Mathematics for the Biosciences

Contents CHAPTER 1 Preparations: elementary functions and the limit concept 1 Section 1 The function concept 2 Exercises 8 Section 2 Solving inequalities 11 Exercises 16 Section 3 Linear functions 17 Exercises 23 Section 4 Power, polynomial, and rational functions 26 Exercises 37 Section 5 Inverse functions 41 Exercises 51 Section 6 Limits of functions 57 Exercises 63 Section 7 Continuous functions and limits 65 Exercises 75 CHAPTER 2 The derivative and its applications 78 Section 8 The derivative concept 80 Exercises 87 Section 9 Formulas for obtaining derivatives 91 Exercises 98 Section 10 Composite functions and the chain rule 101 Exercises 106 Section 11 The derivative as a rate of change 108 Exercises 114 Section 12 The first derivative test and curve sketching 119 Exercises 129 Section 13 The second derivative and concavity 131 Exercises 138 Section 14 Applied problems in optimization 141 Exercises 150 Section 15 Exponential and logarithm functions 159 Exercises 165 Section 16 Derivatives of exponential and logarithm functions 169 Exercises 176 Section 17 Applications of exponential functions 182 Exercises 191 CHAPTER 8 An introduction to discrete probability 643 Section 57 Sample spaces, events, and probability 644 Exercises 653 Section 58 Compound events and the laws of probability 659 Exercises 667 Section 59 Conditional probability and independence 672 Exercises 680 Section 60 Sequential experiments and Bayes ' theorem 685 Exercises 695 Section 61 Probability models in population genetics 701 Exercises 709 References A1 Answers to selected exercises A5 Tables A31 Index A41 *Optional section