About

I see myself as a typically mathematics enthusiast and an avid reader. I have completed my bachelor and master degrees majored in mathematics from Pakistan and subsequently went to Germany to pursue higher studies on HEC (Higher Education Commission) overseas scholarship program. My research is related to the problems of existence and uniqueness of the surface waves in generalized continuum models, in particular micromorphic models. It is well established fact that classical continuum theory is inadequate to described the size effect of contractual motion, for example in unbounded elastic medium the propagation of plane wave is not dispersive. However, experiments with real solids show that wave propagation is dispersive (the wave speed depends on frequency). To incorporate the better the microstructure of the matter into classical theories generalized contimumm models are introduced.

The surface waves are the type of elastic wave that propagate near the surface without penetrating into deep. I have extended the method matrix impedance method to generalized continuum model. This method allows me to established existence and uniqueness of surface wave speed in Cosserat elastic material (a special case of micromorphic model).

I have been teaching, number of courses, i.e., Calculus and Analytical geometry, Multivariable calculus,Linear Algebra, Differential Equation, Numerical Computing, and Statistic and Probability.