What is meant by calculus of variations?

Definition of calculus of variations : a branch of mathematics concerned with applying the methods of calculus to finding the maxima and minima of a function which depends for its values on another function or a curve.

What is the purpose of calculus of variations?

The calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

What is the difference between variation and differentiation?

variation (delta) is simply the change in a dependent variable due to a change in an independent variable (=delta y) while differentiation is the variation divided by a the change in the independent variable in a small range (=dy/dx).

Who found the calculus of variation?

Modern interest in the calculus of variations began in 1696 when Johann Bernoulli of Switzerland proposed a brachistochrone (“least-time”) problem as a challenge to his peers. Suppose that a thin wire in the shape of a curve joins two points at different elevations.

Who invented the calculus of variations?

It was in his 1744 book, though, that Euler transformed a set of special cases into a systematic approach to general problems: the calculus of variations was born.

What is second variation?

From Encyclopedia of Mathematics. A special case of the n-th variation of a functional (see also Gâteaux variation), generalizing the concept of the second derivative of a function of several variables. It is used in the calculus of variations.

What are the different kinds of variation in math?

Examples of types of variation include direct, inverse, joint, and combined variation. What Is Direct Variation? In direct variation, as one variable is multiplied by a constant and increases, another variable (the quotient) also increases.

What are the differences of variation?

The differences in characteristics between individuals of the same species is called variation . Some variation is passed on from parents to offspring, via genes during reproduction. This is inherited variation. Some variation is the result of differences in the surroundings, or what an individual does.

What branch of math is variation?

calculus of variations, branch of mathematics concerned with the problem of finding a function for which the value of a certain integral is either the largest or the smallest possible.

What is the second variation?

What is the function of domain in calculus of variations?

In calculus of variations your domain is a set of functions. The outputs are still numbers. The functions of functions are called functionals. In classic physics problems calculus of variations is used to find functions which minimize/maximize an integral.

How many solos are there in calculus of variations?

18. 18 SOLO General Formulation of the Simplest Problem of Calculus of Variations Calculus of Variations Examples of Calculus of Variations Problems 5.

Who solved the brachistochrone problem in calculus?

The brachistochrone problem was posed by John Bernoulli in 1696, and played an important part in the development of calculus of variations. The problem was solved by Johann Bernoulli, Jacob Bernoulli, Isaac Newton, Gottfried Leibniz and Guillaume de L’Hôpital.

What is real-valued calculus and how do you do it?

Real-valued calculus, the type that you know as an advanced freshman undergrad, concerns itself with solving extremes: where on an interval is the function f ( x) at a minimum or maximum.