Calculus for the Life Sciences, 2nd edition

Published by Pearson (July 14, 2021) © 2015

  • Raymond N. Greenwell Hofstra University
  • Nathan P. Ritchey Edinboro University of PA , Youngstown State University
  • Margaret L. Lial American River College
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In this eTextbook — More ways to learn

  • More flexible. Start learning right away, on any device.
  • More supportive. Get AI explanations and practice questions (select titles).
  • More interactive. Bring learning to life with audio, videos, and diagrams.
  • More memorable. Make concepts stick with highlights, search, notes, and flashcards.
  • More understandable. Translate text into 100+ languages with one tap.
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Title overview

Calculus for the Life Sciences shows you interesting, relevant applications that constantly connect mathematics to the life sciences. A review chapter at the start of the text helps you brush up on needed algebra skills. Proven learning aids, robust exercise sets, and comprehensive end-of-chapter study tools help you succeed.

The 2nd Edition includes new features such as Your Turn exercises. Exercises and examples have been updated to reflect recent data and incorporate user feedback; a list of important formulas and definitions has been added; revised review exercises now include Concept Check exercises; and much more.

Table of contents

  • R. 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

 

Author bios

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