Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | A Chapman & Hall book |
| Physical Description: | IX, 349 S. graph. Darst. |
| ISBN: | 9781420083484 |
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MARC
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| 100 | 1 | |a Barnes, Belinda |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical modelling with case studies |b a differential equations approach using Maple and MATLAB |c Belinda Barnes ; Glenn Robert Fulford |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a IX, 349 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Fulford, Glenn |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804139004754395136 |
|---|---|
| adam_text | Titel: Mathematical modelling with case studies
Autor: Barnes, Belinda
Jahr: 2009
Contents
Preface v
Acknowledgements viii
1 Introduction to mathematical modelling 1
1.1 Mathematical models .............................. 2
1.2 An overview of the book ............................ 3
1.3 Some modelling approaches........................... 5
1.4 Modelling for decision-making ......................... 7
2 Compartmental models 9
2.1 Introduction ................................... 10
2.2 Exponential decay and radioactivity...................... 10
2.3 Case Study: Detecting art forgeries ...................... 17
2.4 Case Study: Pacific rats colonise New Zealand ................ 19
2.5 Lake pollution models.............................. 20
2.6 Case Study: Lake Burley Griffin........................ 26
2.7 Drug assimilation into the blood........................ 28
2.8 Case Study: Dull, dizzy or dead?........................ 33
2.9 Cascades of compartments ........................... 37
2.10 First-order linear DEs.............................. 38
2.11 Equilibrium points and stability ........................ 40
2.12 Case Study: Money, money, money makes the world go around....... 41
2.13 Exercises for Chapter 2 ............................. 44
3 Models of single populations 51
3.1 Exponential growth ............................... 52
3.2 Density dependent growth ........................... 56
3.3 Limited growth with harvesting ........................ 63
3.4 Case Study: Anchovy wipe-out ......................... 65
3.5 Case Study: How can 2 x 106 birds mean rare?................ 66
3.6 Discrete population growth and chaos..................... 67
3.7 Time-delayed regulation............................. 74
3.8 Case Study: Australian blowflies ........................ 76
3.9 Exercises for Chapter 3 ............................. 77
4 Numerical solution of differential equations 83
4.1 Introduction ................................... 84
4.2 Basic numerical schemes ............................ 84
4.3 Computer implementation using Maple and MATLAB............ 87
4.4 Instability .................................... 89
4.5 Discussion .................................... 90
4.6 Exercises for Chapter 4 ............................. 91
5 Interacting population models 95
5.1 Introduction ................................... 96
5.2 An epidemic model for influenza........................ 97
5.3 Predators and prey ............................... 106
5.4 Case Study: Nile Perch catastrophe ...................... 113
5.5 Competing species................................ 114
5.6 Case Study: Aggressive protection of lerps and nymphs ........... 119
5.7 Model of a battle ................................ 120
5.8 Case Study: Rise and fall of civilisations ................... 125
5.9 Exercises for Chapter 5 ............................. 128
6 Phase-plane analysis 135
6.1 Introduction ................................... 136
6.2 Phase-plane analysis of epidemic model .................... 139
6.3 Analysis of a battle model ........................... 143
6.4 Analysis of a predator-prey model ....................... 148
6.5 Analysis of competing species models ..................... 152
6.6 Closed trajectories for the predator-prey ................... 158
6.7 Case Study: Bacteria battle in the gut..................... 160
6.8 Exercises for Chapter 6 ............................. 162
7 Linearisation analysis 169
7.1 Introduction ................................... 170
7.2 Linear theory................................... 170
7.3 Applications of linear theory .......................... 179
7.4 Nonlinear theory................................. 181
7.5 Applications of nonlinear theory ........................ 184
7.6 Exercises for Chapter 7 ............................. 187
8 Some extended population models 191
8.1 Introduction ................................... 192
8.2 Case Study: Competition, prédation and diversity .............. 192
8.3 Extended predator-prey model......................... 193
8.4 Case Study: Lemming mass suicides? ..................... 198
8.5 Case Study: Prickly-pear meets its moth.................... 200
8.6 Case Study: Geese defy mathematical convention............... 202
8.7 Case Study: Possums threaten New Zealand cows .............. 206
8.8 Exercises for Chapter 8 ............................. 212
9 Formulating basic heat models 217
9.1 Introduction ................................... 218
9.2 Some basic physical laws ............................ 219
9.3 Model for a hot water heater.......................... 222
