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