Mathematical analysis has developed in interaction with engineering and natural sciences such as physics and science. Nonlinear differential equation theory is vital for understanding nonlinear phenomena such as fluid, heat, and interface(under linear circumstances as well). Functional analysis, asymptotic analysis and special functions are used in dealing with liquid crystal, super conductivity and nonlinear wave motion, and these mathematical methods play an important role in quantum mechanics as well. Taking these facts into account, we aim to study mathematical analysis that centers on differential equation theory and, by means of it, examine various problems in the above mathematical physics.

Fields of study ; Functional equation, variational problem, nonlinear phenomenon, asymptotic analysis, quantum mechanics, measure theory, special function