Introduction to Mathematical Modeling and Computer Simulations /

Introduction to Mathematical Modeling and Computer Simulations /

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Bibliographic Details
Author / Creator:Mityushev, Vladimir, author.
Edition:First edition.
Imprint:Boca Raton, FL : CRC Press, 2018.
Description:1 online resource : text file, PDF
Language:English
Subject:
Computer simulation.
Mathematical models.
Digital computer simulation.
Computer simulation.
Mathematical models.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/13419413
Hidden Bibliographic Details
Other authors / contributors:Nawalaniec, Wojciech, author.
Rylko, Natalia, author.
ISBN:9781315277240
1315277247
9781351998765
1351998765
9781138197657
9781351998758
1351998757
9781351998741
1351998749
Notes:Includes bibliographical references and index.
Summary:"Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students."--Provided by publisher.
Other form:9781351998765 9781351998758
Table of Contents:
  • Cover; Half Title; Title Page; Copyright Page; Table of Contents; List of Figures; List of Tables; Preface; I: General Principles and Methods; 1: Principles of Mathematical Modeling; 1.1 How to develop a mathematical model; 1.1.1 A simple mathematical model; 1.1.2 Use of a computer; 1.1.3 Development of mathematical models; 1.2 Types of models; 1.3 Stability of models; 1.4 Dimension, units, and scaling; 1.4.1 Dimensional analysis; 1.4.2 Scaling; Exercises; 2: Numerical and symbolic computations; 2.1 Numerical and symbolic computations of derivatives and integrals; 2.2 Iterative methods.
  • 2.3 Newton's method2.4 Method of successive approximations; 2.5 Banach Fixed Point Theorem; 2.6 Why is it difficult to numerically solve some equations?; Exercises; II: Basic Applications; 3: Application of calculus to classic mechanics; 3.1 Mechanical meaning of the derivative; 3.2 Interpolation; 3.3 Integrals; 3.4 Potential energy; Exercises; 4: Ordinary differential equations and their applications; 4.1 Principle of transition for ODE; 4.2 Radioactive decay; 4.3 Logistic differential equation and its modifications; 4.3.1 Logistic differential equation; 4.3.2 Modified logistic equation.
  • 4.3.3 Stability analysis4.3.4 Bifurcation; 4.4 Time delay; 4.5 Approximate solution to differential equations; 4.5.1 Taylor approximations; 4.5.2 PadeĢ approximations; 4.6 Harmonic oscillation; 4.6.1 Simple harmonic motion; 4.6.2 Harmonic oscillator with friction and exterior forces; 4.6.3 Resonance; 4.7 Lotka-Volterra model; 4.8 Linearization; Exercises; 5: Stochastic models; 5.1 Method of least squares; 5.2 Fitting; 5.3 Method of Monte Carlo; 5.4 Random walk; Exercises; 6: One-dimensional stationary problems; 6.1 1D geometry; 6.2 Second order equations; 6.3 1D Green's function.
  • 8.3 Green's function for the 1D heat equation8.4 Fourier series; 8.5 Separation of variables; 8.6 Discrete approximations of PDE; 8.6.1 Finite-difference method; 8.6.2 1D finite element method; 8.6.3 Finite element method in R2; 8.7 Universality in Mathematical Modeling. Table; Exercises; 9: Asymptotic methods in composites; 9.1 Effective properties of composites; 9.1.1 General introduction; 9.1.2 Strategy of investigations; 9.2 Maxwell's approach; 9.2.1 Single-inclusion problem; 9.2.2 Self consistent approximation; 9.3 Densely packed balls; 9.3.1 Cubic array.

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