The Calculus of variations is a field of mathematical analysis that uses variations , which are small changes in functions and functional to find maxima and minima of functional; mappings from a set of functions to the real numbers. The Euler-Lagrange differential equation is the fundamental equation of calculus of variation.
Leonhard Euler (15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory.
Source – Wikipedia.
8 Leonhard Euler Quotes
- e^(iπ)+1 = 0
2. Logic is the foundation of the certainty of all the knowledge we acquire.
3. Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
4. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error.
5. Nothing takes place in the world whose meaning is not that of some maximum or minimum.
6. Madam, I have just come from a country where people are hanged if they talk.
7. For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear.
8. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.