Contents. UNIT 1 Descriptive Statistics 1. vii. Preface Summary of Goals for This Text

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1 Preface Summary of Goals for This Text vii ix UNIT 1 Descriptive Statistics 1 CHAPTER 1 Basic Descriptive Statistics Types of Biological Data Summary Descriptive Statistics of DataSets Matlab Skills Exercises 11 CHAPTER 2 Visual Display of Data Introduction Frequency Distributions Bar Charts and Histograms Scatter Plots Matlab Skills Exercises 27 CHAPTER 3 Bivariate Data and Linear Regression Introduction to Linear Regression Bivariate Data Linear Analysis of Data Correlation Matlab Skills Exercises 43 CHAPTER 4 Exponential and Logarithmic Functions Exponential and Logarithmic Functions in Biology Review of Exponential and Logarithm Properties 47

2 xiv 4.3 Allometry Rescaling Data: Log-Log and Semilog Graphs Matlab Skills Exercises 67 UNIT 1 Student Projects 71 UNIT 2 Discrete Time Modeling 79 CHAPTER 5 Sequences and Discrete Difference Equations Sequences Limit of a Sequence Discrete Difference Equations Geometric and Arithmetic Sequences Linear Difference Equation with Constant Coefficients Introduction to Pharmacokinetics Matlab Skills Exercises 102 CHAPTER 6 Vectors and Matrices Vector Structure: Order Matters! Vector Algebra Dynamics: Vectors Changing over Time Matlab Skills Exercises 120 CHAPTER 7 Matrix Algebra Matrix Arithmetic Applications Matlab Skills Exercises 138 CHAPTER 8 Long-Term Dynamics or Equilibrium Notion of an Equilibrium Eigenvectors Stability Matlab Skills Exercises 149 CHAPTER 9 Leslie Matrix Models and Eigenvalues Leslie Matrix Models Long-Term Growth Rate (Eigenvalues) Long-Term Population Structure (Corresponding Eigenvectors) Matlab Skills Exercises 168 UNIT 2 Student Projects 171 UNIT 3 Probability 175 CHAPTER 10 Probability of Events Sample Spaces and Events Probability of an Event 181

3 xv 10.3 Combinations and Permutations Binomial Experiments Matlab Skills Exercises 198 CHAPTER 11 Probability of Compound Events Compound Events Finding the Probability of a Compound Event Probability Viewed as Darts Tossed at a Dart Board Matlab Skills Exercises 213 CHAPTER 12 Conditional Probability Conditional Probability Independence Matlab Skills Exercises 230 CHAPTER 13 Sequential Events Partition Theorem Bayes Theorem Exercises 242 CHAPTER 14 Population Genetics Models Hardy-Weinberg Equilibrium Hardy-Weinberg Selection Model Exercises 253 UNIT 3 Student Projects 255 UNIT 4 Limits and Continuity 259 CHAPTER 15 Limits of Functions Limit of a Function Limit Properties Matlab Skills Exercises 277 CHAPTER 16 Limits of Continuous Functions Right and Left Limits Continuity Intermediate Value Theorem Matlab Skills Exercises 294 UNIT 4 Student Projects 299 UNIT 5 Derivatives 303 CHAPTER 17 Rates of Change Average Rate of Change Estimating Rates of Change for Data Velocity 309

4 xvi 17.4 Photosynthesis Other Examples of Rates of Change Definition of a Derivative at a Point Matlab Skills Exercises 320 CHAPTER 18 Derivatives of Functions Concept of a Derivative Limit Definition of a Derivative of a Function Derivatives of Exponential Functions Derivatives of Trigonometric Functions Derivatives and Continuity Derivatives of Logarithmic Functions Matlab Skills Exercises 350 CHAPTER 19 Computing Derivatives Derivatives of Frequently Used Functions The Chain Rule for the Composition of Functions Quotient and Reciprocal Rules Exponential Models Higher Derivatives Exercises 372 CHAPTER 20 Using Derivatives to Find Maxima and Minima Maxima and Minima First Derivative Test Mean Value Theorem Concavity Optimization Problems Matlab Skills Exercises 404 UNIT 5 Student Projects 410 UNIT 6 Integration 413 CHAPTER 21 Estimating the Area under a Curve The Area under a Curve Increasing the Accuracy of the Area Estimation Area below the Horizontal Axis Matlab Skills Exercises 436 CHAPTER 22 Antiderivatives and the Fundamental Theorem of Calculus Definition of an Integral Antiderivatives Fundamental Theorem of Calculus Antiderivatives and Integrals 446

5 xvii 22.5 Average Values Matlab Skills Exercises 456 CHAPTER 23 Methods of Integration Substitution Method Integration by Parts Exercises 469 CHAPTER 24 Applications of Integrals to Area and Volume The Area between Two Curves The Volume of a Solid of Revolution Density Functions Exercises 485 CHAPTER 25 Probability in a Continuous Context Expected Value and Median Value Normal Distribution Waiting Times Matlab Skills Exercises 507 UNIT 6 Student Projects 510 UNIT 7 Introduction to Differential Equations 513 CHAPTER 26 Separation of Variables Separation of Variables Method Matlab Skills Exercises 527 CHAPTER 27 Equilibria and Limited Population Growth Models of Limited Population Growth Equilibria and Stability Homeostasis Exercises 541 CHAPTER 28 Implicit Differentiation and Related Rates Explicitly and Implicitly Defined Functions Implicit Differentiation Related Rates Exercises 551 UNIT 7 Student Projects 555 References 557 Appendix A 561 Appendix B 571 Answers to Selected Problems 000 Index 000