Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Purchase Benefits
What is included with this book?
For a two-semester or three-semester course in Calculus for Life Sciences.
Calculus for Biology and Medicine, Third Edition, addresses the needs of students in the biological sciences by showing them how to use calculus to analyze natural phenomena without compromising the rigorous presentation of the mathematics.
While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides students with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. Since this textbook is written for college freshmen, the examples were chosen so that no formal training in biology is needed.
This volume teaches calculus in the biology context without compromising the level of regular calculus. The material is organized in the standard way and explains how the different concepts are logically related. Each new concept is typically introduced with a biological example; the concept is then developed without the biological context and then the concept is tied into additional biological examples. The book features exceptionally detailed, step-by-step, worked-out examples and a variety of problems, including an unusually large number of word problems.
Preview and Review; Discrete Time Models, Sequences, and Difference Equations; Limits and Continuity; Differentiation; Applications of Differentiation; Integration; Integration Techniques and Computational Methods; Differential Equations; Linear Algebra and Analytic Geometry; Multivariable Calculus; Systems of Differential Equations; Probability and Statistics
For all readers interested in calculus for biology and medicine.
1. Preview and Review
1.1 Preliminaries
1.2 Elementary Functions
1.3 Graphing
2. Discrete Time Models, Sequences, and Difference Equations
2.1 Exponential Growth and Decay
2.2 Sequences
2.3 More Population Models
3. Limits and Continuity
3.1 Limits
3.2 Continuity
3.3 Limits at Infinity
3.4 The Sandwich Theorem and Some Trigonometric Limits
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 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials
4.3 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
4.4 The Chain Rule and Higher Derivatives
4.5 Derivatives of Trigonometric Functions
4.6 Derivatives of Exponential Functions
4.7 Derivatives of Inverse Functions, Logarithmic Functions, and the Inverse Tangent Function
4.8 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, Inflection Points, and Graphing
5.4 Optimization
5.5 L’Hôpital’s Rule
5.6 Difference Equations: Stability (Optional)
5.7 Numerical Methods: The Newton-Raphson Method (Optional)
5.8 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
7.5 Numerical Integration
7.6 The Taylor Approximation
7.7 Tables of Integrals (Optional)
8. Differential Equations
8.1 Solving Differential Equations
8.2 Equilibria and Their Stability
8.3 Systems of Autonomous Equations (Optional)
9. Linear Algebra and Analytic Geometry
9.1 Linear Systems
9.2 Matrices
9.3 Linear Maps, Eigenvectors, and Eigenvalues
9.4 Analytic Geometry
10. Multivariable Calculus
10.1 Functions of Two or More Independent Variables
10.2 Limits and Continuity
10.3 Partial Derivatives
10.4 Tangent Planes, Differentiability, and Linearization
10.5 More about Derivatives (Optional)
10.6 Applications (Optional)
10.7 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: Applications
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