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by Ron Larson, Robert Hostetler and Bruce H. Edwards

Cover type: HardbackEdition: 4TH 07

Copyright: 2007

Publisher: Houghton Mifflin Harcourt

Published: 2007

International: No

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Designed for the first two semesters of a three-semester engineering calculus course, Calculus of a Single Variable: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.

Calculus of a Single Variable: Early Transcendental Functions, 4/e, contains Chapters 1-10 of the full Calculus: Early Transcendental Functions, 4/e, text.

Every edition from the first to the fourth of Calculus: Early Transcendental Function, 4/e, has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

- Exercise sets have been carefully examined and revised to ensure they cover all calculus topics appropriately. Many new exercises have been added.
- A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
- Putnam Exam Questions--taken from the William Lowell Putnam Mathematical Competition--offer challenging problems that often require students to look for creative solutions; Graphical Analysis exercises offer the opportunity to analyze graphs; Think About It exercises require students to use critical reasoning skills to explore the intricacies of calculus.
- Explanations, theorems, and definitions in the text have been thoroughly reviewed to ensure the text is mathematically precise and easily comprehensible.
- Clear, multi-step examples with worked-out solutions help students learn difficult mathematical concepts. Examples correspond to the exercises, serving as a supportive reference for students. This is the only text on the market where every example, proof, and explanation begins and ends on the same page.
- Explorations help students develop their intuitive understanding of calculus concepts. These optional activities are short enough to integrate into class, but they can also be omitted without loss of continuity.
- Theorem boxes clearly explain important mathematical concepts.
- The Integrated Learning System resources are available in print, CD-ROM, and online formats.
- Eduspace, powered by Blackboard, Houghton Mifflin's online learning tool, offers your students quality online homework, tutorials, multimedia, and testing that correspond to the Calculus: Early Transcendental Functions text. This content is paired with the course management tools of Blackboard. In addition, eSolutions, the complete solutions to the odd-numbered text exercises, provides students with a convenient and comprehensive way to do homework and view the course materials.

