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The [course_title] course introduces you to the stochastic process through numerical simulations. In probability theory, a stochastic process is a time sequence representing the evolution of some system represented by a variable whose change is subject to a random variation.

Throughout the course, you will learn the basic theories of stochastic processes that will be followed by the lessons to develop python codes to perform numerical simulations of small particles diffusing in a fluid. Then, you will learn to analyse the simulation data based on the above theories.

Upon completion, you will be able to analyse the dynamical data of more complicated systems.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit:  Kyoto University.

Course Curriculum

Introduction
Welcome! 00:03:00
Lesson 1
Part 1 | Using Python, iPython, and Jupyter notebook 00:09:00
Part 2 | Making graphs with matplotlib 00:08:00
Part 3 | The Euler method for numerical integration 00:11:00
Part 4 | Simulating a damped harmonic oscillator 00:08:00
Lesson 2
Part 1 | Stochastic variable and distribution functions 00:21:00
Part 2 | Generating random numbers with Gaussian/binomial/Poisson distributions 00:13:00
Part 3 | The central limiting theorem 00:15:00
Part 4 | Random walk 00:13:00
Lesson 3
Part 1 | Basic knowledge of Stochastic process 00:13:00
Part 2 | Brownian motion and the Langevin equation 00:14:00
Part 3 | The linear response theory and the Green-Kubo formula 00:11:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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