Mathematical methods in biology:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2009
|
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 417 S. graph. Darst. |
| ISBN: | 9780470525876 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical methods in biology |c J. David Logan ; William R. Wolesensky |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XIII, 417 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Biology | |
| 650 | 4 | |a Biomathematics | |
| 650 | 4 | |a Biometry | |
| 650 | 4 | |a Mathematics | |
| 650 | 0 | 7 | |a Biomathematik |0 (DE-588)4139408-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804139361514553344 |
|---|---|
| adam_text | Titel: Mathematical methods in biology
Autor: Logan, John David
Jahr: 2009
Contents
Preface......................................................... xi
1. Introduction to Ecological Modeling........................ 1
1.1 Mathematical Models..................................... 1
1.2 Rates of Change.......................................... 6
1.2.1 Taylor Polynomials................................. 9
1.2.2 Foraging Theory................................... 12
1.3 Balance Laws............................................ 18
1.4 Temperature in the Environment........................... 25
1.4.1 Heat Transfer...................................... 25
1.4.2 Dynamic Temperatures ............................. 27
1.4.3 Development Rate.................................. 32
1.5 Dimensionless Variables................................... 37
1.6 Descriptive Statistics...................................... 40
1.7 Regression and Curve Fitting.............................. 44
1.8 Reference Notes.......................................... 51
2. Population Dynamics for Single Species..................... 55
2.1 Laws of Population Dynamics.............................. 56
2.2 Continuous-Time Models.................................. 60
2.3 Qualitative Analysis of Population Models................... 65
2.4 Dynamics of Predation.................................... 73
2.5 Discrete-Time Models..................................... 81
2.6 Equilibria, Stability, and Chaos............................ 87
2.7 Reference Notes.......................................... 96
viii ______ Mathematical Methods in Biology _______________
3. Structure and Interacting Populations...................... 99
3.1 Structure: Juveniles and Adults............................ 99
3.2 Structured Linear Models .................................102
3.2.1 Sensitivity and Elasticity............................107
3.3 Nonlinear Interactions ....................................115
3.4 Appendix: Matrices.......................................124
3.4.1 Matrix Notation and Algebra........................124
3.4.2 Linear Algebraic Equations..........................130
3.4.3 The Eigenvalue Problem............................135
3.5 Reference Notes..........................................141
4. Interactions in Continuous Time............................143
4.1 Interacting Populations ...................................143
4.2 Phase Plane Analysis.....................................151
4.3 Linear Systems...........................................158
4.4 Nonlinear Systems........................................165
4.5 Bifurcation..............................................173
4.5.1 Rosenzweig-MacArthur Model.......................177
4.6 Reference Notes..........................................186
5. Concepts of Probability.....................................189
5.1 Introductory Examples and Definitions......................189
5.2 The Hardy-Weinberg Law.................................199
5.3 Continuous Random Variables .............................202
5.3.1 The Normal Distribution............................203
5.3.2 General Random Variables ..........................206
5.3.3 Predation with a Random Search.....................212
5.3.4 Central Limit Theorem .............................216
5.4 Discrete Random Variables................................220
5.4.1 Likelihood.........................................226
5.5 Joint Probability Distributions.............................232
5.6 Covariance and Correlation................................238
5.6.1 Covariance........................................238
5.6.2 Covariance Matrix..................................241
5.7 Reference Notes................... 243
6. Statistical Inference .................. 247
6.1 Introduction.................... 248
6.2 Interval Analysis..................... 250
6.2.1 Known Variance....................................250
6.2.2 The Gamma Distribution............................254
6.2.3 The Sample Variance............... ___257
Contents ix
6.2.4 The Mean with Unknown Variance...................258
6.3 Estimating Proportions ...................................260
6.4 The Chi-Squared Test.....................................263
6.5 Hypothesis Testing.......................................267
6.6 Bootstrap Methods.......................................275
6.6.1 Nonparametric Bootstrapping........................277
6.6.2 Parametric Bootstrapping...........................286
6.6.3 Permutation Methods...............................289
6.7 Reference Notes..........................................300
7. Stochastic Processes........................................303
7.1 Introduction.............................................303
7.2 Randomizing Discrete Dynamics ...........................308
7.2.1 Environmental and Demographic Stochasticity.........314
7.3 Random Walk ...........................................319
7.4 Birth Processes ..........................................323
7.4.1 Linear Differential Equations ........................323
7.4.2 Simple Birth Process ...............................325
7.4.3 Interevent Times and Simulation.....................329
7.5 Stochastic Differential Equations...........................331
7.5.1 Examples .........................................331
7.5.2 The Wiener Process................................332
7.5.3 Stochastic Differential Equations.....................337
7.6 SDEs from Markov Models................................342
7.7 Solving SDEs............................................347
7.7.1 The Ito Identity....................................347
7.7.2 Stochastic Integrals.................................349
7.7.3 Solving SDEs......................................350
7.8 The Fokker-Planck Equation ..............................352
7.9 Reference Notes..........................................358
A. Hints and Solutions to Exercises............................361
Index...........................................................415
|
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| discipline | Biologie Mathematik |
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| id | DE-604.BV035667677 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:42:52Z |
| institution | BVB |
| isbn | 9780470525876 |
| language | English |
| lccn | 2009013339 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017721992 |
| oclc_num | 317456951 |
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| physical | XIII, 417 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
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| series2 | Pure and applied mathematics |
| spelling | Logan, J. David 1944- Verfasser (DE-588)120361000 aut Mathematical methods in biology J. David Logan ; William R. Wolesensky Hoboken, NJ Wiley 2009 XIII, 417 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Includes bibliographical references and index Mathematik Biology Biomathematics Biometry Mathematics Biomathematik (DE-588)4139408-2 gnd rswk-swf Biomathematik (DE-588)4139408-2 s b DE-604 Wolesensky, William R. 1962- Verfasser (DE-588)139389032 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017721992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Logan, J. David 1944- Wolesensky, William R. 1962- Mathematical methods in biology Mathematik Biology Biomathematics Biometry Mathematics Biomathematik (DE-588)4139408-2 gnd |
| subject_GND | (DE-588)4139408-2 |
| title | Mathematical methods in biology |
| title_auth | Mathematical methods in biology |
| title_exact_search | Mathematical methods in biology |
| title_full | Mathematical methods in biology J. David Logan ; William R. Wolesensky |
| title_fullStr | Mathematical methods in biology J. David Logan ; William R. Wolesensky |
| title_full_unstemmed | Mathematical methods in biology J. David Logan ; William R. Wolesensky |
| title_short | Mathematical methods in biology |
| title_sort | mathematical methods in biology |
| topic | Mathematik Biology Biomathematics Biometry Mathematics Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Mathematik Biology Biomathematics Biometry Mathematics Biomathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017721992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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