**1. Preparation for Calculus**

1.1 Graphs and Models

1.2 Linear Models and Rates of Change

1.3 Functions and Their Graphs

1.4 Fitting Models to Data

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

**2. Limits and Their Properties**

2.1 A Preview of Calculus

2.2 Finding Limits Graphically and Numerically

2.3 Evaluating Limits Analytically

2.4 Continuity and One-Sided Limits

2.5 Infinite Limits

Section Project: Graphs and Limits of Trig Functions

**3. Differentiation**

3.1 The Derivative and the Tangent Line Problem

3.2 Basic Differentiation Rules and Rates of Change

3.3 The Product and Quotient Rules and Higher-Order Derivatives

3.4 The Chain Rule

3.5 Implicit Differentiation

Section Project: Optical Illusions

3.6 Derivatives of Inverse Functions

3.7 Related Rates

3.8 Newton's Method

**4. Applications of Differentiation**

4.1 Extrema on an Interval

4.2 Rolle's Theorem and the Mean Value Theorem

4.3 Increasing and Decreasing Functions and the First Derivative Test

Section Project: Rainbows

4.4 Concavity and the Second Derivative Test

4.5 Limits at Infinity

4.6 A Summary of Curve Sketching

4.7 Optimization Problems

Section Project: Connecticut River

4.8 Differentials

**5. Integration**

5.1 Antiderivatives and Indefinite Integration

5.2 Area

5.3 Riemann Sums and Definite Integrals

5.4 The Fundamental Theorem of Calculus

Section Project: Demonstrating the Fundamental Theorem

5.5 Integration by Substitution

5.6 Numerical Integration

5.7 The Natural Logarithmic Function: Integration

5.8 Inverse Trigonometric Functions: Integration

5.9 Hyperbolic Functions

Section Project: St. Louis Arch

**6. Differential Equations**

6.1 Slope Fields and Euler's Method

6.6 Differential Equations: Growth and Decay

6.7 Differential Equations: Separation of Variables

6.4 The Logistic Equation

6.5 First-Order Linear Differential Equations

Section Project: Weight Loss

6.6 Predator-Prey Differential Equations

**7. Applications of Integration**

7.1 Area of a Region Between Two Curves

7.2 Volume: The Disk Method

7.3 Volume: The Shell Method

7.4 Arc Length and Surfaces of Revolution

7.5 Work

7.6 Moments, Centers of Mass, and Centroids

7.7 Fluid Pressure and Fluid Force

**8. Integration Techniques, L'Hopital's Rule, and Improper Integrals**

8.1 Basic Integration Rules

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitution

8.5 Partial Fractions

8.6 Integration by Tables and Other Integration Techniques

8.7 Indeterminate Forms and L'Hopital's Rule

8.8 Improper Integrals

**9. Infinite Series**

9.1 Sequences

9.2 Series and Convergence

9.3 The Integral Test and p-Series

9.4 Comparisons of Series

9.5 Alternating Series

9.6 The Ratio and Root Tests

9.7 Taylor Polynomials and Approximations

9.8 Power Series

9.9 Representation of Functions by Power Series

9.10 Taylor and Maclaurin Series

**10. Conics, Parametric Equations, and Polar Coordinates**

10.1 Conics and Calculus

10.2 Plane Curves and Parametric Equations

10.3 Parametric Equations and Calculus

10.4 Polar Coordinates and Polar Graphs

10.5 Area and Arc Length in Polar Coordinates

10.6 Polar Equations of Conics and Kepler's Laws

**Appendices**

Appendix A Proofs of Selected Theorems

Appendix B Integration Tables

Appendix C Business and Economic Applications

**Additional Appendices**

The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM.

Appendix D Precalculus Review

Appendix E Rotation and the General Second-Degree Equation

Appendix F Complex Numbers

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Summary

Designed for the first two semesters of a three-semester engineering calculus course, Calculus of a Single Variable: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.

Calculus of a Single Variable: Early Transcendental Functions, 4/e, contains Chapters 1-10 of the full Calculus: Early Transcendental Functions, 4/e, text.

Every edition from the first to the fourth of Calculus: Early Transcendental Function, 4/e, has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

- Exercise sets have been carefully examined and revised to ensure they cover all calculus topics appropriately. Many new exercises have been added.
- A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
- Putnam Exam Questions--taken from the William Lowell Putnam Mathematical Competition--offer challenging problems that often require students to look for creative solutions; Graphical Analysis exercises offer the opportunity to analyze graphs; Think About It exercises require students to use critical reasoning skills to explore the intricacies of calculus.
- Explanations, theorems, and definitions in the text have been thoroughly reviewed to ensure the text is mathematically precise and easily comprehensible.
- Clear, multi-step examples with worked-out solutions help students learn difficult mathematical concepts. Examples correspond to the exercises, serving as a supportive reference for students. This is the only text on the market where every example, proof, and explanation begins and ends on the same page.
- Explorations help students develop their intuitive understanding of calculus concepts. These optional activities are short enough to integrate into class, but they can also be omitted without loss of continuity.
- Theorem boxes clearly explain important mathematical concepts.
- The Integrated Learning System resources are available in print, CD-ROM, and online formats.
- Eduspace, powered by Blackboard, Houghton Mifflin's online learning tool, offers your students quality online homework, tutorials, multimedia, and testing that correspond to the Calculus: Early Transcendental Functions text. This content is paired with the course management tools of Blackboard. In addition, eSolutions, the complete solutions to the odd-numbered text exercises, provides students with a convenient and comprehensive way to do homework and view the course materials.

