Course Syllabus for Introduction to Stochastics | ME 5774, Study notes of Mechanical Engineering

Download Course Syllabus for Introduction to Stochastics | ME 5774 and more Study notes Mechanical Engineering in PDF only on Docsity! Introduction to Stochastics Course ID: ME 5774 CRN: 94478 Time: Tues, Thurs at 11:00 - 12:15 Location: Rand 100L and Hawk 117 (IALR) John B. Ferris, PhD Associate Professor Department of Mechanical Engineering Virginia Tech Office hours Time: Thurs 3:00 – 4:00 Location: Durham 137 (VAL conference room) or by appointment Contact info jbferris@vt.edu office 434 766 6708 540 231 4797 (Durham 143) Text: An Introduction to Stochastic Modeling, Taylor, H.M., and Karlin, S., Academic Press / Elsevier, San Diego, 3rd Edition, 1998., Office Location Charles R. Hawkins Research Building (HAWK) Institute for Advanced Learning and Research 150 Slayton Ave Danville, VA 24540 Contact me immediately if you don’t understand something! URL for Recorded Lectures: http://www.vbs.vt.edu/register?ID=cpfqrl3xkcg0k0k8oscsc40o4 Major Measurable Learning Objectives Many problems faced by engineers are random in nature; an understanding of stochastic processes is necessary to properly analyze these problems. This course aims to provide graduate students with a strong foundation for analyzing stochastic processes and to expose them to state-of-the-art techniques. This course will strengthen existing knowledge of probability and statistics to form the basis for understanding stochastic processes. This basic understanding includes covariance functions and properties, stationarity and ergodicity, and spectral density. The concepts of stochastic processes are then developed and students are introduced to techniques for modeling and analyzing stochastic processes such as Martingales, Markov Chains, and ARIMA models. Having successfully completed this course, the student will be able to: 1. Develop and test hypotheses for possible outcomes of an experiment, using the axioms of probability and the theorems developed in class. 2. Analyze the distribution of test data using the central limit theorem. 3. Define random variables and the sigma-algebra associated with an experiment and calculate the corresponding probabilities 4. Categorize random data and identify appropriate analysis tools for different types of random data. 5. Model stochastic processes as ARIMA models and Markov Chains and compare the advantages/disadvantages for each technique given the particular application. 6. Demonstrate an understanding of the concepts of stationarity and ergodicity and the implication in analyzing and modeling stochastic processes. Outline of Topics 1. Probability and Statistics (Topic of Exam 1) 1.1. Introduction and Philosophy of Stochastics 1.2. Descriptive Statistics 1.3. Inferential Statistics 1.4. Basic Algebraic Structures 1.5. Random Variables 1.6. Combinatorial Analysis 1.7. Axioms of Probability 1.8. Conditional Probability and Independence 1.9. Discrete Random Variables 1.10. Continuous Random Variables 2. Stochastic Processes (Topic of Exam 2) 2.1. Jointly Distributed Random Variables 2.2. Stochastic Process Definition 2.3. Covariance Functions and Properties 2.4. Stationarity and Ergodicity 2.5. Spectral Density 3. Stochastic Modeling (Topic of Project) 3.1. Categories of Stochastic Processes 3.2. ARIMA models 3.3. Martingales 3.4. Markov Processes and Properties 3.5. Markov Chains 3.6. Brownian Motion 3.7. HHT 3.8. Fractals 3.9. Others… Students with Disabilities If you are a student with special needs or circumstances, if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please make an appointment with me as soon as possible. Please also contact the Services for Students with Disabilities office for further information and accommodations (see www.ssd.vt.edu). Attendance policy Class meetings are an integral part of the learning process in this class. Attendance is expected, though no part of the final grade is explicitly affected by attendance. If students cannot attend a class, it is their responsibility to make arrangements for any work that is missed. When in class, it is required to work on class material only. Unacceptable activities include (but are not limited to): checking email, text messages, web surfing, reading the paper, chatting with your friends. Again, the final assignment of grades is left to the discretion of the professor. If your activities during class are not pertinent to the class, or disruptive in any way, then this will adversely affect your grade. If you must miss a test due to an illness, you must get a formal letter from Schiffert Health Center specifically stating that you have a medical condition that will cause you to miss a test. This is different than the generic slip of paper saying that the student was seen at the center. Schiffert will NOT write excuses if they don't think it's necessary (example – a student with pink eye was not given an excuse to miss 3 tests). No exceptions. Unexcused absences will result in a ‘zero’ for your grade on the test. If you need to miss a test due to a funeral, etc., you must get a formal excuse from the Dean of Students (231-3787, 109 East Eggleston), who will require proof from you that you actually attended the funeral (example – airplane tickets, funeral program, etc.). No exceptions. Unexcused absences will result in a ‘zero’ for your grade on the test. Application of Honor System It is my intention that students collaborate to solve the ungraded problems given in the assignments, and then validate their results with the answers provided. No assistance is to be given or received on graded assignments, including but not limited to, graded homework, take- home exams, quizzes, or in-class exams. The honor code applies to all assignments; regardless of whether the pledge is written (“I have neither given nor received unauthorized assistance on this assignment”). Contact me if there are questions regarding the application of the honor code in this class. Prerequisites • Mastery of calculus and matrix math. • Mastery of basic probability and statistics • Working knowledge of MATLAB. Course expectations and grading practices will be the same for all students regardless of whether all prerequisites were satisfied. Required Text An Introduction to Stochastic Modeling, Taylor, H.M., and Karlin, S., Academic Press / Elsevier, San Diego, 3rd Edition, 1998. Related Texts Probability and Statistics for Engineering and the Sciences, Devore, J. L., Brooks/Cole Publishing, Monterey, CA, 1987. A First Course in Probability, Ross, S., Prentice Hall, Upper Saddle River, NJ, 2002. Statistics for Experimenters, Box, G.E.P., Hunter, W.G., and Hunter, J.S., John Wiley and Sons, New York, 1978. Applied Algebra and Functional Analysis, Michel, A.N., and Herget, C.J., Dover, Publications, New York, 1981. Stochastic Processes in Engineering Systems, Wong, E, and Hajek, B., Springer-Verlag, New York, 1985. Introduction to Stochastic Processes, Hoel, P.G., Port, S.C., and Stone, C.J., Waveland Press, Prospect Heights, Il, 1987. Random Data: Analysis and Measurement Proceedures., Bendat, J.S., and Piersol, A.G., John Wiley and Sons, New York, 2000.