Who discovered the 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 the 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.

What is variational equation?

The variational equation of order k is a linear differential (difference) equation whose solution is the k-th derivative with respect to a parameter of the solution of a differential (difference) equation.

What is the history of variation in math?

History. The calculus of variations may be said to begin with Newton’s minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696).

What is the history of calculus?

History. Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz (independently of each other, first publishing around the same time) but elements of it appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India.

What is extremal function?

The expected extremal function v is harmonic, at least in a certain region, and is a symmetric decreasing function on circles |z| = r. From: Handbook of Complex Analysis, 2002.

What is a variation in 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 are the 4 types of variation in math?

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

What are the 4 types of calculus?

Integral calculus is another important concept of calculus….The 4 main concepts of calculus are:

  • Limits.
  • Differential Calculus (Differentiation)
  • Integral Calculus (Integration)
  • Multivariable Calculus (Function theory)

What is extremal curve?

In general, an extremal graph is the largest graph of order which does not contain a given graph as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that do not contain a complete graph. as a subgraph.