Analysis of Applied Mathematics

Abstract

Mathematics applied to applications involves using mathematics for issues that arise in various fields, e.g., science, engineering, engineering, or other areas, and developing new or better techniques to address the demands of the unique challenges. We consider it applied math to apply maths to problems in the real world with the double purpose of describing observed phenomena and forecasting new yet unknown phenomena. Thus, the focus is on math, e.g., creating new techniques to tackle the issues of the unique challenges and the actual world. The issues arise from a variety of applications, including biological and physical sciences as well as engineering and social sciences. They require knowledge of different branches of mathematics including the analysis of differential equations and stochastics. They are based on mathematical and numerical techniques. Most of our faculty and students work directly with the experimentalists to watch their research findings come to life. This research team investigates mathematical issues arising out of geophysical, chemical, physical, and biophysical sciences. The majority of these problems are explained by time-dependent partial integral or ordinary differential equations. They are also accompanied by complex boundary conditions, interface conditions, and external forces. Nonlinear dynamical systems provide an underlying geometrical and topological model for understanding, identifying, and quantifying the complex phenomena in these equations. The theory of partial differential equations lets us correctly formulate well-posed problems and study the behavior of solutions, which sets the stage for effective numerical simulations. Nonlocal equations result from the macroscopically modeling stochastic dynamical systems characterized by Levy noise and the modeling of long-range interactions. They also provide a better understanding of anomalous diffusions.