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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

Data ScientistSoftware Quality Assurance EngineerResearch Scientist

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)

1: What is the main focus of the Modeling Stochastic Phenomena for Engineering Applications: Part-1 Certification Course?

The course focuses on key concepts such as the theory of stochastic phenomena and their applications in fields such as engineering, finance, and more.

2: Is this course recognised by industry or academic institutions?

This certification course is recognised by industry professionals and academic institutions, providing participants with valuable credentials in the foundations of proteins.

3: How is the Modeling Stochastic Phenomena for Engineering Applications: Part-1 online course structured and assessed?

The course consists of short video lectures where the concept of modelling phenomena is discussed.

4: Are students provided with a completion certificate for the Modeling Stochastic Phenomena for Engineering Applications: Part-1 course?

Yes, students are provided with completion certificates only after they qualify for the end examinations.

5: Is there work experience required for this online certification course?

The course does not require candidates to have any work experience, thus fresher candidates can join the programme.