Calculus of Variations and Integral Equations video lectures, D. Bahuguna of IIT Kanpur

Home »Mathematics »IIT Kanpur » Calculus of Variations and Integral Equations



Calculus of Variations and Integral Equations

Lecture 1: Mod-01 Lec-01 Calculus of Variations and Integral Equations

Embed
Download:   MP4, FLV and 3GP 13904 views

SEE: Guide to Download NPTEL Video Lecture

Lecture Details :

Calculus of Variations and Integral Equations by Prof. D. Bahuguna,Dr. Malay Banerjee, Department of Mathematics and Statistics, IIT Kanpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Contents:
Introduction, problem of brachistochrone, problem of geodesics, isoperimetric problem,Variation and its properties, functions and functionals, Comparison between the notion of extrema of a function and a functional.

Variational problems with the fixed boundaries, Euler's equation, the fundamental lemma of the calculus of variations, examples, Functionals in the form of integrals, special cases contaning only some of the variables, examples, Functionals involving more than one dependent variables and their first derivatives, the system of Euler's equations, Functionals depending on the higher derivatives of the dependent variables, Euler- Poisson equation, examples, Functionals containing several independent variables, Ostrogradsky equation, examples, Variational problems in parametric form, applications to differential equations, examples, Variational problems with moving boundaries, pencil of extremals, Transversality condition, examples.

Moving boundary problems with more than one dependent variables, transversality condition in a more general case, examples, Extremals with corners, refraction of extremals, examples, One-sided variations, conditions for one sided variations.

Field of extremals, central field of extremals, Jacobi's condition, The Weierstrass function, a weak extremum, a strong extremum, The Legendre condition, examples, Transforming the Euler equations to the canonical form, Variational problems involving conditional extremum, examples, constraints involving several variables and their derivatives, Isoperimetric problems, examples.

Introduction and basic examples, Classification, Conversion of Volterra Equation to ODE, Conversion of IVP and BVP to Integral Equation.
Decomposition, direct computation, Successive approximation, Successive substitution methods for Fredholm Integral Equations.

A domain decomposition, series solution, successive approximation, successive substitution method for Volterra Integral Equations, Volterra Integral Equation of first kind, Integral Equations with separable Kernel.

Fredholm's first, second and third theorem, Integral Equations with symmetric kernel, Eigenfunction expansion, Hilbert-Schmidt theorem.
Fredholm and Volterra Integro-Differential equation, Singular and nonlinear Integral Equation.

Other Resources :

Syllabus | Citation |

Other Mathematics Courses

» check out the complete list of Mathematics Video lectures          

 

Get Your Degree!

Find schools and get information on the program that’s right for you.

Powered by Campus Explorer

Comments

Post your Comments