence theorem, Stokes' theorem. Matrix operations, inversion techniques. Fundamentals of linear algebra, vector space, dimension, rank, eigenvalues and eigenvectors.  Systems of ordinary differential equations.   

Prerequisite:            MATH 203.  

Textbook:                   Erwin Kreyszig, Advanced Engineering Mathematics, 8th, Ed. 

                            John  Wiley,1999  

References:               Murray. Spiegel, Vector Analysis (Schaum's Outline)    

                                     Seymour Lipschutz, Linear Algebra (Schaum's Outline)

                                     Frank Ayres, Jr., Matrices (Schaum's Outline)   

Course Goals:          To understand the analytic and computational mathematical tools of

                                    vector calculus, needed for subsequent study of  electromagnetic

                                     fields and mechanics, and of linear algebra and matrices,

                                     fundamental  to the analysis of all linear systems.  

Course Objectives:  The student will develop a working knowledge of vector

                                    differential and integral calculus and matrices with concurrent use of

                                     computer applications programs.  That knowledge will include 

                                    (i) vector products and operations, (ii) gradient, divergence, curl,

                                    and their physical interpretation, (iii) line and surface integrals, (iv)

                                    matrix definitions, products, and operations, and systems of linear

                                    eqs., and (v) eigenvalues and eigenvectors.                                   

Prerequisite by Topic:  

1.               Calculus  

2.               Ordinary Differential Equations

3.               Vector Algebra 

Topics:   

1.               Vector spaces and vector products (8 lectures)

2.               Gradient, divergence, curl  (6 lectures)

3.               Curves and Surfaces    (2 lectures)

4.               Line, surface, triple integrals (6 lectures)

5.               Divergence theorem and Stokes' theorem   (2 lectures)

6.               Systems of linear algebraic equations   (5 lectures)

7.               Rank of matrix   (1 lecture)

8.               Matrix multiplication and inversion (2 lectures)

9.               Determinants  (3 lectures)

                                10.             Eigenvalues and eigenvectors (4 lectures)

11.             Testing (three tests, final examination) (5 hours)  

Computer Usage:  

Computer  homework paralleling written homework is assigned in the areas of vectors and vector integral calculus, integration, and matrices utilizing the MATHCAD and maple software packages.

 ABET category content as estimated by the faculty member who prepared this course description:                                   Mathematics  3 Credits or 100%

 Prepared  by:   Dr. Romeo Pascone                 Date: June 18, 2001