Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The online Variational Calculus and its applications in Control Theory and Nanomechanics training course has been designed as an introductory session to the main theory and applications that are related to variational calculus to problems with respect to- physics, geometry, and differential equations along with mechanics. This course on Variational Calculus and its applications in Control Theory and Nanomechanics by Swayam provides the students with adequate knowledge on the topics of- ordinary differential equations, vector calculus, and basic mechanics. In the course tenure, the applicants will be learning about the new applications that are being applied in- physics, biology, mathematics, chemistry, and engineering.
The Variational Calculus and its applications in Control Theory and Nanomechanics certification benefit the students as this will serve as a reference for advanced study and research in the same domain. After completing the course the students will have their skills increased in the field of functionals that contains several dependent variables.
The Highlights
- Course offered by Swayam
- Course partnered by IIIT Delhi
- 12 weeks program
- The certificate recognized by the government
- Course type- elective
- AICTIE approved FD course
Programme Offerings
- audio lectures
- video lectures
- Reading Material
- references
- Books
- Online discussion forum
- online learning
- assessments
- assignments
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIIT Delhi |
- Variational Calculus and its applications in Control Theory and Nanomechanics fee for the registration is kept free.
- Rs.1,000/- has to be paid by the students to apply for the examination.
Particulars | Amount |
Registration fee | Free |
Examination fee | Rs.1,000/- |
Eligibility Criteria
Education
It is necessary that the students are having a basic understanding of- ordinary differential equations (optional) or multivariable calculus before they apply for the Variational Calculus and its applications in Control Theory and Nanomechanics program.
Certification Qualification Details
The Variational Calculus and its applications in Control Theory and Nanomechanics certification will be only offered to candidates who will register for examination by paying a fee and thereafter secure a 75% minimum in it. Also, they should also get a 25% average in 8 out of 12 assignments. Thereafter they will be awarded Variational Calculus and its applications in Control Theory and Nanomechanics online courses.
What you will learn
In the Variational Calculus and its applications in Control Theory and Nanomechanics training, the following topics will be covered-
- The students will be introduced to the problems that involve calculus as a concept.
- They will be learning about the functions that pertain to X dependence.
- Candidates will have their skills improved on generalization.
- In the Variational Calculus and its applications in Control Theory and Nanomechanics certification syllabus, the students will cover isoperimetric problems.
- Students will further be learning about the independent variables.
- Candidates will also be taught about non-holonomic and holonomic functions.
- They will be solving questions that are related to variable endpoints.
- Applicants will also be taught about Lagrange multipliers.
- The registered students will be covering the chapters of a single constraint.
- Candidates in the course will further study the solutions of elastia
Who it is for
The Variational Calculus and its applications in Control Theory and Nanomechanics online course is for-
- Students who want to secure a career in the field of software development can apply for this course.
Application Details
For securing the seat in the Variational Calculus and its applications in Control Theory and Nanomechanics program the students have to visit the given link-
Step 1: The mentioned URL has to be visited by the candidates-https://onlinecourses.nptel.ac.in/noc21_ma14/preview
Note- Since, the course is currently being held therefore, the program application is not available currently.
The Syllabus
Introduction
- Problems involving Calculus of Variations: Gold-diggers Problem, Catenary,
- Brachistochrone, Dido's problem, Geodesics, minimal surface, optimal harvest,
- Revision: Extremals in Finite Dim Calculus (Functions of one and several variables), Euler Lagrange equation (E-L eqns)
Special cases E-L eqns
- Functions depending on y',
- Functions with no explicit 'x' dependence,
- Functions with no explicit 'y' dependence,
- Degenerate functions.
- Invariance of E-L eqns, existence, uniqueness of solutions,
- Generalization: Functionals containing higher derivatives
Special cases E-L eqns
- Functionals containing several dependent variables,
- Functionals containing two independent variables.
- Numerical solution: Euler's FD Method, Ritz Method, Kantorovich's Method
Isoperimetric Problem
- Finite dim case/ Lagrange Multipliers including (a) single constraint, (b) multiple constraints, (c) Abnormal problems. Isoperimetric Problems involving functional including cases of generalization in a higher dimension, multiple isoperimetric constraints, several dependent variables
- Holonomic and non-Holonomic Constraints
- Problems with Variable endpoints: Natural BCs, Solution of Elastica
Problems with Variable endpoints
- Case of several dependent variable
- Transversality conditions
- Broken extremals (Weierstrass Erdmann Condition)
- Newton's Aerodynamic Problem
- Hamiltonian formulation of E-L Eqns
Hamiltonian formulation
- Case of several dependent variables
- Symplectic Maps
- Hamilton-Jacobi Equations (HJ Eqns)
- Method of seperation of variables for HJ Eqns
- Variational Symmetries
- Noether's Theorem
- Finding Variational Symmetries
- Second Variation: Finite dim case, Legendre Condition
- Conjugate points
- Jacobi necessary condition
- Jacobi Accessory Eqns (JA Eqns)
- Sufficient Conditions
- Finding Conjugate points
- Saddle points
- Optimal Control Theory (OC): solving OC systems via Variational Techniques
OC Theory
- Constrained Optimization
- Pontrygin Minimum Principle (PMP)
- Hamilton-Jacobi-Bellmann Eqns (HJB)
- Penalty function method, Slack Variable Method
Nanomechanics
- Oscillatory motion of Carbon Nanotube (CNT)
- Basics (special functions): Pochammer symbol
- Hypergeometric Function (HF)
- Basics (Physical Chemistry): van der Waal Interaction Energy
- Lennard Jones Potential
- Oscillatory Motion of DWCNT via Hamilton's Principle
- Additional problem solving sessions
Instructors
IIIT Delhi Frequently Asked Questions (FAQ's)
The students can apply for the listed industries- Control System and Instrumentation Engineering, Software Development, and Nanoscience.
The students need not pay an amount as the Variational Calculus and its applications in Control Theory and Nanomechanics fee for the application.
No, in the Variational Calculus and its applications in Control Theory and Nanomechanics online course no scholarship will be issued.
The course on Variational Calculus and its applications in Control Theory and Nanomechanics training will be organized for twelve weeks.
The students will get the certificate from the Institute of NPTEL and IIIT Delhi.
No, the course on Variational Calculus and its applications in Control Theory and Nanomechanics online course is an independent course.
No, for the Variational Calculus and its applications in Control Theory and Nanomechanics training placement assistance will not be provided.
No, the examination on the Variational Calculus and its applications in Control Theory and Nanomechanics certification course will take place from an exam center.
The students can access the details for eligibility from the official site of Swayam.