Calculus for the Life Sciences

Chapter 1 Functions and Graphs 1.1 Slope and Linear Functions 1.2 Polynomial Functions 1.3 Rational and Radical Functions 1.4 Trigonometric Functions 1.5 Trigonometric Functions and the Unit Circle Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Carbon Dioxide Concentrations Chapter 2 Differentiation 2.1 Limits and Continuity: Numerically and Graphically 2.2 Limits: Algebraically 2.3 Average Rates of Change 2.4 Differentiation Using Limits of Difference Quotients 2.5 Differentiation Techniques: Introduction 2.6 Instantaneous Rates of Change 2.7 Differentiation Techniques: The Product and Quotient Rules 2.8 The Chain Rule 2.9 Higher-Order Derivatives Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Rate of Epidemic Spread: SARS Chapter 3 Applications of Differentiation 3.1 Using the First Derivatives to Find Maximum and Minimum Values and Sketch Graphs 3.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs 3.3 Graph Sketching: Asymptotes and Rational Functions 3.4 Using Derivatives to Find Absolute Maximum and Minimum Values 3.5 Maximum-Minimum Problems 3.6 Approximation Techniques 3.7 Implicit Differentiation of Related Rates Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Polymorphism Chapter 4 Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Applications: The Uninhibited Growth Model, dP/dt = kP 4.4 Applications: Decay 4.5 The Derivatives of ax and logax Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Maximum Sustainable Harvest Chapter 5 Integration 5.1 Integration 5.2 Riemann Sums and Definite Integrals 5.3 Fundamental Theorem of Calculus 5.4 Properties of Definite Integrals 5.5 Integration Techniques: Substitution 5.6 Integration Techniques: Integration by Parts 5.7 Integration Techniques: Tables and Technology 5.8 Volume 5.9 Improper Integrals Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Estimating Dinosaur Mass Chapter 6 Matrices 6.1 Matrix Operations 6.2 Solving Linear Systems of Equations 6.3 Finding a Matrix Inverse and Determinant 6.4 Computing Eigenvalues and Eigenvectors 6.5 Solving Difference Equations Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Population Growth Chapter 7 Functions of Several Variables 7.1 Functions of Several Variables 7.2 Partial Derivatives 7.3 Maximum-Minimum Problems 7.4 An Application: The Method of Least Squares 7.5 Multiple Integration Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Stocking Fish Chapter 8 First-Order Differential Equations 8.1 Differential Equations and Initial-Value Problems 8.2 Linear First-Order Differential Equations 8.3 Stability of Autonomous Differential Equations 8.4 Separable Differential Equations 8.5 Numerical Solutions of Differential Equations Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Larvae and Forest Defoliation Chapter 9 Higher-Order and Systems of Differential Equations 9.1 Higher-Order Homogeneous Differential Equations 9.2 Higher-Order Nonhomogeneous Differential Equations 9.3 Systems of Linear Differential Equations 9.4 Matrices and Trajectories 9.5 Models of Population Biology 9.6 Numerical Methods Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Epidemics Chapter 10 Probability 10.1 Probability 10.2 Multiplication Trees and Bayes’ Rule 10.3 The Binomial Distribution 10.4 Expected Value and Standard Deviation for Discrete Random Variables 10.5 Continuous Random Variables 10.6 Poisson Process 10.7 The Normal Distribution Summary and Review Test EXTENDED LIFE SCIENCE CONNECTION: Axenic Cultures Appendix A: Review of Basic Algebra Appendix B: Functions Tables Integration Formulas Areas for a Standard Normal Distribution Answers Index