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Full Description
Calculus for Biology and Medicine shows how calculus is used to analyze phenomena in nature. The text motivates life and health science majors to learn calculus through relevant and strategically placed applications to their chosen fields.
Contents
(NOTE: Each chapter concludes with Key Terms and Review Problems.) 1. Preview and Review
1.1 Precalculus Skills Diagnostic Test
1.2 Preliminaries
1.3 Elementary Functions
1.4 Graphing
2. Discrete-Time Models, Sequences, and Difference Equations
2.1 Exponential Growth and Decay
2.2 Sequences
2.3 Modeling with Recurrence Equations
3. Limits and Continuity
3.1 Limits
3.2 Continuity
3.3 Limits at Infinity
3.4 Trigonometric Limits and the Sandwich Theorem
3.5 Properties of Continuous Functions
3.6 A Formal Definition of Limits (Optional)
4. Differentiation
4.1 Formal Definition of the Derivative
4.2 Properties of the Derivative
4.3 Power Rules and Basic Rules
4.4 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
4.5 Chain Rule
4.6 Implicit Functions and Implicit Differentiation
4.7 Higher Derivatives
4.8 Derivatives of Trigonometric Functions
4.9 Derivatives of Exponential Functions
4.10 Inverse Functions and Logarithms
4.11 Linear Approximation and Error Propagation
5. Applications of Differentiation
5.1 Extrema and the Mean-Value Theorem
5.2 Monotonicity and Concavity
5.3 Extrema and Inflection Points
5.4 Optimization
5.5 L'Hôpital's Rule
5.6 Graphing and Asymptotes
5.7 Recurrence Equations: Stability (Optional)
5.8 Numerical Methods: The Newton - Raphson Method (Optional)
5.9 Modeling Biological Systems Using Differential Equations (Optional)
5.10 Antiderivatives
6. Integration
6.1 The Definite Integral
6.2 The Fundamental Theorem of Calculus
6.3 Applications of Integration
7. Integration Techniques and Computational Methods
7.1 The Substitution Rule
7.2 Integration by Parts and Practicing Integration
7.3 Rational Functions and Partial Fractions
7.4 Improper Integrals (Optional)
7.5 Numerical Integration
7.6 The Taylor Approximation (optional)
7.7 Tables of Integrals (Optional)
8. Differential Equations
8.1 Solving Separable Differential Equations
8.2 Equilibria and Their Stability
8.3 Differential Equation Models
8.4 Integrating Factors and Two-Compartment Models
9. Linear Algebra and Analytic Geometry
9.1 Linear Systems
9.2 Matrices
9.3 Linear Maps, Eigenvectors, and Eigenvalues
9.4 Demographic Modeling
9.5 Analytic Geometry
10. Multivariable Calculus
10.1 Two or More Independent Variables
10.2 Limits and Continuity (optional)
10.3 Partial Derivatives
10.4 Tangent Planes, Differentiability, and Linearization
10.5 The Chain Rule and Implicit Differentiation (Optional)
10.6 Directional Derivatives and Gradient Vectors (Optional)
10.7 Maximization and Minimization of Functions (Optional)
10.8 Diffusion (Optional)
10.9 Systems of Difference Equations (Optional)
11. Systems of Differential Equations
11.1 Linear Systems: Theory
11.2 Linear Systems: Applications
11.3 Nonlinear Autonomous Systems: Theory
11.4 Nonlinear Systems: Lotka - Volterra Model of Interspecific Interactions
11.5 More Mathematical Models (Optional)
12. Probability and Statistics
12.1 Counting
12.2 What Is Probability?
12.3 Conditional Probability and Independence
12.4 Discrete Random Variables and Discrete Distributions
12.5 Continuous Distributions
12.6 Limit Theorems
12.7 Statistical Tools
Appendices
A: Frequently Used Symbols
B: Table of the Standard Normal Distribution
Answers to Odd-Numbered Problems References Photo Credits Index
