Calculus for the Life Sciences, 2nd edition

18. Algebra Reference
    • R.1 Polynomials
    • R.2 Factoring
    • R.3 Rational Expressions
    • R.4 Equations
    • R.5 Inequalities
    • R.6 Exponents
    • R.7 Radicals

1. Functions
   • 1.1 Lines and Linear Functions
   • 1.2 The Least Squares Line
   • 1.3 Properties of Functions
   • 1.4 Quadratic Functions; Translation and Reflection
   • 1.5 Polynomial and Rational Functions
   • Chapter Review
   • Extended Application: Using Extrapolation to Predict Life Expectancy
2. Exponential, Logarithmic, and Trigonometric Functions
   • 2.1 Exponential Functions
   • 2.2 Logarithmic Functions
   • 2.3 Applications: Growth and Decay
   • 2.4 Trigonometric Functions
   • Chapter Review
   • Extended Application: Power Functions
3. The Derivative
   • 3.1 Limits
   • 3.2 Continuity
   • 3.3 Rates of Change
   • 3.4 Definition of the Derivative
   • 3.5 Graphical Differentiation
   • Chapter Review
   • Extended Application: A Model For Drugs Administered Intravenously
4. Calculating the Derivative
   • 4.1 Techniques for Finding Derivatives
   • 4.2 Derivatives of Products and Quotients
   • 4.3 The Chain Rule
   • 4.4 Derivatives of Exponential Functions
   • 4.5 Derivatives of Logarithmic Functions
   • 4.6 Derivatives of Trigonometric Functions
   • Chapter Review
   • Extended Application: Managing Renewable Resources
5. Graphs and the Derivative
   • 5.1 Increasing and Decreasing Functions
   • 5.2 Relative Extrema
   • 5.3 Higher Derivatives, Concavity, and the Second Derivative Test
   • 5.4 Curve Sketching
   • Chapter Review
   • Extended Application: A Drug Concentration Model for Orally Administered Medications
6. Applications of the Derivative
   • 6.1 Absolute Extrema
   • 6.2 Applications of Extrema
   • 6.3 Implicit Differentiation
   • 6.4 Related Rates
   • 6.5 Differentials: Linear Approximation
   • Chapter Review
   • Extended Application: A Total Cost Model for a Training Program
7. Integration
   • 7.1 Antiderivatives
   • 7.2 Substitution
   • 7.3 Area and the Definite Integral
   • 7.4 The Fundamental Theorem of Calculus
   • 7.5 The Area Between Two Curves
   • Chapter Review
   • Extended Application: Estimating Depletion Dates for Minerals
8. Further Techniques and Applications of Integration
   • 8.1 Numerical Integration
   • 8.2 Integration by Parts
   • 8.3 Volume and Average Value
   • 8.4 Improper Integrals
   • Chapter Review
   • Extended Application: Flow Systems
9. Multivariable Calculus
   • 9.1 Functions of Several Variables
   • 9.2 Partial Derivatives
   • 9.3 Maxima and Minima
   • 9.4 Total Differentials and Approximations
   • 9.5 Double Integrals
   • Chapter Review
   • Extended Application: Optimization for a Predator
10. Matrices
    • 10.1 Solution of Linear Systems
    • 10.2 Addition and Subtraction of Matrices
    • 10.3 Multiplication of Matrices
    • 10.4 Matrix Inverses
    • 10.5 Eigenvalues and Eigenvectorsx
    • Chapter Review
    • Extended Application: Contagion
11. Differential Equations
    • 11.1 Solutions of Elementary and Separable Differential Equations
    • 11.2 Linear First-Order Differential Equations
    • 11.3 Euler’s Method
    • 11.4 Linear Systems of Differential Equations
    • 11.5 Non-Linear Systems of Differential Equations
    • 11.6 Applications of Differential Equations
    • Chapter Review
    • Extended Application: Pollution of the Great Lakes
12. Probability
    • 12.1 Sets
    • 12.2 Introduction to Probability
    • 12.3 Conditional Probability; Independent Events; Bayes’ Theorem
    • 12.4 Discrete Random Variables; Applications to Decision Making
    • Chapter Review
    • Extended Application: Medical Diagnosis
13. Probability and Calculus
    • 13.1 Continuous Probability Models
    • 13.2 Expected Value and Variance of Continuous Random Variables.
    • 13.3 Special Probability Density Functions
    • Chapter Review
    • Extended Application: Exponential Waiting Times
14. Discrete Dynamical Systems
    • 14.1 Sequences
    • 14.2 Equilibrium Points
    • 14.3 Determining Stability
    • Chapter Review
    • Extended Application: Mathematical Modeling in a Dynamic World

Special Topics (available online)

Sequences and Series

• Geometric Sequences
• Annuities: An Application of Sequences
• Taylor Polynomials
• Infinite Series
• Taylor Series
• Newton’s Method
• L’Hôpital’s Rule

Markov Chains