| Edition |
First edition. |
| Description |
1 online resource : text file, PDF |
| 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. |
| 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. |
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6.4 Green's function as a source6.5 The δ-function; Exercises; III: Advanced Applications; 7: Vector analysis; 7.1 Euclidean space R3; 7.1.1 Polar coordinates; 7.1.2 Cylindrical coordinates; 7.1.3 Spherical coordinates; 7.2 Scalar, vector and mixed products; 7.3 Rotation of bodies; 7.4 Scalar, vector and mixed product in Mathematica; 7.5 Tensors; 7.6 Scalar and vector fields; 7.6.1 Gradient; 7.6.2 Divergence; 7.6.3 Curl; 7.6.4 Formulae for gradient, divergence and curl; 7.7 Integral theorems; Exercises; 8: Heat equations; 8.1 Heat conduction equations; 8.2 Initial and boundary value problems. |
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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. |
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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 Padé 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. |
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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. |
| Bibliography |
Includes bibliographical references and index. |
| Local Note |
Taylor & Francis Taylor & Francis eBooks: Open Access |
| Subject |
Computer simulation.
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Mathematical models.
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Mathematical Modeling.
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Computational Numerical Analysis.
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MATHnetBASE.
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SCI-TECHnetBASE.
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STMnetBASE.
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Computer simulation. (OCoLC)fst00872518
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Mathematical models. (OCoLC)fst01012085
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| Added Author |
Nawalaniec, Wojciech, author.
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Rylko, Natalia, author.
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| Other Form: |
9781351998765 9781351998758 |
| ISBN |
9781315277240 (e-book) |
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9781351998765 (e-book ; PDF) |
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9781138197657 (hardback ; acid-free paper) |
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9781351998758 (ePub ebook) |
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9781351998741 (Mobipocket ebook) |
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1315277247 |
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1351998765 |
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1351998757 |
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1351998749 |
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