## 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 story of calculus of variations?

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.

**Why is calculus of variations important?**

The calculus of variations is a powerful technique to solve some dynamic problems that are not intuitive to solve otherwise. It is the precursor to optimal control theory as it allows us to solve non-complex control systems.

**Who worked on the calculus of variation *?**

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 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 invented calculus of variations?

**What are the Extremals the functional?**

A solution of the Euler-Lagrange equation is called an extremal of the functional. By considering y+g, where y is the solution from exercise 1 and g(x) is a variation in y(x) satisfying g(0)=g(1)=0, and then considering I(y+g), show explicitly that y(x) minimizes I(y) in Exercise 1 above.

**Why is calculus called calculus?**

In Latin, calculus means “pebble.” Because the Romans used pebbles to do addition and subtraction on a counting board, the word became associated with computation. Calculus has also been borrowed into English as a medical term that refers to masses of hard matter in the body, such as kidney stones.

#### What are the different kinds of variation in math?

Examples of types of variation include direct, inverse, joint, and combined variation.