Calculus for Biology and Medicine / Edition 3

Calculus for Biology and Medicine / Edition 3

by Claudia Neuhauser
     
 

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

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Overview

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. This allows readers to first see why a certain concept is important, then lets them focus on how to use the concepts without getting distracted by applications, and then, once readers feel more comfortable with the concepts, it revisits the biological applications to make sure that they can apply the concepts. The book features exceptionally detailed, step-by-step, worked-out examples and a variety of problems, including an unusually large number of word problems. The volume begins with a preview and review and moves into discrete time models, sequences, and difference equations, limits and continuity, differentiation, applications of differentiation, integration techniques and computational methods, differential equations, linear algebra and analytic geometry, multivariable calculus, systems of differential equations and probability and statistics. For faculty and postdocs in biology departments.

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Product Details

ISBN-13:
9780321673176
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
01/01/2011
Pages:
840
Product dimensions:
8.54(w) x 10.87(h) x 1.06(d)

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Table of Contents

1. Preview and Review.

Preliminaries. Elementary Functions. Graphing. Key Terms. Review Problems.

2. Discrete Time Models, Sequences, and Difference Equations.

Exponential Growth and Decay. Sequences. More Population Models. Key Terms. Review Problems.

3. Limits and Continuity.

Limits. Continuity. Limits at Infinity. The Sandwich Theorem and Some Trigonometric Limits. Properties of Continuous Functions. Formal Definition of Limits. Key Terms. Review Problems.

4. Differentiation.

Formal Definition of the Derivative. The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials. Product Rule and Quotient Rule. The Chain Rule and Higher Derivatives. Derivatives of Trigonometric Functions. Derivatives of Exponential Functions. Derivatives of Inverse and Logarithmic Functions. Approximation and Local Linearity. Key Terms. Review Problems.

5. Applications of Differentiation.

Extrema and the Mean Value Theorem. Monotonicity and Concavity. Extrema, Inflection Points and Graphing. Optimization. L'Hopital's Rule. Difference Equations - Stability. Numerical Methods: The Newton-Raphson Method. Antiderivatives. Key Terms. Review Problems.

6. Integration.

The Definite Integral. The Fundamental Theorem of Calculus. Applications of Integration. Key Terms. Review Problems.

7. Integration Techniques and Computational Methods.

The Substitution Rule. Integration by Parts. Practicing Integration and Partial Fractions. Improper Integrals. Numerical Integration. Tables of Integration. The Taylor Approximation. Key Terms. Review Problems.

8. Differential Equations.

Solving Differential Equations. Equilibria and Their Stability. Systems of Autonomous Equations. Key Terms. Review Problems.

9. Linear Algebra and Analytic Geometry.

Linear Systems. Matrices. Linear Maps, Eigenvectors and Eignvalues. Analytic Geometry. Key Terms. Review Problems.

10. Multivariable Calculus.

Functions of Two or More Independent Variables. Limits and Continuity. Partial Derivatives. Tangent Planes, Differentiability, and Linearization. More About Derivatives. Applications. Systems of Difference Equations. Key Terms. Review Problems.

11. Systems of Differential Equations.

Linear Systems: Theory. Linear Systems: Applications. Nonlinear Autonomous Systems: Theory. Nonlinear Systems: Applications. Key Terms. Review Problems.

12. Probability and Statistics.

Counting. What Is Probability? Conditional Probability and Independence. Discrete Random Variables and Discrete Distributions. Continuous Distributions. Limit Theorems. Statistical Tools. Key Terms. Review Problems.

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