Mathematical models in natural science and engineering
Choice Reviews Online · 2003
Dynamic system.- Fluid flowing-out from a vessel.- Equilibrium and auto-oscillations of fluid level in a vessel with simultaneous inflow and outflow.- Transitive process, equilibrium state and auto-oscillations.- Dynamics of water level in a reservoired hydropower station.- Energetic model of a heart.- Soiling a water reservoir with a bay and the Caspian Sea puzzles.- Exponential processes.- Populations coexistence dynamics.- Flow biological reactor.- Mathematical model of an immune response of a living organism to an infectious invastion.- Mathematic model for the community 'Manufacturers-Products-Managers'.- Linear oscillator.- Electromechanical analogies. Lagrange-Maxwell equations.- Galileo-Huygens watch.- Generator of electric oscillations.- Soft and hard regimes of exciting auto-oscillations.- Stochastic oscillator.- Instability and auto-oscillations caused by friction.- Forced oscillations of a linear oscillator.- Parametric excitation and stabilization.- Normal oscillations and beatings.- Stabilizing an inverted pendulum.- Controllable pendulum and a two-legged pacing.- Dynamic models for games, teaching and rational behaviour.- Perceptron and pattern recognition.- Kepler laws and the two-body problem solved by Newton.- Distributed dynamic models in mechanics and physics.- Fundamental solution of the thermal conductivity equation.- Travelling waves and the dispersion equation.- Faraday-Maxwell theory of electromagnetism and Maxwell-Hertz electromagnetic waves.- Wave reflection and refraction.- Standing waves and oscillations of a bounded string.- Microparticle.- Space and time.- Speeding up relativistic microparticles in a cyclotron.- Mathematics as a language and as an operating system and models.- Geometrical, physical, analogous, mathematical and imitative types of modelling.- General scheme of methematical modelling.- Models of vibratory pile driving.- The fundamental mathematical model of the modern science and the theory of oscillations.- Mathematicalmodel as a fruitful idea of research. D-partition.- Idealization, mathematical correctness and reality.- Dynamical interpretation of the least square method and global searching optimization with an adaptive model.- Theoretic game model of the human society.