As a participant in this course, you’ll be introduced to mathematical models formulated in terms of ordinary and partial differential equations. It has been shown that symmetries help us to better understand methods of integration of differential equations and to find new classes of integrable equations. The course exposition includes the Malthusian model of population growth, the comparison of a free fall with the fall of a body in Earth’s atmosphere, an explanation of the collapse of driving shafts in motor ships, the mathematical model of tumor growth, the symmetry nature of wave beams in the deep ocean, and more.
- Get an overview of some mathematical models formulated by differential equations and approaches to solving them.
- Comprehend the difference between modelling by differential equations and by functions.
- Understand the concept of symmetry of a differential equation.
- Use symmetry to solve differential equations and to find new solvable mathematical models.