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Index
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
UNIT 1 Descriptive Statistics
CHAPTER 1 Basic Descriptive Statistics
1.1 Types of Biological Data
1.2 Summary Descriptive Statistics of Datasets
1.3 Matlab Skills
1.4 Exercises
CHAPTER 2 Visual Display of Data
2.1 Introduction
2.2 Frequency Distributions
2.3 Bar Charts and Histograms
2.4 Scatter Plots
2.5 Matlab Skills
2.6 Exercises
CHAPTER 3 Bivariate Data and Linear Regression
3.1 Introduction to Linear Regression
3.2 Bivariate Data
3.3 Linear Analysis of Data
3.4 Correlation
3.5 Matlab Skills
3.6 Exercises
CHAPTER 4 Exponential and Logarithmic Functions
4.1 Exponential and Logarithmic Functions in Biology
4.2 Review of Exponential and Logarithm Properties
4.3 Allometry
4.4 Rescaling Data: Log-Log and Semilog Graphs
4.5 Matlab Skills
4.6 Exercises
UNIT 1 Student Projects
UNIT 2 Discrete Time Modeling
CHAPTER 5 Sequences and Discrete Difference Equations
5.1 Sequences
5.2 Limit of a Sequence
5.3 Discrete Difference Equations
5.4 Geometric and Arithmetic Sequences
5.5 Linear Difference Equation with Constant Coefficients
5.6 Introduction to Pharmacokinetics
5.7 Matlab Skills
5.8 Exercises
CHAPTER 6 Vectors and Matrices
6.1 Vector Structure: Order Matters!
6.2 Vector Algebra
6.3 Dynamics: Vectors Changing over Time
6.4 Matlab Skills
6.5 Exercises
CHAPTER 7 Matrix Algebra
7.1 Matrix Arithmetic
7.2 Applications
7.3 Matlab Skills
7.4 Exercises
CHAPTER 8 Long-Term Dynamics or Equilibrium
8.1 Notion of an Equilibrium
8.2 Eigenvectors
8.3 Stability
8.4 Matlab Skills
8.5 Exercises
CHAPTER 9 Leslie Matrix Models and Eigenvalues
9.1 Leslie Matrix Models
9.2 Long-Term Growth Rate (Eigenvalues)
9.3 Long-Term Population Structure (Corresponding Eigenvectors)
9.4 Matlab Skills
9.5 Exercises
UNIT 2 Student Projects
UNIT 3 Probability
CHAPTER 10 Probability of Events
10.1 Sample Spaces and Events
10.2 Probability of an Event
10.3 Combinations and Permutations
10.4 Binomial Experiments
10.5 Matlab Skills
10.6 Exercises
CHAPTER 11 Probability of Compound Events
11.1 Compound Events
11.2 Finding the Probability of a Compound Event
11.3 Probability Viewed as Darts Tossed at a Dart Board
11.4 Matlab Skills
11.5 Exercises
CHAPTER 12 Conditional Probability
12.1 Conditional Probability
12.2 Independence
12.3 Matlab Skills
12.4 Exercises
CHAPTER 13 Sequential Events
13.1 Partition Theorem
13.2 Bayes’ Theorem
13.3 Exercises
CHAPTER 14 Population Genetics Models
14.1 Hardy-Weinberg Equilibrium
14.2 Hardy-Weinberg Selection Model
14.3 Exercises
UNIT 3 Student Projects
UNIT 4 Limits and Continuity
CHAPTER 15 Limits of Functions
15.1 Limit of a Function
15.2 Limit Properties
15.3 Matlab Skills
15.4 Exercises
CHAPTER 16 Limits of Continuous Functions
16.1 Right and Left Limits
16.2 Continuity
16.3 Intermediate Value Theorem
16.4 Matlab Skills
16.5 Exercises
UNIT 4 Student Projects
UNIT 5 Derivatives
CHAPTER 17 Rates of Change
17.1 Average Rate of Change
17.2 Estimating Rates of Change for Data
17.3 Velocity
17.4 Photosynthesis
17.5 Other Examples of Rates of Change
17.6 Definition of a Derivative at a Point
17.7 Matlab Skills
17.8 Exercises
CHAPTER 18 Derivatives of Functions
18.1 Concept of a Derivative
18.2 Limit Definition of a Derivative of a Function
18.3 Derivatives of Exponential Functions
18.4 Derivatives of Trigonometric Functions
18.5 Derivatives and Continuity
18.6 Derivatives of Logarithmic Functions
18.7 Matlab Skills
18.8 Exercises
CHAPTER 19 Computing Derivatives
19.1 Derivatives of Frequently Used Functions
19.2 The Chain Rule for the Composition of Functions
19.3 Quotient and Reciprocal Rules
19.4 Exponential Models
19.5 Higher Derivatives
19.6 Exercises
CHAPTER 20 Using Derivatives to Find Maxima and Minima
20.1 Maxima and Minima
20.2 First Derivative Test
20.3 Mean Value Theorem
20.4 Concavity
20.5 Optimization Problems
20.6 Matlab Skills
20.7 Exercises
UNIT 5 Student Projects
UNIT 6 Integration
CHAPTER 21 Estimating the Area under a Curve
21.1 The Area under a Curve
21.2 Increasing the Accuracy of the Area Estimation
21.3 Area below the Horizontal Axis
21.4 Matlab Skills
21.5 Exercises
CHAPTER 22 Antiderivatives and the Fundamental Theorem of Calculus
22.1 Definition of an Integral
22.2 Antiderivatives
22.3 Fundamental Theorem of Calculus
22.4 Antiderivatives and Integrals
22.5 Average Values
22.6 Matlab Skills
22.7 Exercises
CHAPTER 23 Methods of Integration
23.1 Substitution Method
23.2 Integration by Parts
23.3 Exercises
CHAPTER 24 Applications of Integrals to Area and Volume
24.1 The Area between Two Curves
24.2 The Volume of a Solid of Revolution
24.3 Density Functions
24.4 Exercises
CHAPTER 25 Probability in a Continuous Context
25.1 Expected Value and Median Value
25.2 Normal Distribution
25.3 Waiting Times
25.4 Matlab Skills
25.5 Exercises
UNIT 6 Student Projects
UNIT 7 Introduction to Differential Equations
CHAPTER 26 Separation of Variables
26.1 Separation of Variables Method
26.2 Matlab Skills
26.3 Exercises
CHAPTER 27 Equilibria and Limited Population Growth
27.1 Models of Limited Population Growth
27.2 Equilibria and Stability
27.3 Homeostasis
27.4 Exercises
CHAPTER 28 Implicit Differentiation and Related Rates
28.1 Explicitly and Implicitly Defined Functions
28.2 Implicit Differentiation
28.3 Related Rates
28.4 Exercises
UNIT 7 Student Projects
Bibliography
Appendix A
Appendix B
Answers to Selected Problems
Index
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