Modeling Stochastic Phenomena for Engineering Applications: Part-1
Learn about Modeling Stochastic Phenomena with the Modeling Stochastic Phenomena for Engineering Applications: Part-1 certification course from IIT Bombay.
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
Modeling Stochastic Phenomena for Engineering Applications: Part-1 is a 12-week certification course by the IIT Bombay. This course provides students with a comprehensive understanding of techniques for modelling stochastic phenomena in engineering systems. Students are provided with both practical as well as theoretical concepts in the course.
The Modeling Stochastic Phenomena for Engineering Applications: Part 1 certification by NPTEL will teach students the skill and knowledge of modeling techniques used in engineering design, decision-making, and another process. The course with its practical understanding makes engineers flourish in the professional working space.
Also Read: Online Software Engineering Certification Courses
The Highlights
- IIT Bombay recognised Completion Certificate
- Learning from Trained Faculty Members
- Free Course Readings
- Hands-on projects
Programme Offerings
- online learning
- Robust curriculum
- Hands-on Learning
- Certified faculty and mentors
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | IIT Bombay |
Eligibility Criteria
Academic Qualifications
Candidates for the Modeling Stochastic Phenomena for Engineering Applications: Part-1 online course are required to have an undergraduate, postgraduate, and Ph.D. degree.
Certification Qualifying Details
Candidates for the Modeling Stochastic Phenomena for Engineering Applications: Part-1 certification course are required to qualify for the final examination to receive the completion certificate.
What you will learn
After completing the Modeling Stochastic Phenomena for Engineering Applications: Part-1 certification syllabus, candidates will gain an essential understanding of modelling phenomena in engineering. They will be able to grab its applications in engineering and learn about the potential outcomes and the importance of informed decisions in engineering applications.
Who it is for
The Modeling Stochastic Phenomena for Engineering Applications: Part-1 Certification course is designed for students and professionals in engineering streams and looking to use the applications of Modeling Stochastic in engineering applications.
The course is apt for the following professionals:
Admission Details
To join the Modeling Stochastic Phenomena for Engineering Applications: Part-1 classes, candidates must follow the below-mentioned steps:
Step 1: Visit the official course URL:
https://nptel.ac.in/courses/103101354
Step 2: Log in to the website and enrol for the programme.
Step 3: Enter relevant academic and personal details.
Step 4: Pay the course fee to complete the enrollment process
Step 5: Start learning
Application Details
Aspiring candidates must visit the official course page to enrol in the online Modeling Stochastic Phenomena for Engineering Applications: Part-1 training. After that, they need to complete the enrollment process by entering their details and course fees.
The Syllabus
- Stirling’s Approximation
- Fourier Transforms and characteristic function
- Dirac Delta function
- Applications of delta function and Generating functions
- Laplace Transforms & Convolution theorem
- Generating function for discrete variables and Binomial distribution
- Bernoulli and Poisson distributions
- Waiting time distributions; Gaussian approximation to Poisson distribution;
- Introduction to Central Limit Theorem
- Proof of Central Limit Theorem (CLT)
- Universality of Normal distribution and Exceptions
- Introduction to Random Walk: Extension of Central Limit Theorem
- Random walk and Diffusion coefficient: Conditional and Transition probabilities
- Characteristics of Stochastic Phenomena: Markov Processes
- Examples of Propagating the Markov process via Transition probability matrix
- Chapman-Kolmogorov Equation for Multistep Transition probability and solution methods
- Transient solutions and Continuous time Markov process
- Exact solution to Symmetric (or unbiased) one-dimensional Random walk (1-D RW) using Generating function method.
- Properties of the solution for 1-D unbiased RW
- 1-D unbiased RW: Asymptotic form of occupancy probability and transition to continuous variables
- Solution to the problem of 1-D Random Walk with bias
- Generalized Random Walk with Bias and Pausing
- Effect of Pausing on Mean and Variance of Random walk
- Random-walk in the presence of reflecting barrier
- Boundary conditions for reflected Random-Walk and formulating absorbing barrier problem
- The survival probability and residence time distribution for Random walker in the presence of an absorber
- Random Walk with Bias and Absorber
- Drift and Survival probability for Random walk with bias and absorber.
- Introduction to gambler’s ruin problem.
- Solution for ultimate winning probability in Gambler’s ruin problem
- Solution to gambler’s ruin problem with site dependent jump probabilities
- Fourier transform method of solving lattice Random walks
- Two and higher dimensional Random walks
- Formulating the problem of Probability of Return to the origin
- Relationship between occupancy probability and first-time-return probability
- Proof of Polya’s theorem on the probability of return
- Return probability estimates in various dimensions and effect of bias in 1-D
- Dependence of first time return probability ( on steps
- Equilibrium solutions in lattice random walk models
- Equilibrium solution to Ehrenfest’s flea mode
- Differential equation formulation of stochastic phenomena
- Derivation of Fokker-Planck equation
- Generalized transition probability functions for Fokker-Planck equation
- Solution to 1-D Fokker-Planck equation for free particle: Method of Fourier transforms
- General non-gaussian solution to translationally invariant Chapman-Kolmogorov equation
- Cauchy distribution, power-law and other non-gaussian solutions
- Wiener process and solution to absorbing barrier problems from Fokker-Planck Perspective
- Application of Fourier Sine transform for single absorber problem
- Setting up Langevin equation for velocity fluctuations of Brownian particles
- Understanding the origin of systematic and random parts of force from kinetic theory perspective
- Kinetic derivation of a formula for delta-correlated random force
- Mean square velocity, thermal equilibrium and relationship between relaxation rate and random force coefficient.
- Velocity autocorrelation in Brownian motion
- Derivation of Stokes-Einstein relationship between diffusion coefficient and friction coefficient from Langevin equations
- Alternative derivation of Stokes-Einstein relationship & Brownian motion with external force
- Numerical simulation of the Langevin equation
- Derivation of Klein-Kramers equation from Langevin equation for joint position-velocity fluctuations of Brownian particle.
- Illustrative solutions to the Klein-Kramers equation
- Numerical simulation: Sampling from general distributions and Central Limit theorem
- Numerical simulation of Random walk trajectories and method of solving Fokker-Planck Equation in bounded domain
Evaluation process
Candidates for the Modeling Stochastic Phenomena for Engineering Applications: Part-1 certification course are required to appear for the examinations to receive the completion certificate.
IIT Bombay Frequently Asked Questions (FAQ's)
The course focuses on key concepts such as the theory of stochastic phenomena and their applications in fields such as engineering, finance, and more.
This certification course is recognised by industry professionals and academic institutions, providing participants with valuable credentials in the foundations of proteins.
The course consists of short video lectures where the concept of modelling phenomena is discussed.
Yes, students are provided with completion certificates only after they qualify for the end examinations.
The course does not require candidates to have any work experience, thus fresher candidates can join the programme.