Textbook: None

Instructor: Goodarz Ahmadi (CAMP 267, 268-2322) 
Office Hours: Monday and Wednesday 12:30 - 3:30 p.m. 

Course Site: https://webspace.clarkson.edu/projects/fluidflow/public_html/courses/me529/

https://sites.clarkson.edu/gahmadi/courses/me529/

Prerequisites: MA212, MA 330, Graduate Standing. 

Course Learning Objectives

1. To provide the students with a fundamental understanding of probabilistic methods in engineering.
2. To familiarize the students with the stochastic processes. 
3. To provide the students with the essential mathematical tools for handling random processes. 
4. To familiarize the students with the stochastic simulation techniques.
5. To familiarize the students with the applications of  probabilistic and stochastic methods in modern engineering problems.

Course Learning Outcomes

Objective 1:

• Students will be able to evaluate the statistical properties of random variables and can handle probabilistic transformations.

Objective 2:

• Students will become familiar with stationary and nonstationary stochastic processes, including Poisson, Winer and white noise processes.
• Students will be able to analyze linear stochastic differential equations with the use of spectral and correlation techniques.

Objective 3:

• Students will become familiar with Markov processes and Langevin equation.
• Students will be able to formulate the Fokker-Planck equation for linear and nonlinear stochastic differential equations. 
• Students will be able to analyze nonlinear stochastic differential equations with the use of perturbation and equivalent linearization techniques.
• Students will become familiar with the concept of stochastic stability.

Objective 4:

• Students will perform stochastic simulations in their respective fields of interest.
• Students will become familiar with the applications of stochastic processes in engineering including random vibrations, turbulence, and related topics.

Evaluation Methods

• Homework 10% 
• Exam-1       25%     November 3, 2023, CAMP 178, 3:00-4:20 pm
• Final Exam 40%      Final Exam Week 
• Projects      25%      Due November 30, 2021

Course Description

ME 529 Stochastic Process for Engineers R-3, C-3. 
Prerequisites: Math 222 or equivalent. 

Review of the theory of probability. Stochastic processes.  Stationary and nonstationary processes.  Time averaging and ergodicity.  Correlation and power spectrum. Langevin's equation and Markov processes.  Poisson and Gaussian processes. Response of linear systems.  Approximate methods for analysis of nonlinear stochastic equations.  Introduction to stochastic stability.  Mean square and almost sure stability analysis. Random vibrations, turbulence and other applications to engineering problems.

Exam & Homework Policies

Exam Policy

Exams will be open book with one book allowed.
 

Homework Policy

Homework will be collected as assigned.  Homework will be graded and returned to the students.