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Calculus for Life Sciences

Book Description

In this much anticipated first edition, the authors present the basic canons of first-year calculus, but motivated through real biological problems. The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, analytical techniques, and numerical methods and to have students understand how, when, and why calculus can be used to model biological phenomena. Both students and instructors will find the book to be a gateway to the exciting interface of mathematics and biology.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. ABOUT THE AUTHORS
  5. Dedication
  6. PREFACE
  7. Contents
  8. APPLICATIONS AND MODELS INDEXS
  9. Preview of Modeling and Calculus
  10. CHAPTER 1: Modeling with Functions
    1. 1.1 Real Numbers and Functions
    2. 1.2 Data Fitting with Linear and Periodic Functions
    3. 1.3 Power Functions and Scaling Laws
    4. 1.4 Exponential Growth
    5. 1.5 Function Building
    6. 1.6 Inverse Functions and Logarithms
    7. 1.7 Sequences and Difference Equations
  11. CHAPTER 2: Limits and Derivatives
    1. 2.1 Rates of Change and Tangent Lines
    2. 2.2 Limits
    3. 2.3 Limit Laws and Continuity
    4. 2.4 Asymptotes and Infinity
    5. 2.5 Sequential Limits
    6. 2.6 Derivative at a Point
    7. 2.7 Derivatives as Functions
  12. CHAPTER 3: Derivative Rules and Tools
    1. 3.1 Derivatives of Polynomials and Exponentials
    2. 3.2 Product and Quotient Rules
    3. 3.3 Chain Rule and Implicit Differentiation
    4. 3.4 Derivatives of Trigonometric Functions
    5. 3.5 Linear Approximation
    6. 3.6 Higher Derivatives and Approximations
    7. 3.7 l'Hôpital's Rule
  13. CHAPTER 4: Applications of Differentiation
    1. 4.1 Graphing Using Calculus
    2. 4.2 Getting Extreme
    3. 4.3 Optimization in Biology
    4. 4.4 Decisions and Optimization
    5. 4.5 Linearization and Difference Equations
  14. CHAPTER 5: Integration
    1. 5.1 Antiderivatives
    2. 5.2 Accumulated Change and Area under a Curve
    3. 5.3 The Definite Integral
    4. 5.4 The Fundamental Theorem of Calculus
    5. 5.5 Substitution
    6. 5.6 Integration by Parts and Partial Fractions
    7. 5.7 Numerical Integration
    8. 5.8 Applications of Integration
  15. CHAPTER 6: Differential Equations
    1. 6.1 A Modeling Introduction to Differential Equations
    2. 6.2 Solutions and Separable Equations
    3. 6.3 Linear Models in Biology
    4. 6.4 Slope Fields and Euler's Method
    5. 6.5 Phase Lines and Classifying Equilibria
    6. 6.6 Bifurcations
  16. CHAPTER 7: Probabilistic Applications of Integration
    1. 7.1 Histograms, PDFs, and CDFs
    2. 7.2 Improper Integrals
    3. 7.3 Mean and Variance
    4. 7.4 Bell-Shaped Distributions
    5. 7.5 Life Tables
  17. CHAPTER 8: Multivariable Extensions
    1. 8.1 Multivariate Modeling
    2. 8.2 Matrices and Vectors
    3. 8.3 Eigenvalues and Eigenvectors
    4. 8.4 Systems of Linear Differential Equations
    5. 8.5 Nonlinear Systems
  18. ANSWERS TO SELECTED PROBLEMS
  19. INDEX