Biocalculus: Calculus, Probability, and Statistics for the Life Sciences 1st edition

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• Chapter 1: Functions and Sequences
  • 1.1: Four Ways to Represent a Function
  • 1.2: A Catalog of Essential Functions
  • 1.3: New Functions from Old Functions
  • 1.4: Exponential Functions
  • 1.5: Logarithms; Semilog and Log-Log Plots
  • 1.6: Sequences and Difference Equations
  • 1: Review
  • 1: True-False
  
  
• Chapter 2: Limits
  • 2.1: Limits of Sequences
  • 2.2: Limits of Functions at Infinity
  • 2.3: Limits of Functions at Finite Numbers
  • 2.4: Limits: Algebraic Methods
  • 2.5: Continuity
  • 2: Review
  • 2: True-False
  
  
• Chapter 3: Derivatives
  • 3.1: Derivatives and Rates of Change
  • 3.2: The Derivative as a Function
  • 3.3: Basic Differentiation Formulas
  • 3.4: The Product and Quotient Rules
  • 3.5: The Chain Rule
  • 3.6: Exponential Growth and Decay
  • 3.7: Derivatives of the Logarithmic and Inverse Tangent Functions
  • 3.8: Linear Approximations and Taylor Polynomials
  • 3: Review
  • 3: True-False
  
  
• Chapter 4: Applications of Derivatives
  • 4.1: Maximum and Minimum Values
  • 4.2: How Derivatives Affect the Shape of a Graph
  • 4.3: L'Hospital's Rule: Comparing Rates of Growth
  • 4.4: Optimization Problems
  • 4.5: Recursions: Equilibria and Stability
  • 4.6: Antiderivatives
  • 4: Review
  • 4: True-False
  
  
• Chapter 5: Integrals
  • 5.1: Areas, Distances, and Pathogenesis
  • 5.2: The Definite Integral
  • 5.3: The Fundamental Theorem of Calculus
  • 5.4: The Substitution Rule
  • 5.5: Integration by Parts
  • 5.6: Partial Fractions
  • 5.7: Integration Using Tables and Computer Algebra Systems
  • 5.8: Improper Integrals
  • 5: Review
  • 5: True-False
  
  
• Chapter 6: Applications of Integrals
  • 6.1: Areas Between Curves
  • 6.2: Average Values
  • 6.3: Further Applications to Biology
  • 6.4: Volumes
  • 6: Review
  • 6: True-False
  
  
• Chapter 7: Differential Equations
  • 7.1: Modeling with Differential Equations
  • 7.2: Phase Plots, Equilibria, and Stability
  • 7.3: Direction Fields and Euler's Method
  • 7.4: Separable Equations
  • 7.5: Systems of Differential Equations
  • 7.6: Phase Plane Analysis
  • 7: Review
  • 7: True-False
  
  
• Chapter 8: Vectors and Matrix Models
  • 8.1: Coordinate Systems
  • 8.2: Vectors
  • 8.3: The Dot Product
  • 8.4: Matrix Algebra
  • 8.5: Matrices and the Dynamics of Vectors
  • 8.6: The Inverse and Determinant of a Matrix
  • 8.7: Eigenvectors and Eigenvalues
  • 8.8: Iterated Linear Transformations
  • 8: Review
  • 8: True-False
  
  
• Chapter 9: Multivariable Calculus
  • 9.1: Functions of Several Variables
  • 9.2: Partial Derivatives
  • 9.3: Tangent Planes and Linear Approximations
  • 9.4: The Chain Rule
  • 9.5: Directional Derivatives and the Gradient Vector
  • 9.6: Maximum and Minimum Values
  • 9: Review
  • 9: True-False
  
  
• Chapter 10: Systems of Linear Differential Equations
  • 10.1: Qualitative Analysis of Linear Systems
  • 10.2: Solving Systems of Linear Differential Equations
  • 10.3: Applications
  • 10.4: Systems of Nonlinear Differential Equations
  • 10: Review
  • 10: True-False
  
  
• Chapter 11: Descriptive Statistics
  • 11.1: Numerical Descriptions of Data
  • 11.2: Graphical Descriptions of Data
  • 11.3: Relationships between Variables
  • 11.4: Populations, Samples, and Inference
  • 11: Review
  • 11: True-False
  
  
• Chapter 12: Probability
  • 12.1: Principles of Counting
  • 12.2: What Is Probability?
  • 12.3: Conditional Probability
  • 12.4: Discrete Random Variables
  • 12.5: Continuous Random Variables
  • 12: Review
  • 12: True-False
  
  
• Chapter 13: Inferential Statistics
  • 13.1: The Sampling Distribution
  • 13.2: Confidence Intervals
  • 13.3: Hypothesis Testing
  • 13.4: Contingency Table Analysis
  • 13: Review
  • 13: True-False
  
  
• Chapter A: Appendixes
  • A.A: Intervals, Inequalities, and Absolute Values
  • A.B: Coordinate Geometry
  • A.C: Trigonometry
  • A.D: Precise Definition of Limits
  • A.E: A Few Proofs
  • A.F: Sigma Notation
  • A.G: Complex Numbers
  • A.H: Statistical Tables
  • A.I: Glossary of Biological Terms
  • A.J: Answers to Odd-Numbered Exercises
  
  
• Chapter DT: Diagnostic Tests
  • DT.1: Basic Algebra
  • DT.2: Analytic Geometry
  • DT.3: Functions
  • DT.4: Trigonometry
  
  
• Chapter QP: Quick Prep Topics
  • QP.1: Definition and Representations of Functions
  • QP.2: Working with Representations of Functions
  • QP.3: Function Notation
  • QP.4: Domain and Range of a Function
  • QP.5: Solving Linear Equations
  • QP.6: Linear Functions
  • QP.7: Parabolas
  • QP.8: Factoring Quadratic Equations and Finding x-intercepts of a Quadratic Function
  • QP.9: Polynomials
  • QP.10: More about Factoring Polynomials
  • QP.11: Finding Roots
  • QP.12: Dividing Polynomials
  • QP.13: Rational Functions
  • QP.14: Root Functions
  • QP.15: Rationalizing the Numerator or Denominator
  • QP.16: Exponential Functions
  • QP.17: Logarithmic Functions
  • QP.18: Trigonometric Functions and the Unit Circle
  • QP.19: Graphs of Trigonometric Functions
  • QP.20: Trigonometric Identities
  • QP.21: Special Functions
  • QP.22: Algebraic Combinations of Functions
  • QP.23: Composition of Functions
  • QP.24: Transformations of Functions
  • QP.25: Inverse Functions