Mathematical Models in Natural Science and Engineering [Hardcover]

This book has come into being as a result ofthe author's lectures on mathematical modelling rendered to the students, BS and MS degree holders specializing in applied mathematics and computer science and to post-graduate students in exact sciences of the Nizhny Novgorod State University after N.!. Lobatchevsky. These lectures are adapted and presented as a single whole ab out mathematical models and modelling. This new course of lectures appeared because the contemporary Russian educational system in applied mathematics rested upon a combination of fundamental and applied mathematics training; this way of training oriented students upon solving only the exactly stated mathematical problems, and thus there was created a certain estrangement to the most essential stages and sides of real solutions for applied problems, such as thinking over and deeply piercing the essence of a specific problem and its mathematical statement. This statement embraces simplifications, adopted idealizations and creating a mathematical model, its correction and matching the results obtained against a real system. There also existed another main objective, namely to orient university graduates in their future research not only upon purely mathematical issues but also upon comprehending and widely applying mathematics as a universal language of contemporary exact science, and mathematical modelling as a powerful me ans for studying nature, engineering and human society.1 Dynamical system.- 2 Fluid outflow from a vessel.- 3 Equilibrium and auto-oscillations of fluid level in the vessel with simultaneous inflow and outflow.- 4 Transitive processes, equilibrium states and auto-oscillations.- 5 Dynamics of the water surface level in a reservoired hydropower station.- 6 Energetic model of the heart.- 7 Soiling a water reservoir with a bay and the Caspian Sea puzzles.- 8 Exponential processes.- 9 Dynamics in coexistence of populations.- 10 Flow biological reactor.- 11 Mathematical model for the iml³E