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.
Project: The Biomechanics of Human Movement.
1.4 Exponential Functions.
1.5 Logarithms; Semilog and Log-Log Plots.
Project: The Coding Function of DNA.
1.6 Sequences and Difference Equations.
Project: Drug Resistance in Malaria.
Review.
Case Study 1a: Kill Curves and Antibiotic Effectiveness.
Case Study 3a: Vaccines and The Evolution of Disease Severity.
CHAPTER 2: LIMITS.
2.1 Limits of Functions.
2.2 Limits: Algebraic Methods.
2.3 Continuity.
2.4 Limits of Functions at Infinity.
2.5 Limits of Sequences.
Project: Modeling the Dynamics of Viral Infections.
Review.
Case Study 2a: Hosts, Parasites, and Time-Travel.
Case Study 3b: Vaccines and the Evolution of Disease Severity.
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.
Project: Controlling Red Blood Cell Loss During Surgery.
3.7 Derivatives of the Logarithmic and Inverse Tangent Functions.
3.8 Linear Approximations and Differentials.
Project: Harvesting Renewable Resources.
Review.
Case Study 1b: Kill Curves and Antibiotic Effectiveness.
CHAPTER 4: APPLICATIONS AND DERIVATIVES.
4.1 Maximum and Minimum Values.
Project: The Calculus of Rainbows.
4.2 How Derivatives Affect the Shape of a Graph.
4.3 L’Hospital’s Rule: Comparing Rates of Growth.
Project: Mutation-Selection Balance in Genetic Diseases.
4.4 Optimization Problems.
Project: Flapping and Gliding.
Project: The Tragedy of the Commons: An Introduction to Game Theory.
4.5 Recursions: Equilibria and Stability.
4.6 Antiderivatives.
Review.
Case Study 3c: Vaccines and the Evolution of Disease Severity.
CHAPTER 5: INTEGRALS.
5.1 Areas, Distances, and Pathogenesis.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
Project: The Outbreak Size of an Infectious Disease.
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.
Review.
Case Study 1c: Kill Curves and Antibiotic Effectiveness.
CHAPTER 6: APPLICATIONS OF INTEGRALS.
6.1 Areas Between Curves.
Project: Disease Progression and Immunity.
Project: The Gini Index.
6.2 Average Values.
6.3 Further Applications to Biology.
6.4 Numerical Integration.
6.5 Volumes.
Review.
Case Study 1d: Kill Curves and Antibiotic Effectiveness.
Case Study 2b: Hosts, Parasites, and Time-Travel.
CHAPTER 7: DIFFERENTIAL EQUATIONS.
7.1 Modeling with Differential Equations.
Project: Sterile Insect Technique.
7.2 Separable Equations.
Project: Why Does Urea Concentration Rebound After Dialysis?
7.3 Phase Plots, Equilibria, and Stability.
Project: Catastrophic Population Collapse: An Introduction to Bifurcation Theory.
7.4 Direction Fields and Euler’s Method.
7.5 Systems of Differential Equations.
Project: The Flight Path of Hunting Raptors.
7.6 Phase Plane Analysis.
Project: Determining the Critical Vaccination Coverage.
Review.
Case Study 2c: Hosts, Parasites, and Time-Travel.
Case Study 3d: Vaccines and the Evolution of Disease Severity.
CHAPTER 8: VECTORS AND MATRIX MODELS.
8.1 Coordinate Systems.
8.2 Vectors.
8.3 The Dot Product.
Project: Microarray Analysis of Genome Expression.
Project: Vaccine Escape.
8.4 Matrix Algebra.
8.5 Matrix Models.
8.6 The Inverse and Determinant of a Matrix.
Project: Cubic Splines.
Project: Color Vision and Chromaticity Diagrams.
8.7 Eigenvectors and Eigenvalues.
8.8 Iterated Matrix Models.
Project: The Emergence of Geometric Order in Proliferating Cells.
Review.
CHAPTER 9: MULTIVARIATE CALCULUS.
9.1 Functions of Several Variables.
9.2 Partial Derivatives.
9.3 Tangent Planes and Linear Approximations.
Project: The Speedo LZR Racer.
9.4 The Chain Rule.
9.5 Directional Derivatives and the Gradient Vector.
9.6 Maximum and Minimum Values.
Review.
CHAPTER 10: PROBABILITY.
10.1 Principles of Counting.
10.2 What is Probability?
10.3 Conditional Probability.
Project: Testing for Rare Diseases.
10.4 Discrete Random Variables.
Project: DNA Supercoiling.
Project: The Probability of an Avian Influenza Pandemic in Humans.
10.5 Continuous Random Variables.
Review.
CHAPTER 11: DATA ANALYSIS: EXPLORATION, PREDICTION, AND INFERENCE.
11.1 Exploring Data Numerically.
11.2 Exploring Data Graphically.
11.3 Relationships Between Variables, Statistical Modeling, and Prediction.
11.4 Populations, Samples, and Statistical Inference.
Project: The Birth Weight Paradox.
Review.
