Mathematical Methods in Mechanics
The course consists of two parts. The first part is devoted to tensor calculus and the second one is devoted to nonlinear dynamics.
This part of course provides students with invariant formulations of theory of tensor calculus. Concepts and techniques of tensor algebra, theory of tensor functions and tensor analysis are introduced. The symmetries of tensors and tensor functions are considered. The attention is drawn to application of tensor algebra and calculus in various fields of science. Students who have completed the course should be aware of application of techniques of tensor calculus to solve a wide range of problems in different area of mechanics.
The course introduces students to the current state of nonlinear wave mechanics problems. Students learn how to solve these problems and apply methods of mathematical and numerical modeling by using Wolfram Mathematica. Students who have completed the course should be aware of up-to-date state of mechanics of deformable media, theoretical and applied mechanics. They should know how to formulate the major mechanics problems. Students have to be able to apply this knowledge to solve nonlinear dynamic problems of mechanics and conduct experimental studies using software packages. Students have to use methods of mathematical modelling for the analysis and solution of problems of natural science.