The world is a variety. When we remove the noises around us, we see the beauty of that variety. That is the message of the Euler-Lagrange equation. But where is that beautiful message in ordinary life? Did algebra steal Euler-Lagrange?
Dear Fred Amonya
Euler- Lagrange equation is one of the most important equations that provides an optimum solution of some integral functional equation. It raised in several applications. It is the most famous equation in the calculus of variation regardless of the advances in all branches of mathematics.
Algebra may show some numerical algorithms that help in solving the partial differential Euler Lagrange equation.
So, we can say algebra supports and not ignore such an elegant original equation.
Best regards
It is the calculus of variations, a branch of mathematical analysis, not algebra. It usually gives you a differential equation to solve, partial or not.
Servs to formulate the principle of least action.
Algebra (from Arabic: الجبر (al-jabr, meaning "reunion of broken parts" and "bonesetting") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
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