Calculus of variations and functional analysis - Lim, Wen Jun (Nanyang Technological University, 2021)
This report studied a new topic called Calculus of Variation which is considered to be a new branch of calculus in the field of Mathematics. Generally, it is used to optimize some real life problems i.e. finding a minimum or a maximum to a problem. Some of the important concepts and theorem such as Euler-Lagrange equation, functionals and the second variation will be discussed. We will also investigate some other necessary conditions for our solution to be an extremal to our problem. Various examples such as the brachistochrone problem will also be included in this thesis in hope to elaborate the significance of this topic. Some of its applications in other fields including Physics and Economics will also be studied briefly.