Holdings: Introduction to mathematical modeling and computer simulations

Introduction to mathematical modeling and computer simulations:

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Bibliographic Details
Main Authors:	Mitiuszew, Władimir 1958- (Author), Rylko, Natalia (Author), Nawalaniec, Wojciech (Author)
Format:	Book
Language:	English
Published:	Boca Raton, Florida CRC Press [2018]
Subjects:	Computer simulation Mathematical models Mathematische Modellierung Computersimulation
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	XVII, 222 Seiten Illustrationen, Diagramme
ISBN:	9781138197657

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MARC


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adam_text	Contents List of Figures ix List of Tables xiii Preface xv I General Principles and Methods 1 1 Principles of Mathematical Modeling 3 1.1 How to develop a mathematical model.......................... 4 1.1.1 A simple mathematical model............................ 4 1.1.2 Use of a computer...................................... 6 1.1.3 Development of mathematical models.................... 12 1.2 Types of models ............................................ 16 1.3 Stability of models......................................... 21 1.4 Dimension, units, and scaling............................... 22 1.4.1 Dimensional analysis.................................. 22 1.4.2 Scaling .............................................. 24 Exercises ....................................................... 25 2 Numerical and symbolic computations 27 2.1 Numerical and symbolic computations of derivatives and inte- grals ....................................................... 27 2.2 Iterative methods .......................................... 29 2.3 Newton’s method ............................................ 30 2.4 Method of successive approximations ........................ 32 2.5 Banach Fixed Point Theorem.................................. 34 2.6 Why is it difficult to numerically solve some equations? ... 37 Exercises ....................................................... 40 II Basic Applications 43 v 45 45 46 52 54 55 57 58 59 61 61 61 64 66 68 68 69 71 73 73 76 80 83 86 88 93 93 97 102 105 109 113 113 116 120 123 126 130 Contents Application of calculus to classic mechanics 3.1 Mechanical meaning of the derivative ...................... 3.2 Interpolation.............................................. 3.3 Integrals ................................................. 3.4 Potential energy........................................... Exercises ...................................................... 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 analysis ................................. 4.3.4 Bifurcation......................................... 4.4 Time delay................................................. 4.5 Approximate solution to differential equations ............ 4.5.1 Taylor approximations............................... 4.5.2 Pade 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 ...................................................... Stochastic models 5.1 Method of least squares.................................... 5.2 Fitting ................................................... 5.3 Method of Monte Carlo...................................... 5.4 Random walk ............................................... Exercises ...................................................... One-dimensional stationary problems 6.1 ID geometry................................................ 6.2 Second order equations .................................... 6.3 ID Green’s function........................................ 6.4 Green’s function as a source ........................ . . . . 6.5 The ¿-function............................................. Exercises ...................................................... Contents vii III Advanced Applications 131 7 Vector analysis 133 7.1 Euclidean space R3 .......................................... 133 7.1.1 Polar coordinates..................................... 135 7.1.2 Cylindrical coordinates .............................. 135 7.1.3 Spherical coordinates................................. 137 7.2 Scalar, vector and mixed products............................ 138 7.3 Rotation of bodies........................................... 142 7.4 Scalar, vector and mixed product in Mathematica.............. 144 7.5 Tensors...................................................... 145 7.6 Scalar and vector fields .................................... 148 7.6.1 Gradient.............................................. 148 7.6.2 Divergence............................................ 152 7.6.3 Curl.................................................. 156 7.6.4 Formulae for gradient, divergence and curl............ 156 7.7 Integral theorems ........................................... 159 Exercises ........................................................ 161 8 Heat equations 163 8.1 Heat conduction equations ................................. 163 8.2 Initial and boundary value problems.......................... 168 8.3 Green’s function for the ID heat equation.................... 169 8.4 Fourier series............................................... 173 8.5 Separation of variables ..................................... 177 8.6 Discrete approximations of PDE............................. 180 8.6.1 Finite-difference method.............................. 180 8.6.2 ID finite element method.............................. 183 8.6.3 Finite element method in R2........................... 186 8.7 Universality in Mathematical Modeling. Table ................ 189 Exercises ........................................................ 189 9 Asymptotic methods in composites 193 9.1 Effective properties of composites .......................... 194 9.1.1 General introduction.................................. 194 9.1.2 Strategy of investigations............................ 196 9.2 Maxwell’s approach .......................................... 199 9.2.1 Single-inclusion problem.............................. 199 9.2.2 Self consistent approximation......................... 201 9.3 Densely packed balls......................................... 202 9.3.1 Cubic array........................................... 202 9.3.2 Densely packed balls and Voronoi diagrams............. 204 viii Contents 9.3.3 Optimal random packing........................... 208 Exercises .................................................. 213 Bibliography 217 Index 221
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author	Mitiuszew, Władimir 1958- Rylko, Natalia Nawalaniec, Wojciech
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discipline	Informatik Mathematik
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spelling	Mitiuszew, Władimir 1958- (DE-588)1056104716 aut Introduction to mathematical modeling and computer simulations Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko Boca Raton, Florida CRC Press [2018] XVII, 222 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Computer simulation Mathematical models Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 s Computersimulation (DE-588)4148259-1 s DE-604 Rylko, Natalia aut Nawalaniec, Wojciech aut Erscheint auch als Online-Ausgabe 9781315277240 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030318529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Mitiuszew, Władimir 1958- Rylko, Natalia Nawalaniec, Wojciech Introduction to mathematical modeling and computer simulations Computer simulation Mathematical models Mathematische Modellierung (DE-588)7651795-0 gnd Computersimulation (DE-588)4148259-1 gnd
subject_GND	(DE-588)7651795-0 (DE-588)4148259-1
title	Introduction to mathematical modeling and computer simulations
title_auth	Introduction to mathematical modeling and computer simulations
title_exact_search	Introduction to mathematical modeling and computer simulations
title_full	Introduction to mathematical modeling and computer simulations Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko
title_fullStr	Introduction to mathematical modeling and computer simulations Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko
title_full_unstemmed	Introduction to mathematical modeling and computer simulations Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko
title_short	Introduction to mathematical modeling and computer simulations
title_sort	introduction to mathematical modeling and computer simulations
topic	Computer simulation Mathematical models Mathematische Modellierung (DE-588)7651795-0 gnd Computersimulation (DE-588)4148259-1 gnd
topic_facet	Computer simulation Mathematical models Mathematische Modellierung Computersimulation
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030318529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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