▶Japanese
Post to SNS
- Home
- > School of Engineering
- > Graduate major in Systems and Control Engineering
- > Stochastic Dynamics
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Systems and Control Engineering
- Instructor(s)
- Kimura Koji
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(W331)
- Group
- -
- Course number
- SCE.A502
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 4Q
- Syllabus updated
- 2017/4/26
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
How do we approach to dynamical problems in which identical waveforms won’t be observed and the responses of systems and structures cannot be predicted as the deterministic quantity? This course presents basic ideas for introducing probabilistic viewpoints and methods to these dynamical problems. The course will cover fundamental theory of probability and theory of stochastic processes, and focus on stochastic differential equations. We will also go over wide range of applications of stochastic dynamics.
Student learning outcomes
By the end of this course, the students will be able to:
1) Understand the basic concepts of stochastic dynamics
2) Learn the probabilistic approach to random or uncertain phenomena
3) Acquire knowledge of stochastic differential equations
Keywords
Probabilistic Viewpoint, Stochastic Dynamics, Stationarity and Nonstationarity, Markov Process, Wiener Process, Stochastic Differential Equations,
Stochastic Response Analysis
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
At the beginning of each class, the points of the previous class are reviewed. Towards the end of class, the subjects planned on that day will be explained and discussed.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction to Stochastic Dynamics －Probabilistic viewpoint, Random phenomena, Uncertain system | Probabilistic viewpoint |
| Class 2 | Probability Theory －Probability space, Random Variable, Moments, Convergence, Conditional Expectation | Understanding of probability and random variables |
| Class 3 | Stochastic Processes －Basic concepts, Moment function, Stationary process, Mean square calculus | Basic concepts of stochastic processes |
| Class 4 | Stochastic Processes －Markov process, Independent increment process, Wiener process, White noise | Classification of stochastic processes |
| Class 5 | Stochastic Processes －Kinetic equation, Fokker-Planck equation | Derivation of Fokker-Planck equation |
| Class 6 | Stochastic Processes －Diffusion process | Basic concepts of diffusion process |
| Class 7 | Stochastic Differential Equations －SDE and its solutions, Stochastic integral | Concepts of stochastic integral |
| Class 8 | Stochastic Dynamics －Stochastic dynamics in various research fields | Stochastic dynamics in various research fields |
Textbook(s)
None required.
Reference books, course materials, etc.
None required.
Assessment criteria and methods
1) Students will be assessed on understanding of the basic theory and its application associated with stochastic dynamics.
2) Grades will be evaluated based on exercise problems and course reports.
Related courses
- SCE.A401 ： Stochastic Systems
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites are necessary, but enrollment in the related courses is desirable.
