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Mathematical Models in Natural Science and Engineering
Author
Title
Mathematical Models in Natural Science and Engineering [electronic resource] / by Juri I. Neimark.
ISBN
9783540478782
Published
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
Physical Description
1 online resource.
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
Summary
<P>This book helps the reader become familiar with various mathematical models for mechanical, electrical, physical, atronomical, chemical, biological, ecological, cybernetical and other systems and processes. The models examined are evolutionary models, i.e. the models of time-varying processes known as dynamic systems, such as fluid flow, biological processes, oscillations in mechanical and electromagnetic systems, and social systems. The book shows readers how to identify appropriate situations for modelling, how to address difficulties in creating models, and how to learn what mathematics teaches us about the modelling of dynamical phenomena in our surrounding world.It is interesting for a wide spectrum of readers, students of natural science and engineering, and also for researchers in these fields.</P>
Variant and related titles
Springer ebooks.
Other formats
Printed edition:
Format
Books / Online
Language
English
Added to Catalog
February 05, 2013
Series
Foundations of Engineering Mechanics,
Contents
<P>Dynamical system
Fluid outflow from a vessel
Equilibrium and auto-oscillations of fluid level in the vessel with simultaneous inflow and outflow
Transitive processes, equilibrium states and auto-oscillations
Dynamics of the water surface level in a reservoired hydropower station
Energetic model of the heart
Soiling a water reservoir with a bay and the Caspian Sea puzzles
Exponential processes
Dynamics in coexistence of populations
Flow biological reactor
Mathematical model for the immune response of a living organism to an infectious invasion
Mathematical model for the community "Producers –Products – Managers"
Linear oscillators
Electromechanical analogies
Lagrange-Maxwell equations
Galileo-Huygens clock
Generator of electric oscillations
Soft and hard regimes of exciting auto-oscillations
Stochastic oscillator (the "contrary clock")
Instability and auto-oscillations caused by friction
Forced oscillations of a linear oscillator
Parametric excitation and stabilisation
Normal oscillations and beatings
Stabilising an inverted pendulum
Controllable pendulum and a two-legged pacing
Dynamical models for games, teaching and rational behaviour
Perceptron and pattern recognition
Kepler laws and the two-body problem solved by Newton
Distributed dynamical models in mechanics and physics
Fundamental solution of the thermal conductivity equation
Running waves and the dispersion equation
Faraday-Maxwell theory of electromagnetism and the Maxwell-Hertz electromagnetic waves
Wave reflection and refraction
Standing waves and oscillations of a bounded string
Microparticles
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 mathematical modelling
Models of vibratory pile driving
The fundamental mathematical model of the modern science and the theory of oscillations
Mathematical model as a fruitful idea of research. The D-partition
Idealisation, mathematical correctness and reality
Dynamical interpretation of the least square method and global searching optimisation with use of an adaptive model
Theoretical game model of the human society.</P>.
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