Table of Contents

**1. Preparation for Calculus**

1.1 Graphs and Models

1.2 Linear Models and Rates of Change

1.3 Functions and Their Graphs

1.4 Fitting Models to Data

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

**2. Limits and Their Properties**

2.1 A Preview of Calculus

2.2 Finding Limits Graphically and Numerically

2.3 Evaluating Limits Analytically

2.4 Continuity and One-Sided Limits

2.5 Infinite Limits

Section Project: Graphs and Limits of Trig Functions

**3. Differentiation**

3.1 The Derivative and the Tangent Line Problem

3.2 Basic Differentiation Rules and Rates of Change

3.3 The Product and Quotient Rules and Higher-Order Derivatives

3.4 The Chain Rule

3.5 Implicit Differentiation

Section Project: Optical Illusions

3.6 Derivatives of Inverse Functions

3.7 Related Rates

3.8 Newton's Method

**4. Applications of Differentiation**

4.1 Extrema on an Interval

4.2 Rolle's Theorem and the Mean Value Theorem

4.3 Increasing and Decreasing Functions and the First Derivative Test

Section Project: Rainbows

4.4 Concavity and the Second Derivative Test

4.5 Limits at Infinity

4.6 A Summary of Curve Sketching

4.7 Optimization Problems

Section Project: Connecticut River

4.8 Differentials

**5. Integration**

5.1 Antiderivatives and Indefinite Integration

5.2 Area

5.3 Riemann Sums and Definite Integrals

5.4 The Fundamental Theorem of Calculus

Section Project: Demonstrating the Fundamental Theorem

5.5 Integration by Substitution

5.6 Numerical Integration

5.7 The Natural Logarithmic Function: Integration

5.8 Inverse Trigonometric Functions: Integration

5.9 Hyperbolic Functions

Section Project: St. Louis Arch

**6. Differential Equations**

6.1 Slope Fields and Euler's Method

6.6 Differential Equations: Growth and Decay

6.7 Differential Equations: Separation of Variables

6.4 The Logistic Equation

6.5 First-Order Linear Differential Equations

Section Project: Weight Loss

6.6 Predator-Prey Differential Equations

**7. Applications of Integration**

7.1 Area of a Region Between Two Curves

7.2 Volume: The Disk Method

7.3 Volume: The Shell Method

7.4 Arc Length and Surfaces of Revolution

7.5 Work

7.6 Moments, Centers of Mass, and Centroids

7.7 Fluid Pressure and Fluid Force

**8. Integration Techniques, L'Hopital's Rule, and Improper Integrals**

8.1 Basic Integration Rules

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitution

8.5 Partial Fractions

8.6 Integration by Tables and Other Integration Techniques

8.7 Indeterminate Forms and L'Hopital's Rule

8.8 Improper Integrals

**9. Infinite Series**

9.1 Sequences

9.2 Series and Convergence

9.3 The Integral Test and p-Series

9.4 Comparisons of Series

9.5 Alternating Series

9.6 The Ratio and Root Tests

9.7 Taylor Polynomials and Approximations

9.8 Power Series

9.9 Representation of Functions by Power Series

9.10 Taylor and Maclaurin Series

**10. Conics, Parametric Equations, and Polar Coordinates**

10.1 Conics and Calculus

10.2 Plane Curves and Parametric Equations

10.3 Parametric Equations and Calculus

10.4 Polar Coordinates and Polar Graphs

10.5 Area and Arc Length in Polar Coordinates

10.6 Polar Equations of Conics and Kepler's Laws

**Appendices**

Appendix A Proofs of Selected Theorems

Appendix B Integration Tables

Appendix C Business and Economic Applications

**Additional Appendices**

The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM.

Appendix D Precalculus Review

Appendix E Rotation and the General Second-Degree Equation

Appendix F Complex Numbers

Digital Rights
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Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.

Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

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**Sharing:** Not Allowed

**Min. Software Version:** Online: No additional software required

Offline: VitalSource Bookshelf

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**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

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**Printing** - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."

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Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2007

International: No

Published: 2007

International: No

Designed for the first two semesters of a three-semester engineering calculus course, Calculus of a Single Variable: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.

Calculus of a Single Variable: Early Transcendental Functions, 4/e, contains Chapters 1-10 of the full Calculus: Early Transcendental Functions, 4/e, text.

Every edition from the first to the fourth of Calculus: Early Transcendental Function, 4/e, has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

- Exercise sets have been carefully examined and revised to ensure they cover all calculus topics appropriately. Many new exercises have been added.
- A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
- Putnam Exam Questions--taken from the William Lowell Putnam Mathematical Competition--offer challenging problems that often require students to look for creative solutions; Graphical Analysis exercises offer the opportunity to analyze graphs; Think About It exercises require students to use critical reasoning skills to explore the intricacies of calculus.
- Explanations, theorems, and definitions in the text have been thoroughly reviewed to ensure the text is mathematically precise and easily comprehensible.
- Clear, multi-step examples with worked-out solutions help students learn difficult mathematical concepts. Examples correspond to the exercises, serving as a supportive reference for students. This is the only text on the market where every example, proof, and explanation begins and ends on the same page.
- Explorations help students develop their intuitive understanding of calculus concepts. These optional activities are short enough to integrate into class, but they can also be omitted without loss of continuity.
- Theorem boxes clearly explain important mathematical concepts.
- The Integrated Learning System resources are available in print, CD-ROM, and online formats.
- Eduspace, powered by Blackboard, Houghton Mifflin's online learning tool, offers your students quality online homework, tutorials, multimedia, and testing that correspond to the Calculus: Early Transcendental Functions text. This content is paired with the course management tools of Blackboard. In addition, eSolutions, the complete solutions to the odd-numbered text exercises, provides students with a convenient and comprehensive way to do homework and view the course materials.

