Mathematics is used to help understand the real world and to help to change parts of it for Man's benefit. Especially Applied Mathematics concerns the application of mathematics in a wide range of disciplines in various areas such as science, technology, business and commerce. Applied mathematicians are engaged in the creation, study and application of advanced mathematical methods relevant to specific problems in such diverse fields as engineering, physics (General Relativity, Mechanics and Fluid Dynamics), biology, economics, environmental studies, chemistry, political studies, medicine etc. Currently, applied mathematics has assumed a much broader meaning and embraces such diverse fields as communication theory, theory of optimisation, theory of games and numerical analysis. Indeed, today there is a remarkable range and variety of applications of mathematics in industry and government, involving important real-world problems such as materials processing, design, medical diagnosis, development of financial products, network management and weather prediction.
The first step is often the construction of a mathematical model, i.e. a description of the problem in mathematical terms. This model is then studied by using analytical or numerical methods to obtain exact or approximate solutions. Finally, the conclusions are interpreted in the language of the original problem. Often the model is changed to be more realistic or to include more features of the problem. Thus, the modeling process may involve false starts, modifications, and simplifications.
Mathematics enters primarily in the second stage: the solution of mathematically well-formulated problems and the development and analysis of the underlying theory. This stage may include analytical or numerical methods. The approach can range from specific algorithms and formal methods to abstract, general theories. It is often not clear which mathematical skills will be useful in the study of a new problem; thus, applied mathematicians need to be broadly trained so they will have a wide variety of mathematical tools available.
The research is mainly focused in the following fields of Applied Mathematics in the Department of Mathematics, CIIT Abbottabad.
Symmetry Method for Differential Equations, Fluid Mechanics, General Relativity, Computational Mathematics, Numerical Analysis