Mathematical Biology: an introduction with Maple and Matlab
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dodrecht ; Heidelberg ; London ; New York
Springer
2009
|
| Edition: | Second Edition |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Ausg. u.d.T.: Yeargers, Edward K.: An introduction to the mathematics of biology |
| Physical Description: | XIII, 551 Seiten Ill., graph. Darst. |
| ISBN: | 9780387709833 |
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Record in the Search Index
| _version_ | 1804139318780887040 |
|---|---|
| adam_text | Titel: Mathematical biology
Autor: Shonkwiler, Ronald W.
Jahr: 2009
Contents
Preface......................................................... v
1 Biology, Mathematics, and a Mathematical Biology Laboratory..... 1
1.1 The Natural Linkage Between Mathematics and Biology.......... 1
1.2 The Use of Models in Biology................................ 2
1.3 What Can Be Derived from a Model and How Is It Analyzed?..... 5
References..................................................... 8
2 Some Mathematical Tools ..................................... 9
2.1 Linear Dependence......................................... 10
Exercises ................................................. 15
2.2 Linear Regression, the Method of Least Squares................. 17
Exercises ................................................. 25
2.3 Multiple Regression........................................ 28
Exercises ................................................. 34
2.4 Modeling with Differential Equations.......................... 36
Exercises ................................................. 45
2.5 Modeling with Difference Equations .......................... 48
2.6 Matrix Analysis............................................ 52
Exercises ................................................. 56
2.7 Statistical Data............................................. 58
Exercises ................................................. 66
2.8 Probability................................................ 70
Exercises .................................................
References and Suggested Further Reading.......................... 81
Part I: Cells, Signals, Growth, and Populations
3 Reproduction and the Drive for Survival......................... 85
3.1 The Darwinian Model of Evolution............................ 86
3.2 Cells..................................................... 89
x Contents
3.3 Replication of Living Systems................................ 90
3.4 Population Growth and Its Limitations......................... 93
3.5 The Exponential Model for Growth and Decay.................. 95
Exercises/Experiments...................................... 104
Questions for Thought and Discussion......................... 105
References and Suggested Further Reading.......................... 105
4 Interactions Between Organisms and Their Environment........... 107
4.1 How Population Growth Is Controlled......................... 107
4.2 Community Ecology........................................ 117
4.3 Environmentally Limited Population Growth ................... 118
Exercises/Experiments...................................... 125
4.4 A Brief Look at Multiple Species Systems...................... 128
Exercises/Experiments...................................... 135
Questions for Thought and Discussion......................... 139
References and Suggested Further Reading.......................... 139
5 Age-Dependent Population Structures........................... 141
5.1 Aging and Death........................................... 141
5.2 The Age Structure of Populations............................. 146
5.3 Predicting the Age Structure of a Population.................... 150
Exercises/Experiments...................................... 159
Questions for Thought and Discussion......................... 160
References and Suggested Further Reading.......................... 161
6 Random Movements in Space and Time......................... 163
6.1 Biological Membranes...................................... 164
6.2 The Mathematics of Diffusion................................ 168
Exercises/Experiments...................................... 185
6.3 Transplacental Transfer of Oxygen: Biological and Biochemical
Considerations............................................. 187
6.4 Oxygen Diffusion Across the Placenta: Physical Considerations ... 189
Exercises/Experiments...................................... 197
Questions for Thought and Discussion......................... 197
References and Suggested Further Reading.......................... 198
7 Neurophysiology............................................. 201
7.1 Communication Between Parts of an Organism ................. 201
7.2 The Neuron ............................................... 203
7.3 The Action Potential........................................ 206
7.4 Synapses: Interneuronal Connections.......................... 210
7.5 A Model for the Conduction of Action Potentials................ 214
7.6 Fitzhugh-Nagumo Two-Variable Action Potential System......... 223
Exercises/Experiments...................................... 226
Questions for Thought and Discussion......................... 227
References and Suggested Further Reading.......................... 227
Contents xi
8 The Biochemistry of Cells..................................... 229
8.1 Atoms and Bonds in Biochemistry ............................ 229
8.2 Biopolymers............................................... 237
8.3 Molecular Information Transfer............................... 252
8.4 Enzymes and Their Function................................. 259
8.5 Rates of Chemical Reactions................................. 266
Exercises/Experiments...................................... 270
8.6 Enzyme Kinetics........................................... 271
Exercises/Experiments...................................... 276
Questions for Thought and Discussion......................... 279
References and Suggested Further Reading.......................... 280
Part II: Systems and Diseases
9 The Biological Disposition of Drugs and Inorganic Toxins .......... 283
9.1 The Biological Importance of Lead............................ 283
9.2 Early Embryogenesis and Organ Formation..................... 284
9.3 Gas Exchange ............................................. 290
9.4 The Digestive System....................................... 292
9.5 The Skin.................................................. 294
9.6 The Circulatory System..................................... 295
9.7 Bones.................................................... 304
9.8 The Kidneys............................................... 305
9.9 Clinical Effects of Lead..................................... 307
9.10 A Mathematical Model for Lead in Mammals................... 308
Exercises/Experiments...................................... 312
9.11 Pharmacokinetics .......................................... 313
Exercises/Experiments...................................... 320
Questions for Thought and Discussion......................... 320
References and Suggested Further Reading.......................... 320
10 A Biomathematical Approach to HIV and AIDS 323
10.1 Viruses................................................... 323
10.2 The Immune System........................................ 328
10.3 HIV and AIDS............................................. 337
10.4 An HIV Infection Model..................................... 343
Exercises/Experiments......................................