**1. Preparation for Calculus**

1.1 Graphs and Models

1.2 Linear Models and Rates of Change

1.3 Functions and Their Graphs

1.4 Fitting Models to Data

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

**2. Limits and Their Properties**

2.1 A Preview of Calculus

2.2 Finding Limits Graphically and Numerically

2.3 Evaluating Limits Analytically

2.4 Continuity and One-Sided Limits

2.5 Infinite Limits

Section Project: Graphs and Limits of Trig Functions

**3. Differentiation**

3.1 The Derivative and the Tangent Line Problem

3.2 Basic Differentiation Rules and Rates of Change

3.3 The Product and Quotient Rules and Higher-Order Derivatives

3.4 The Chain Rule

3.5 Implicit Differentiation

Section Project: Optical Illusions

3.6 Derivatives of Inverse Functions

3.7 Related Rates

3.8 Newton's Method

**4. Applications of Differentiation**

4.1 Extrema on an Interval

4.2 Rolle's Theorem and the Mean Value Theorem

4.3 Increasing and Decreasing Functions and the First Derivative Test

Section Project: Rainbows

4.4 Concavity and the Second Derivative Test

4.5 Limits at Infinity

4.6 A Summary of Curve Sketching

4.7 Optimization Problems

Section Project: Connecticut River

4.8 Differentials

**5. Integration**

5.1 Antiderivatives and Indefinite Integration

5.2 Area

5.3 Riemann Sums and Definite Integrals

5.4 The Fundamental Theorem of Calculus

Section Project: Demonstrating the Fundamental Theorem

5.5 Integration by Substitution

5.6 Numerical Integration

5.7 The Natural Logarithmic Function: Integration

5.8 Inverse Trigonometric Functions: Integration

5.9 Hyperbolic Functions

Section Project: St. Louis Arch

**6. Differential Equations**

6.1 Slope Fields and Euler's Method

6.6 Differential Equations: Growth and Decay

6.7 Differential Equations: Separation of Variables

6.4 The Logistic Equation

6.5 First-Order Linear Differential Equations

Section Project: Weight Loss

6.6 Predator-Prey Differential Equations

**7. Applications of Integration**

7.1 Area of a Region Between Two Curves

7.2 Volume: The Disk Method

7.3 Volume: The Shell Method

7.4 Arc Length and Surfaces of Revolution

7.5 Work

7.6 Moments, Centers of Mass, and Centroids

7.7 Fluid Pressure and Fluid Force

**8. Integration Techniques, L'Hopital's Rule, and Improper Integrals**

8.1 Basic Integration Rules

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitution

8.5 Partial Fractions

8.6 Integration by Tables and Other Integration Techniques

8.7 Indeterminate Forms and L'Hopital's Rule

8.8 Improper Integrals

**9. Infinite Series**

9.1 Sequences

9.2 Series and Convergence

9.3 The Integral Test and p-Series

9.4 Comparisons of Series

9.5 Alternating Series

9.6 The Ratio and Root Tests

9.7 Taylor Polynomials and Approximations

9.8 Power Series

9.9 Representation of Functions by Power Series

9.10 Taylor and Maclaurin Series

**10. Conics, Parametric Equations, and Polar Coordinates**

10.1 Conics and Calculus

10.2 Plane Curves and Parametric Equations

10.3 Parametric Equations and Calculus

10.4 Polar Coordinates and Polar Graphs

10.5 Area and Arc Length in Polar Coordinates

10.6 Polar Equations of Conics and Kepler's Laws

**Appendices**

Appendix A Proofs of Selected Theorems

Appendix B Integration Tables

Appendix C Business and Economic Applications

**Additional Appendices**

The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM.

Appendix D Precalculus Review

Appendix E Rotation and the General Second-Degree Equation

Appendix F Complex Numbers

- Windows 7/8, or Mac OS X 10.6 or above

eTextbooks and eChapters can be viewed by using the free reader listed below.

Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.

Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.

Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

VitalSource

**Copying:** Allowed, 10 selections may be copied every 180 days

**Printing:** Allowed, 10 prints for 180 days

**Expires:** Yes, may be used for 180 days after activation

**Reading Aloud:** Allowed

**Sharing:** Not Allowed

**Min. Software Version:** Online: No additional software required

Offline: VitalSource Bookshelf

**Suitable Devices:** PCs, Tablet PCs, Macs, Laptops

**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

Offline: VitalSource Bookshelf

**Digital Rights Management (DRM) Key**

**Printing** - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."

**Expires** - Books that have no expiration (the date upon which you will no longer be able to access your eBook) will read "No Expiration." Otherwise it will state the number of days from activation (the first time you actually read it).

**Reading Aloud** - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."

**Sharing** - Books that cannot be shared with other computers will show "Not Allowed."

**Min. Software Version** - This is the minimum software version needed to read this book.

**Suitable Devices** - Hardware known to be compatible with this book. Note: Reader software still needs to be installed.