Calculus of Variations

Calculus of variations 1

Topic: What is a functional? Introduction to calculus of variations.

Calculus of variations 2

Topic: Examples of variational problems. Brachistochrone problem.

Calculus of variations 3

Topic: Local and non local functionals

Calculus of variations 4

Topic: Normed linear spaces.

Calculus of variations 5

Topic: Continuous linear functional, differentiable functional, differential of a functional.

Calculus of variations 6

Topic: Variation of a functional is unique.

Calculus of variations 7

Topic: Strong and weak extrema. Example of a weak extrema which is not a strong extrema.

Calculus of variations 8

Topic: First-order necessary conditions for extrema of functional.

Calculus of variations 9

Topic: Ingredients for derivation of Euler Lagrange equation.

Calculus of variations 10

Topic: Euler Lagrange equation

Calculus of variations 11

Topic: Solutions of problems of COV using Euler Lagrange equation.

Calculus of variations 12

Topic: Derivation of Ostrogradsky's equation.

Calculus of variations 13

Topic: Example of use of Ostrogradsky's equation

Calculus of variations 14

Topic: Euler Lagrange equation with free terminal conditions.

Calculus of variations 15

Topic: Invariance of Euler's equation.

Calculus of variations 16

Topic: Variational problems in spaces of dimension greater than 1.

Calculus of variations 17

Topic: Problem of finding geodesics in general with particular examples of geodesics on cylinder, sphere and cone.

Calculus of variations 18

Topic: Variational problem in parametric form

Calculus of variations 19

Topic: Euler's equation for functionals involving the higher order derivatives.

Calculus of variations 20 part1

Topic: Variational problems with subsidiary conditions/ isoperimetric problems part 1

Calculus of variations 20 part2

Topic: Variational problems with subsidiary conditions/ isoperimetric problems part 2

Calculus of variations 21

Topic: Examples of variational problems with subsidiary conditions.

Calculus of variations 22

Topic: Variational problems with finite subsidiary conditions.

Calculus of variations 23 part1

Topic: The general variation of a functional-I part 1

Calculus of variations 23 part2

Topic: The general variation of a functional-I part 2

Calculus of variations 24

Topic: The general variation of a functional-II

Calculus of variations 25

Topic: The general variation of a functional-III

Calculus of variations 26

Topic: The general variation of a functional (examples).

Calculus of variations 27

Topic: Broken extremals.

Calculus of variations 28

Topic: Broken extremals examples.