Mathematical Models in Natural Science and Engineering: An Example-Based Approach

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Springer Science & Business Media, Feb 11, 2003 - Computers - 570 pages
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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.
  

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Contents

Metaphors Shape Ministry
3
Children in the Bible
26
Theology and Children
47
The Childs Development
73
Historical Roots of Ministry with Children
88
CONTEXT AND CONTENT MATTER
113
Children in Context
115
Children in the Faith Community
126
Soiling a water reservoir with a bay and the Caspian Sea puzzles 69
69
Exponential processes 83
83
Dynamics in coexistence of populations 97
97
Flow biological reactor
111
Mathematical model for the immune response of a living organism to an infectious invasion 117
117
Mathematical model for the community Producers Products Managers 127
127
Linear oscillators 141
141
Electromechanical analogies LagrangeMaxwell equations 159
159

Children in the Family
150
Children and Story
173
Children and Curriculum
190
In Worship
215
In Learning and Teaching
246
In Specialized Ministries
282
All Children Matter
311
In Leadership
330
CHAMP Orbit and Gravity Instrument Status 3
3
Determination of CHAMP Accelerometer Calibration Parameters 19
19
CHAMP Clock Error Characterization 32
32
The CHAMP Orbit Comparison Campaign 53
53
CHAMP DoubleDifference Kinematic POD with Ambiguity Resolution 70
70
Introduction 1
1
Dynamical system 5
5
Fluid outflow from a vessel 29
29
Equilibrium and autooscillations of fluid level in the vessel with simultaneous inflow and outflow 47
47
Transitive processes equilibrium states and autooscillations 53
53
Dynamics of the water surface level in a reservoired hydropower station 57
57
Energetic model of the heart 65
65
GalileoHuygens clock 173
173
Generator of electric oscillations 189
189
Soft and hard regimes of exciting autooscillations 197
197
Stochastic oscillator the contrary clock 205
205
Instability and autooscillations caused by friction 217
217
Forced oscillations of a linear oscillator 229
229
Parametric excitation and stabilization 243
243
Normal oscillations and beatings 253
253
Stabilizing an inverted pendulum 261
261
Controllable pendulum and a twolegged pacing 275
275
Dynamical models for games teaching and rational behaviour 287
287
Perception and pattern recognition 309
317
Distributed dynamical models in mechanics and physics 337
337
Fundamental solution of the thermal conductivity equation 349
349
Running waves and the dispersion equation 363
363
FaradayMaxwell theory of electromagnetism
375
Wave reflection and refraction 381
381
Standing waves and oscillations of a bounded string 387
387
Microparticles 395
395
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