Introduction to mathematical modeling and computer simulations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Florida
CRC Press
[2018]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVII, 222 Seiten Illustrationen, Diagramme |
| ISBN: | 9781138197657 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to mathematical modeling and computer simulations |c Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko |
| 264 | 1 | |a Boca Raton, Florida |b CRC Press |c [2018] | |
| 300 | |a XVII, 222 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Computer simulation | |
| 650 | 4 | |a Mathematical models | |
| 650 | 0 | 7 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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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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| 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 |
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