书名：Mathematics for the life sciences
责任者：Erin N. Bodine | Suzanne Lenhart | Louis J. Gross.
ISBN\ISSN：9780691150727,0691150729
出版时间：2014
出版社：Princeton University Press
前言
The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone.
Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences.
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目录
Preface xiii
Acknowledgments xix
UNIT 1 Descriptive Statistics 1
CHAPTER 1 Basic Descriptive Statistics 3
1.1 Types of Biological Data 3
1.2 Summary of Descriptive Statistics of Data Sets 4
1.3 Matlab Skills 9
1.4 Exercises 11
CHAPTER 2 Visual Display of Data 14
2.1 Introduction 14
2.2 Frequency Distributions 15
2.3 Bar Charts and Histograms 16
2.4 Scatter Plots 23
2.5 Matlab Skills 24
2.6 Exercises 27
CHAPTER 3 Bivariate Data and Linear Regression 30
3.1 Introduction to Linear Regression 30
3.2 Bivariate Data 31
3.3 Linear Analysis of Data 32
3.4 Correlation 37
3.5 Matlab Skills 41
3.6 Exercises 43
CHAPTER 4 Exponential and Logarithmic Functions 46
4.1 Exponential and Logarithmic Functions in Biology 46
4.2 Review of Exponential and Logarithm Properties 47
4.3 Allometry 54
4.4 Rescaling Data: Log-Log and Semilog Graphs 55
4.5 Matlab Skills 62
4.6 Exercises 67
UNIT 1 Student Projects 71
UNIT 2 Discrete Time Modeling 79
CHAPTER 5 Sequences and Discrete Difference Equations 84
5.1 Sequences 85
5.2 Limit of a Sequence 87
5.3 Discrete Difference Equations 90
5.4 Geometric and Arithmetic Sequences 92
5.5 Linear Difference Equation with Constant Coefficients 93
5.6 Introduction to Pharmacokinetics 97
5.7 Matlab Skills 100
5.8 Exercises 102
CHAPTER 6 Vectors and Matrices 107
6.1 Vector Structure: Order Matters! 108
6.2 Vector Algebra 110
6.3 Dynamics: Vectors Changing over Time 112
6.4 Matlab Skills 120
6.5 Exercises 120
CHAPTER 7 Matrix Algebra 123
7.1 Matrix Arithmetic 123
7.2 Applications 129
7.3 Matlab Skills 133
7.4 Exercises 138
CHAPTER 8 Long-Term Dynamics or Equilibrium 141
8.1 Notion of an Equilibrium 142
8.2 Eigenvectors 142
8.3 Stability 147
8.4 Matlab Skills 149
8.5 Exercises 149
CHAPTER 9 Leslie Matrix Models and Eigenvalues 152
9.1 Leslie Matrix Models 153
9.2 Long-Term Growth Rate (Eigenvalues) 156
9.3 Long-Term Population Structure (Corresponding Eigenvectors) 163
9.4 Matlab Skills 165
9.5 Exercises 168
UNIT 2 Student Projects 171
UNIT 3 Probability 175
CHAPTER 10 Probability of Events 177
10.1 Sample Spaces and Events 178
10.2 Probability of an Event 181
10.3 Combinations and Permutations 186
10.4 Binomial Experiments 188
10.5 Matlab Skills 189
10.6 Exercises 198
CHAPTER 11 Probability of Compound Events 201
11.1 Compound Events 201
11.2 Finding the Probability of a Compound Event 204
11.3 Probability Viewed as Darts Tossed at a Dart Board 209
11.4 Matlab Skills 210
11.5 Exercises 213
CHAPTER 12 Conditional Probability 216
12.1 Conditional Probability 217
12.2 Independence 220
12.3 Matlab Skills 225
12.4 Exercises 230
CHAPTER 13 Sequential Events 233
13.1 Partition Theorem 233
13.2 Bayes’ Theorem 238
13.3 Exercises 242
CHAPTER 14 Population Genetics Models 246
14.1 Hardy-Weinberg Equilibrium 247
14.2 Hardy-Weinberg Selection Model 250
14.3 Exercises 253
UNIT 3 Student Projects 255
UNIT 4 Limits and Continuity 259
