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 WeeksQuick 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
Lecture -1: Introduction to stochastic phenomena
Lecture -2: Examples of stochastic processes from various fields
Lecture -3: Probability distributions (Binomial, Poisson, Gaussian)
Lecture -4: Cauchy distribution, extreme value distributions
Lecture -5: Useful Mathematical Tools: Fourier Transforms, Dirac delta function, Sterling’s approximation
Lecture -6: Generating function and its inversion: examples and usefulness
Lecture -7: Statement of Central Limit theorem and its relevance
Lecture -8: Conditional probability; Derivation of Central Limit theorem (CLT)
Lecture -9: Cauchy distribution and Central limit theorem
Lecture -10: Implications of CLT to random walk models
Lecture -11: Definition and examples of Markov processes
Lecture -12: Constructing transition Matrix
Lecture -13: Chapman-Kolmogorov Equation- implications
Lecture -14: N-Step transition Matrix, Stationarity
Lecture -15: Absorbing, transient and Recurrent states
Lecture -16: Ergodicity, Equilibrium,non-Markovian examples
Lecture -17: Unbiased Random walk on a lattice: Formulation with and without pause
Lecture -18: Exact solution
Lecture -19: Biased Random walk: Formulations and solutions
Lecture -20: Random-walk in higher dimensions
Lecture -21: Probability of return to origin – Generating function formulation
Lecture -22: Proof of Polya’s theorem
Lecture -23: Random walk in the presence of absorbers and reflectors
Lecture -24: Continuous time Random walk
Lecture -25: Taylor expanded Random-walk equation : Concept of drift and diffusion
Lecture -26: Passage to differential equation (Fokker-Planck) for continuous space and time variables
Lecture -27: Solution to Random walk problems in finite domain
Lecture -28: Survival probability estimates
Lecture -29: Gambler’s ruin problem and recurrence equation
Lecture -30: Exact solution to Gamblers ruin problem
Lecture -31: Brownian Motion of colloidal particles: Historical context, Langevin equation formulation,
Lecture -32: Ornstein-Uhlenbeck process, meaning of Gaussian White-noise, autocorrelation function, non-white noise examples
Lecture -33:, Solution for velocity and displacement, limiting behavior,
Lecture -34: fluctuation dissipation theorem and practical implications
Lecture -35: Transition probability, Derivation of Klein-Kramer’s differential equation for probability density in position-velocity space
Lecture -36: Some exact solutions to velocity relaxation of a Brownian particle
Lecture -37: Derivation of Fick's law, diffusion approximation
Lecture -38: Conditions of validity, some examples in high friction limit
Lecture -39: Crossing over potential barriers; escape rate modeling under high friction limit
Lecture -40: Kramer's theory of escape from KKE, Practical applications
Lecture -41: Master-equation formulation of Stochastic processes: Derivation from Chapman-Kolmogorov equation for continuous space & time
Lecture -42: Key assumption on transition probabilities, distinguishing features, Poisson representation, Ehrenfest’s flea model
Lecture -43: Master equation for Discrete space-continuous time, Constructing Master equation from its deterministic counter-part
Lecture -44: Illustration using pure birth Process (Poisson process)
Lecture -45: Study of pure death process
Lecture -46: Solution to random-walk problem from Master-equation Perspective
Lecture -47: Birth & Death processes, Malthus-Verhulst process, Stability analysis of the deterministic counter-part
Lecture -48: General solution for the distribution function, Extinction Probability
Lecture -49: Formulating master equations for Chemical kinetics, Equations for Mean and variance
Lecture -50: Method of solving Master equation, Expansion of the master equation
Lecture -51: Introduction and examples to Branching process, Galton-Watson processes
Lecture -52: 1-member transition probabilities and their generating functions
Lecture -53: Proof of k-member transition probability
Lecture -54: Markov model of occupancy probability
Lecture -55: Population extinction-Proof of criticality theorem
Lecture -56: Examples and implications of criticality theorem
Lecture -57: Numerical simulation of Central Limit theorem
Lecture -58: Numerical approaches to master equation
Lecture -59: Numerical simulations: Markov processes
Lecture -60: Numerical Simulation of Random Walk
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.