## Mathematical Models in Natural Science and Engineering: An Example-Based ApproachThis 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 |

### Common terms and phrases

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