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Differential Equations and their Symmetries via Mathematical Models
The purpose of this online course is to provide the beginners with an easy to follow treatment of ordinary and partial differential equations as a convenient tool for understanding the mathematical content of real world phenomena. Significance of differential equations are explained by simple but realistic mathematical models such as Malthusian model of population growth, comparison of the free fall with a fall of a body in Earth’s atmosphere, explanation of collapse of driving shafts in motor ships by solving differential equations. Symmetries of differential equations appear naturally in explaining Kepler’s laws of planet’s motion from specific symmetries of Newton’s gravitation law. Unified treatment of ordinary and partial differential equations as well as their symmetries via concrete mathematical models give a background for students to make their own research.