CHAPTER 15 Limits of Functions 261
15.1 Limit of a Function 262
15.2 Limit Properties 266
15.3 Matlab Skills 274
15.4 Exercises 277
CHAPTER 16 Limits of Continuous Functions 282
16.1 Right and Left Limits 283
16.2 Continuity 284
16.3 Intermediate Value Theorem 290
16.4 Matlab Skills 292
16.5 Exercises 295
UNIT 4 Student Projects 299
UNIT 5 Derivatives 303
CHAPTER 17 Rates of Change 305
17.1 Average Rate of Change 306
17.2 Estimating Rates of Change for Data 308
17.3 Velocity 309
17.4 Photosynthesis 311
17.5 Other Examples of Rates of Change 315
17.6 Definition of a Derivative at a Point 316
17.7 Matlab Skills 316
17.8 Exercises 320
CHAPTER 18 Derivatives of Functions 324
18.1 Concept of a Derivative 3124
18.2 Limit Definition of a Derivative of a Function 326
18.3 Derivatives of Exponential Functions 330
18.4 Derivatives of Trigonometric Functions 334
18.5 Derivatives and Continuity 336
18.6 Derivatives of Logarithmic Functions 341
18.7 Matlab Skills 345
18.8 Exercises 349
CHAPTER 19 Computing Derivatives 352
19.1 Derivatives of Frequently Used Functions 353
19.2 The Chain Rule for the Composition of Functions 354
19.3 Quotient and Reciprocal Rules 359
19.4 Exponential Models 362
19.5 Higher Derivatives 369
19.6 Exercises 372
CHAPTER 20 Using Derivatives to Find Maxima and Minima 376
20.1 Maxima and Minima 377
20.2 First Derivative Test 377
20.3 Mean Value Theorem 382
20.4 Concavity 385
20.5 Optimization Problems 394
20.6 Matlab Skills 402
20.7 Exercises 404
UNIT 5 Student Projects 410
UNIT 6 Integration 413
CHAPTER 21 Estimating the Area under a Curve 414
21.1 The Area under a Curve 415
21.2 Increasing the Accuracy of the Area Estimation 426
21.3 Area below the Horizontal Axis 430
21.4 Matlab Skills 433
21.5 Exercises 436
CHAPTER 22 Antiderivatives and the Fundamental Theorem of Calculus 440
22.1 Definition of an Integral 441
22.2 Antiderivatives 442
22.3 Fundamental Theorem of Calculus 444
22.4 Antiderivatives and Integrals 446
22.5 Average Values 450
22.6 Matlab Skills 453
22.7 Exercises 456
CHAPTER 23 Methods of Integration 459
23.1 Substitution Method 459
23.2 Integration by Parts 465
23.3 Exercises 469
CHAPTER 24 Applications of Integrals to Area and Volume 471
24.1 The Area between Two Curves 472
24.2 The Volume of a Solid of Revolution 477
24.3 Density Functions 482
24.4 Exercises 485
CHAPTER 25 Probability in a Continuous Context 489
25.1 Expected Value and Median Value 493
25.2 Normal Distribution495
25.3 Waiting Times 498
25.4 Matlab Skills 500
25.5 Exercises 507
UNIT 6 Student Projects 510
UNIT 7 Introduction to Differential Equations 513
CHAPTER 26 Separation of Variables 515
26.1 Separation of Variables Method 518
26.2 Matlab Skills 522
26.3 Exercises 527
CHAPTER 27 Equilibria and Limited Population Growth 529
27.1 Models of Limited Population Growth 531
27.2 Equilibria and Stability 535
27.3 Homeostasis 539
27.4 Exercises 541
CHAPTER 28 Implicit Differentiation and Related Rates 543
28.1 Explicitly and Implicitly Defined Functions 544
28.2 Implicit Differentiation 544
28.3 Related Rates 549
28.4 Exercises 551
UNIT 7 Student Projects 555
Bibliography 557
Appendix A 561
Appendix B 571
Answers to Selected Problems 579
Index 597
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