9.4 Heat conduction and Fourier s law....................... 226
9.5 Heat conduction through a wall........................ 228
9.6 Radial heat conduction ............................. 232
9.7 Heat fins ..................................... 234
9.8 Exercises for Chapter 9 ............................. 238
10 Solving time dependent heat problems 241
10.1 The cooling coffee problem revisited...................... 242
m
10.2 The hot water heater problem revisited .................... 244
10.3 Case Study: It s hot and stuffy in the attic .................. 248
10.4 Spontaneous combustion ............................ 250
10.5 Case Study: Fish and chips explode ...................... 257
10.6 Exercises for Chapter 10 ............................ 258
11 Solving heat conduction problems 263
11.1 Boundary value problems............................ 264
11.2 Heat loss through a wall ............................ 266
11.3 Case Study: Double glazing: What s it worth? ................ 271
11.4 Insulating a water pipe ............................. 274
11.5 Cooling a computer chip ............................ 279
11.6 Exercises for Chapter 11 ............................ 284
12 Introduction to partial differential equations 289
12.1 The heat conduction equation ......................... 290
12.2 Oscillating soil temperatures .......................... 292
12.3 Case Study: Detecting land mines ....................... 296
12.4 Lake pollution revisited............................. 299
12.5 Exercises for Chapter 12 ............................ 306
A Differential equations 309
A.I Properties of differential equations....................... 309
A.2 Solution by inspection.............................. 310
A.3 First-order separable equations......................... 311
A.4 First-order linear equations and integrating factors.............. 312
A.5 Homogeneous equations............................. 313
A.6 Inhomogeneous equations............................ 314
B Further mathematics 317
B.I Linear algebra .................................. 317
B.2 Partial derivatives and Taylor expansions................... 320
B.3 Review of complex numbers .......................... 323
B.4 Hyperbolic functions .............................. 323
B.5 Integration using partial fractions ....................... 325
C Notes on Maple and MATLAB 327
C.I Brief introduction to Maple........................... 327
C.2 Solving differential equations with Maple ................... 327
C.3 Brief introduction to MATLAB ........................ 329
C.4 Solving differential equations with MATLAB................. 330
D Units and scaling 335
D.I Scaling differential equations .......................... 335
D.2 SI Units...................................... 337
References 339
Index 343
|
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV023805224 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:12Z |
| institution | BVB |
| isbn | 9781420083484 |
| language | English |
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| physical | IX, 349 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Barnes, Belinda Verfasser aut Mathematical modelling with case studies a differential equations approach using Maple and MATLAB Belinda Barnes ; Glenn Robert Fulford 2. ed. Boca Raton [u.a.] CRC Press 2009 IX, 349 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Maple Programm (DE-588)4209397-1 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Algebraische Differentialgleichung (DE-588)4001158-6 gnd rswk-swf Algebraische Differentialgleichung (DE-588)4001158-6 s Maple Programm (DE-588)4209397-1 s MATLAB (DE-588)4329066-8 s DE-604 Fulford, Glenn Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barnes, Belinda Fulford, Glenn Mathematical modelling with case studies a differential equations approach using Maple and MATLAB Maple Programm (DE-588)4209397-1 gnd MATLAB (DE-588)4329066-8 gnd Algebraische Differentialgleichung (DE-588)4001158-6 gnd |
| subject_GND | (DE-588)4209397-1 (DE-588)4329066-8 (DE-588)4001158-6 |
| title | Mathematical modelling with case studies a differential equations approach using Maple and MATLAB |
| title_auth | Mathematical modelling with case studies a differential equations approach using Maple and MATLAB |
| title_exact_search | Mathematical modelling with case studies a differential equations approach using Maple and MATLAB |
| title_full | Mathematical modelling with case studies a differential equations approach using Maple and MATLAB Belinda Barnes ; Glenn Robert Fulford |
| title_fullStr | Mathematical modelling with case studies a differential equations approach using Maple and MATLAB Belinda Barnes ; Glenn Robert Fulford |
| title_full_unstemmed | Mathematical modelling with case studies a differential equations approach using Maple and MATLAB Belinda Barnes ; Glenn Robert Fulford |
| title_short | Mathematical modelling with case studies |
| title_sort | mathematical modelling with case studies a differential equations approach using maple and matlab |
| title_sub | a differential equations approach using Maple and MATLAB |
| topic | Maple Programm (DE-588)4209397-1 gnd MATLAB (DE-588)4329066-8 gnd Algebraische Differentialgleichung (DE-588)4001158-6 gnd |
| topic_facet | Maple Programm MATLAB Algebraische Differentialgleichung |
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