A generalization of it utilizing nonlinear techniques to address variational problems is known as Morse theory.  Its fundamental equations include the Euler-Lagrange condition
A generalization of it utilizing nonlinear techniques to address variational problems is known as Morse theory.  Its fundamental equations include the Euler-Lagrange condition and the Beltrami identity it can be defined as the type of mathematics that seeks to find the minimum or maximum parameters for the relationship between two constrained variables.  Developed by a host of 17th century mathematical luminaries, FTP, name this type of calculus used to solve the brachistochrone problem.
A generalization of it utilizing nonlinear techniques to address variational problems is known as Morse theory.  
Calculus of Variations or Variational Calculus