10.5 A Model for a Mutating Virus ................................ 351
10.6 Predicting the Onset of AIDS................................. 358
Exercises/Experiments...................................... 366
Questions for Thought and Discussion......................... 368
References and Suggested Further Reading.......................... 369
xii Contents
11 Parasites and Their Diseases...................................371
11.1 Protozoan Parasites Cause Important Human Diseases............ 371
11.2 The Life Cycle of the Malaria Parasite......................... 376
11.3 Host-Parasite Interactions................................... 378
11.4 Mathematical Models for Parasitic Diseases.................... 382
Exercises/Experiments...................................... 394
Questions for Thought and Discussion......................... 397
References and Suggested Further Reading.......................... 397
12 Cancer: A Disease of the DNA..................................399
12.1 Cell Growth and Division Is an Involved and Complicated Process . 399
12.2 Types and Stages of Cancer.................................. 402
12.3 The Role of Proto-Oncogenes and Tumor Suppressor Genes....... 402
12.4 A Model for Retinoblastoma................................. 405
12.5 Application to the Retinoblastoma Data........................ 412
12.6 Persistence of Germinal Cases................................ 414
Exercises/Experiments...................................... 415
Questions for Thought and Discussion......................... 416
References and Suggested Further Reading.......................... 416
Part III: Genomics
13 Genetics....................................................419
13.1 Asexual Cell Reproduction: Mitosis........................... 419
13.2 Sexual Reproduction: Meiosis and Fertilization................. 425
13.3 Classical Genetics.......................................... 429
13.4 Genetic Drift.............................................. 438
13.5 A Final Look at Darwinian Evolution.......................... 440
13.6 The Hardy-Weinberg Principle............................... 442
13.7 The Fixation of a Beneficial Mutation ......................... 448
Exercises/Experiments...................................... 453
Questions for Thought and Discussion......................... 459
References and Suggested Further Reading.......................... 459
14 Genomics...................................................461
14.1 The Promise of Genomics ................................... 461
14.2 Structural Genomics........................................ 463
14.3 Comparative Genomics ..................................... 465
14.4 Genomics in Medicine...................................... 467
14.5 Protein Substitution Matrices................................. 471
14.6 BLAST for Protein and DNA Search .......................... 475
14.7 The Mathematical Underpinnings of BLAST................... 484
Exercises/Experiments...................................... 494
Questions for Thought and Discussion......................... 495
References and Suggested Further Reading.......................... 495
Contents xiii
15 Phylogenetics................................................ 497
15.1 Phylogeny ................................................ 498
15.2 Branch Lengths Estimate the Separation of Species.............. 508
15.3 Introduction to Algebraic Statistics............................ 514
15.4 Algebraic Analysis of Maximum Likelihood.................... 520
15.5 Characterizing Trees by Their Variety, Phylogenetic Invariants..... 527
15.6 Constructing the Phylogenetic Tree............................ 530
Exercises/Experiments...................................... 535
Questions for Thought and Discussion......................... 537
References and Suggested Further Reading.......................... 537
Code Index...................................................... 539
Index........................................................... 541
|
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| spelling | Shonkwiler, Ronald W. 1942- (DE-588)114726590 aut Mathematical Biology an introduction with Maple and Matlab Ronald W. Shonkwiler ; James Herod Second Edition Dodrecht ; Heidelberg ; London ; New York Springer 2009 XIII, 551 Seiten Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Frühere Ausg. u.d.T.: Yeargers, Edward K.: An introduction to the mathematics of biology MATLAB Maple (Computer file) Biomathematics Biomathematics Computer programs Biomathematik (DE-588)4139408-2 gnd rswk-swf Biomathematik (DE-588)4139408-2 s DE-604 Herod, James V. 1937- (DE-588)114726604 aut Erscheint auch als Online-Ausgabe 978-0-387-70984-0 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017693722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shonkwiler, Ronald W. 1942- Herod, James V. 1937- Mathematical Biology an introduction with Maple and Matlab MATLAB Maple (Computer file) Biomathematics Biomathematics Computer programs Biomathematik (DE-588)4139408-2 gnd |
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| title | Mathematical Biology an introduction with Maple and Matlab |
| title_auth | Mathematical Biology an introduction with Maple and Matlab |
| title_exact_search | Mathematical Biology an introduction with Maple and Matlab |
| title_full | Mathematical Biology an introduction with Maple and Matlab Ronald W. Shonkwiler ; James Herod |
| title_fullStr | Mathematical Biology an introduction with Maple and Matlab Ronald W. Shonkwiler ; James Herod |
| title_full_unstemmed | Mathematical Biology an introduction with Maple and Matlab Ronald W. Shonkwiler ; James Herod |
| title_short | Mathematical Biology |
| title_sort | mathematical biology an introduction with maple and matlab |
| title_sub | an introduction with Maple and Matlab |
| topic | MATLAB Maple (Computer file) Biomathematics Biomathematics Computer programs Biomathematik (DE-588)4139408-2 gnd |
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