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Cover type: Hardback

Edition: 2ND 04

Copyright: 2004

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Edition: 2ND 04

Copyright: 2004

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

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For a two-semester course in Calculus for Life Sciences.

This text addresses the needs of students in the biological sciences by teaching calculus in a biological context without reducing the course level. It is a calculus text, written so that a math professor without a biology background can teach from it successfully. New concepts are introduced in a three step manner. First, a biological example motivates the topic; second, the topic is then developed via a simple mathematical example; and third the concept is tied to deeper biological examples. This allows students: to see why a concept is important; to understand how to use the concept computationally; to make sure that they can apply the concept.

Features

- NEW--Stronger biology focus in Calculus I.
- Enables students to learn the material in the context of their major.

- NEW--Discrete time models, sequences and difference equations chapter added. (New Chapter 2).
- Introduces students to exponential growth decay, sequences and population models.

- Allows for earlier introduction of biological examples.
- NEW--Statistics and probability chapter substantially enlarged.
- Enables students to become better trained quantitively.

- NEW--50-70% increase in problems in first 6 chapters (Calculus I).
- Provides students with up-to-date problems that apply to their field.

- NEW--Section on translating word problems into graphs.
- Provides students with graphing and basic transformations of function information, as well as guidelines for translating word problems into graphs.

- Calculus taught in the context of biology--Not watered down, as in many of the brief calculus versions.
- Enables instructors without a biology background to use the text successfully. Enables students to acquire a firm foundation in calculus to apply calculus concepts to problems in the biological sciences.

- Less emphasis on integration techniques and more coverage of differential equations and systems of differential equations.
- Provides students with a discussion that includes both solution methods, and, to a larger extent, a qualitative discussion.

- Examples worked out in step-by-step detail--Each subsection contains examples which increase in difficulty. The examples are completely worked out with a lot of detail on how one step follows from the previous--unlike in other calculus texts which often simply provide lengthy calculations without explanations.
- A variety of problems after each section--The problems start out as drill problems. These are followed by increasingly harder, more conceptual problems. Finally, word problems tie the concepts into biology.

**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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Summary

For a two-semester course in Calculus for Life Sciences.

This text addresses the needs of students in the biological sciences by teaching calculus in a biological context without reducing the course level. It is a calculus text, written so that a math professor without a biology background can teach from it successfully. New concepts are introduced in a three step manner. First, a biological example motivates the topic; second, the topic is then developed via a simple mathematical example; and third the concept is tied to deeper biological examples. This allows students: to see why a concept is important; to understand how to use the concept computationally; to make sure that they can apply the concept.

Features

- NEW--Stronger biology focus in Calculus I.
- Enables students to learn the material in the context of their major.

- NEW--Discrete time models, sequences and difference equations chapter added. (New Chapter 2).
- Introduces students to exponential growth decay, sequences and population models.

- Allows for earlier introduction of biological examples.
- NEW--Statistics and probability chapter substantially enlarged.
- Enables students to become better trained quantitively.

- NEW--50-70% increase in problems in first 6 chapters (Calculus I).
- Provides students with up-to-date problems that apply to their field.

- NEW--Section on translating word problems into graphs.
- Provides students with graphing and basic transformations of function information, as well as guidelines for translating word problems into graphs.

- Calculus taught in the context of biology--Not watered down, as in many of the brief calculus versions.
- Enables instructors without a biology background to use the text successfully. Enables students to acquire a firm foundation in calculus to apply calculus concepts to problems in the biological sciences.

- Less emphasis on integration techniques and more coverage of differential equations and systems of differential equations.
- Provides students with a discussion that includes both solution methods, and, to a larger extent, a qualitative discussion.

- Examples worked out in step-by-step detail--Each subsection contains examples which increase in difficulty. The examples are completely worked out with a lot of detail on how one step follows from the previous--unlike in other calculus texts which often simply provide lengthy calculations without explanations.
- A variety of problems after each section--The problems start out as drill problems. These are followed by increasingly harder, more conceptual problems. Finally, word problems tie the concepts into biology.

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.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2004

International: No

Published: 2004

International: No

For a two-semester course in Calculus for Life Sciences.

This text addresses the needs of students in the biological sciences by teaching calculus in a biological context without reducing the course level. It is a calculus text, written so that a math professor without a biology background can teach from it successfully. New concepts are introduced in a three step manner. First, a biological example motivates the topic; second, the topic is then developed via a simple mathematical example; and third the concept is tied to deeper biological examples. This allows students: to see why a concept is important; to understand how to use the concept computationally; to make sure that they can apply the concept.

Features

- NEW--Stronger biology focus in Calculus I.
- Enables students to learn the material in the context of their major.

- NEW--Discrete time models, sequences and difference equations chapter added. (New Chapter 2).
- Introduces students to exponential growth decay, sequences and population models.

- Allows for earlier introduction of biological examples.
- NEW--Statistics and probability chapter substantially enlarged.
- Enables students to become better trained quantitively.

- NEW--50-70% increase in problems in first 6 chapters (Calculus I).
- Provides students with up-to-date problems that apply to their field.

- NEW--Section on translating word problems into graphs.
- Provides students with graphing and basic transformations of function information, as well as guidelines for translating word problems into graphs.

- Calculus taught in the context of biology--Not watered down, as in many of the brief calculus versions.
- Enables instructors without a biology background to use the text successfully. Enables students to acquire a firm foundation in calculus to apply calculus concepts to problems in the biological sciences.

- Less emphasis on integration techniques and more coverage of differential equations and systems of differential equations.
- Provides students with a discussion that includes both solution methods, and, to a larger extent, a qualitative discussion.

- Examples worked out in step-by-step detail--Each subsection contains examples which increase in difficulty. The examples are completely worked out with a lot of detail on how one step follows from the previous--unlike in other calculus texts which often simply provide lengthy calculations without explanations.
- A variety of problems after each section--The problems start out as drill problems. These are followed by increasingly harder, more conceptual problems. Finally, word problems tie the concepts into biology.

**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.