Biocalculus: Calculus; Probability; and Statistics for the Life Sciences

Table of contents

Table of contents :
About the Cover Images……Page 3
About the Authors……Page 8
Contents……Page 9
Preface……Page 17
To the Student……Page 27
Calculators, Computers, and Other Graphing Devices……Page 28
Diagnostic Tests……Page 30
Prologue: Mathematics and Biology……Page 35
Case Studies in Mathematical Modeling……Page 43
Case Study 1: Kill Curves and Antibiotic Effectiveness……Page 44
Case Study 2: Hosts, Parasites, and Time-Travel……Page 48
Ch 1: Functions and Sequences……Page 51
1.1: Four Ways to Represent a Function……Page 52
1.2: A Catalog of Essential Functions……Page 67
1.3: New Functions from Old Functions……Page 81
1.4: Exponential Functions……Page 91
1.5: Logarithms; Semilog and Log-Log Plots……Page 102
1.6: Sequences and Difference Equations……Page 120
Chapter 1: Review……Page 130
Ch 2: Limits……Page 139
2.1: Limits of Sequences……Page 140
2.2: Limits of Functions at Infinity……Page 152
2.3: Limits of Functions at Finite Numbers……Page 161
2.4: Limits: Algebraic Methods……Page 175
2.5: Continuity……Page 187
Chapter 2: Review……Page 199
Ch 3: Derivatives……Page 205
3.1: Derivatives and Rates of Change……Page 206
3.2: The Derivative as a Function……Page 218
3.3: Basic Differentiation Formulas……Page 231
3.4: The Product and Quotient Rules……Page 244
3.5: The Chain Rule……Page 252
3.6: Exponential Growth and Decay……Page 265
3.7: Derivatives of the Logarithmic and Inverse Tangent Functions……Page 272
3.8: Linear Approximations and Taylor Polynomials……Page 280
Chapter 3: Review……Page 290
Ch 4: Applications of Derivatives……Page 299
4.1: Maximum and Minimum Values……Page 300
4.2: How Derivatives Affect the Shape of a Graph……Page 311
4.3: L'Hospital's Rule: Comparing Rates of Growth……Page 324
4.4: Optimization Problems……Page 335
4.5: Recursions: Equilibria and Stability……Page 349
4.6: Antiderivatives……Page 356
Chapter 4: Review……Page 362
Ch 5: Integrals……Page 365
5.1: Areas, Distances, and Pathogenesis……Page 366
5.2: The Definite Integral……Page 379
5.3: The Fundamental Theorem of Calculus……Page 392
5.4: The Substitution Rule……Page 404
5.5: Integration by Parts……Page 412
5.6: Partial Fractions……Page 418
5.7: Integration Using Tables and Computer Algebra Systems……Page 421
5.8: Improper Integrals……Page 426
Chapter 5: Review……Page 431
Ch 6: Applications of Integrals……Page 437
6.1: Areas between Curves……Page 438
6.2: Average Values……Page 447
6.3: Further Applications to Biology……Page 450
6.4: Volumes……Page 455
Chapter 6: Review……Page 462
Ch 7: Differential Equations……Page 469
7.1: Modeling with Differential Equations……Page 470
7.2: Phase Plots, Equilibria, and Stability……Page 481
7.3: Direction Fields and Euler's Method……Page 490
7.4: Separable Equations……Page 499
7.5: Systems of Differential Equations……Page 509
7.6: Phase Plane Analysis……Page 518
Chapter 7: Review……Page 530
Ch 8: Vectors and Matrix Models……Page 537
8.1: Coordinate Systems……Page 538
8.2: Vectors……Page 546
8.3: The Dot Product……Page 555
8.4: Matrix Algebra……Page 564
8.5: Matrices and the Dynamics of Vectors……Page 570
8.6: The Inverse and Determinant of a Matrix……Page 578
8.7: Eigenvectors and Eigenvalues……Page 587
8.8: Iterated Matrix Models……Page 597
Chapter 8: Review……Page 610
Ch 9: Multivariable Calculus……Page 615
9.1: Functions of Several Variables……Page 616
9.2: Partial Derivatives……Page 635
9.3: Tangent Planes and Linear Approximations……Page 646
9.4: The Chain Rule……Page 654
9.5: Directional Derivatives and the Gradient Vector……Page 660
9.6: Maximum and Minimum Values……Page 669
Chapter 9: Review……Page 678
Ch 10: Systems of Linear Differential Equations……Page 681
10.1: Qualitative Analysis of Linear Systems……Page 682
10.2: Solving Systems of Linear Differential Equations……Page 690
10.3: Applications……Page 702
10.4: Systems of Nonlinear Differential Equations……Page 715
Chapter 10: Review……Page 726
Ch 11: Descriptive Statistics……Page 733
11.1: Numerical Descriptions of Data……Page 734
11.2: Graphical Descriptions of Data……Page 743
11.3: Relationships between Variables……Page 753
11.4: Populations, Samples, and Inference……Page 763
Chapter 11: Review……Page 772
Ch 12: Probability……Page 777
12.1: Principles of Counting……Page 778
12.2: What is Probability?……Page 787
12.3: Conditional Probability……Page 801
12.4: Discrete Random Variables……Page 817
12.5: Continuous Random Variables……Page 836
Chapter 12: Review……Page 849
Ch 13: Inferential Statistics……Page 853
13.1: The Sampling Distribution……Page 854
13.2: Confidence Intervals……Page 862
13.3: Hypothesis Testing……Page 871
13.4: Contingency Table Analysis……Page 879
Chapter 13: Review……Page 885
Appendixes……Page 889
Appendix A: Intervals, Inequalities, and Absolute Values……Page 890
Appendix B: Coordinate Geometry……Page 895
Appendix C: Trigonometry……Page 905
Appendix D: Precise Definitions of Limits……Page 914
Appendix E: A Few Proofs……Page 920
Appendix F: Sigma Notation……Page 924
Appendix G: Complex Numbers……Page 930
Appendix H: Statistical Tables……Page 938
Glossary of Biological Terms……Page 941
Answers to Odd-Numbered Exercises……Page 943
Biological Index……Page 997
Index……Page 1007