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Mathematical Models in Natural Science and Engineering

  • Book
  • © 2003

Overview

Authors:
  1. Juri I. Neimark

    1. Nizhny Novgorod State University, Nizhny Novgorod, Russian Federation

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  • Introduces to the art of mathematical modelling
  • Illustrates the most relevant types of models by a collection of more than elaborated 30 examples
  • Includes supplementary material: sn.pub/extras

Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)

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Table of contents (46 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Introduction

    • Juri I. Neimark
    Pages 1-3

  3. Dynamical systems

    • Juri I. Neimark
    Pages 5-28

  4. Fluid outflow from a vessel

    • Juri I. Neimark
    Pages 29-45

  5. Equilibrium and auto-oscillations of fluid level in the vessel with simultaneous inflow and outflow

    • Juri I. Neimark
    Pages 47-52

  6. Transitive processes, equilibrium states and auto-oscillations

    • Juri I. Neimark
    Pages 53-56

  7. Dynamics of the water surface level in a reservoired hydropower station

    • Juri I. Neimark
    Pages 57-63

  8. Energetic model of the heart

    • Juri I. Neimark
    Pages 65-68

  9. Soiling a water reservoir with a bay and the Caspian Sea puzzles

    • Juri I. Neimark
    Pages 69-82

  10. Exponential processes

    • Juri I. Neimark
    Pages 83-95

  11. Dynamics in coexistence of populations

    • Juri I. Neimark
    Pages 97-110

  12. Flow biological reactor

    • Juri I. Neimark
    Pages 111-115

  13. Mathematical model for the immune response of a living organism to an infectious invasion

    • Juri I. Neimark
    Pages 117-125

  14. Mathematical model for the community “Producers — Products — Managers”

    • Juri I. Neimark
    Pages 127-139

  15. Linear oscillators

    • Juri I. Neimark
    Pages 141-157

  16. Electromechanical analogies. Lagrange-Maxwell equations

    • Juri I. Neimark
    Pages 159-172

  17. Galileo-Huygens clock

    • Juri I. Neimark
    Pages 173-187

  18. Generator of electric oscillations

    • Juri I. Neimark
    Pages 189-196

  19. Soft and hard regimes of exciting auto-oscillations

    • Juri I. Neimark
    Pages 197-203

  20. Stochastic oscillator (the “contrary clock”)

    • Juri I. Neimark
    Pages 205-216
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About this book

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.

Authors and Affiliations

  • Nizhny Novgorod State University, Nizhny Novgorod, Russian Federation

    Juri I. Neimark

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