Applied Mathematics for Engineers and Scientists




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НазваниеApplied Mathematics for Engineers and Scientists
Дата08.10.2012
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ТипДокументы

Course Code

EE 313

Course Title

Applied Mathematics for Engineers and Scientists

Credit Hours

03

Prerequisites by Course(s) and Topics

Junior Standing

Assessment Instruments

Homework

Quizzes

Assignments




Midterm

Final




Course Coordinator




URL (if any)

-

Current Catalog Description

The objective of the course is three fold: (a) to introduce the student to the basics of probability theory, using axiomatic approach, and familiarize the student with computation of moments of random variables, (b) to make the student comfortable with formulating engineering problems in terms of vectors and matrices and then using matrix and vector space properties to solve the problems and (c) to provide the student with a solid mathematical foundation in differentiation and integration.

Textbook (or Laboratory Manual for Laboratory Courses)

Probability, Random Variables and Stochastic Processes by Athanasios Papoulis and S. U. Pillai, 4th Edition, McGraw Hill.

Linear Algebra and Its Applications by G. Strang, Harcourt Brace Jovanovich.

Reference Material

Probability and Random Processes for Electrical Engineering by Alberto Leon Garcia, 2nd Edition, Prentice Hall.

Calculus and Analytic Geometry by G. Thomas and R. Finney, Addison-Wesley.

Course Goals

Upon completion of this course, students will:

  • Know how to use various computational tools of differentiation and integration in solving engineering problems.

  • Understand random variables, moments and expectations.

  • Understand vector space concepts and become familiar with geometric concepts such as orthogonality, projections, eigenvalues and eigenvectors.

Topics Covered in the Course

  • Basic Concepts [Axiomatic Probability Theory, Discrete Probability Space and Independent Events]

  • Repeated Trials [Single and Multiple Events, Distributions – Binomial and Gaussian]

  • Random Variables [Distribution and Density Functions, Conditional density functions]

  • Functions of A Random Variable, Y = g(X) [Distribution and Density Functions, Conditional density functions]

  • Functions of Two Random Variables, Z = g(X, Y) [Distribution and Density Functions, Conditional density functions]

  • Moment Generating Functions [First and Second order Moments, Conditional Moments and Characteristic Functions]

  • Vector Spaces and Linear Equations [Subspaces, Linear Independence, Basis and Dimension]

  • Orthogonality [Inner products, Projections, Least-Square Approximations and Gram-Schmidt Orthogonalization]

  • Determinants [Properties, Formulae and Applications]

  • Sequence of Random Variables [Sum, Product and Random Vector]

  • Eigenvalues and Eigenvectors [Applications and Study of Hermitian Matrices]

Laboratory Projects/Experiments Done in the Course

N/A

Programming Assignments Done in the Course

N/A

Class Time Spent on (in credit hours)

Theory

Problem Analysis

Solution Design

Social and Ethical Issues

80%

20%

-

-

Oral and Written Communications

N/A

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