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- Calculus Combo

# Calculus Combo

## First Edition| ©2014 Laura Taalman; Peter Kohn

Many calculus textbooks look to engage students with margin notes, anecdotes, and other devices. But many instructors find these distracting, preferring to captivate their science and engineering students with the beauty of the calculus itself. Taalman and Kohn’s refreshing new textbook is

Many calculus textbooks look to engage students with margin notes, anecdotes, and other devices. But many instructors find these distracting, preferring to captivate their science and engineering students with the beauty of the calculus itself. Taalman and Kohn’s refreshing new textbook is designed to help instructors do just that.

Taalman and Kohn’s *Calculus* offers a streamlined, structured exposition of calculus that combines the clarity of classic textbooks with a modern perspective on concepts, skills, applications, and theory. Its sleek, uncluttered design eliminates sidebars, historical biographies, and asides to keep students focused on what’s most important—the foundational concepts of calculus that are so important to their future academic and professional careers.

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Many calculus textbooks look to engage students with margin notes, anecdotes, and other devices. But many instructors find these distracting, preferring to captivate their science and engineering students with the beauty of the calculus itself. Taalman and Kohn’s refreshing new textbook is designed to help instructors do just that.

Taalman and Kohn’s *Calculus* offers a streamlined, structured exposition of calculus that combines the clarity of classic textbooks with a modern perspective on concepts, skills, applications, and theory. Its sleek, uncluttered design eliminates sidebars, historical biographies, and asides to keep students focused on what’s most important—the foundational concepts of calculus that are so important to their future academic and professional careers.

**Maximize Teaching and Learning with WebAssign Premium**

Macmillan Learning and WebAssign have partnered to deliver WebAssign *Premium* – a comprehensive and flexible suite of resources for your calculus course. Combining the most widely used online homework platform with authoritative textbook content and Macmillan’s esteemed Calctools, WebAssign *Premium* extends and enhances the classroom experience for instructors and students. Preview course content and sample assignments at www.webassign.net/whfreeman.

Features

**Compact, Structured Exposition**

Taalman and Kohn provide compact instruction on the important concepts of calculus in a linear, straightforward, and predictable format. Each section begins with uncluttered exposition that introduces and explains the key concepts (definitions, short examples and figures, and key theorems with proofs). The section is followed by more complex examples that prepare students for the exercise sets.

**An Awareness of Students’ Learning and Study Habits**

The authors understand how students use a textbook and have crafted their book to accommodate students’ learning styles. Students who want to read for understanding before attempting the exercises will appreciate the short, clear explanations. Students who want to tackle exercises first can look back to calculation-based examples and compact exposition for guidance. For these students, Concept and Proof exercises test comprehension of the definitions and theory.

**Easy Proofs**

Every theorem is discussed as a development that requires justification. The text always makes clear what is proved and what is left to the exercises or to future mathematics courses. Every set of exercises includes a range of accessible proofs, some based on the reading and others focusing on special cases that illustrate basic concepts.

**Categorized Exercises**

Exercises reflect concepts and skills introduced in the section examples; but also test student understanding of the development of the material and the reading itself and. Each exercise set includes the following categories of problems: *Thinking Back, Concepts, Skills, Applications, Proofs, *and *Thinking Forward.* Each chapter concludes with a set of *Chapter Review* exercises.

New to This Edition

**
Calculus Combo**

First Edition| ©2014

Laura Taalman; Peter Kohn

# Digital Options

**Calculus Combo**

First Edition| 2014

Laura Taalman; Peter Kohn

## Table of Contents

**Part I. Differential Calculus**

**0. Functions and Precalculus**0.1 Functions and Graphs

0.2 Operations, Transformations, and Inverses

0.3 Algebraic Functions

0.4 Exponential and Trigonometric Functions

0.5 Logic and Mathematical Thinking*

*Chapter Review, Self-Test, and Capstones*

**1. Limits**

1.1 An Intuitive Introduction to Limits

1.2 Formal Definition of Limit

1.3 Delta-Epsilon Proofs*

1.4 Continuity and Its Consequences

1.5 Limit Rules and Calculating Basic Limits

1.6 Infinite Limits and Indeterminate Forms*Chapter Review, Self-Test, and Capstones*

**2. Derivatives**

2.1 An Intuitive Introduction to Derivatives

2.2 Formal Definition of the Derivative

2.3 Rules for Calculating Basic Derivatives

2.4 The Chain Rule and Implicit Differentiation

2.5 Derivatives of Exponential and Logarithmic Functions

2.6 Derivatives of Trigonometric and Hyperbolic Functions**Chapter Review, Self-Test, and Capstones*

**3. Applications of the Derivative**

3.1 The Mean Value Theorem

3.2 The First Derivative and Curve Sketching

3.3 The Second Derivative and Curve Sketching

3.4 Optimization

3.5 Related Rates

3.6 L’Hopital’s Rule*Chapter Review, Self-Test, and Capstones*

**Part II. Integral Calculus**

**4. Definite Integrals**

4.1 Addition and Accumulation

4.2 Riemann Sums

4.3 Definite Integrals

4.4 Indefinite Integrals

4.5 The Fundamental Theorem of Calculus

4.6 Areas and Average Values

4.7 Functions Defined by Integrals*Chapter Review, Self-Test, and Capstones*

**5. Techniques of Integration**

5.1 Integration by Substitution

5.2 Integration by Parts

5.3 Partial Fractions and Other Algebraic Techniques

5.4 Trigonometric Integrals

5.5 Trigonometric Substitution

5.6 Improper Integrals

5.7 Numerical Integration**Chapter Review, Self-Test, and Capstones*

**6. Applications of Integration**

6.1 Volumes By Slicing

6.2 Volumes By Shells

6.3 Arc Length and Surface Area

6.4 Real-World Applications of Integration

6.5 Differential Equations**Chapter Review, Self-Test, and Capstones*

**Part III. Sequences and Series**

**7. Sequences and Series**

7.1 Sequences

7.2 Limits of Sequence

7.3 Series

7.4 Introduction to Convergence Tests

7.5 Comparison Tests

7.6 The Ratio and Root Tests

7.7 Alternating Series*Chapter Review, Self-Test, and Capstones*

**8. Power Series**

8.1 Power Series

8.2 Maclaurin Series and Taylor Series

8.3 Convergence of Power Series

8.4 Differentiating and Integrating Power Series*Chapter Review, Self-Test, and Capstones*

**Part IV. Vector Calculus**

**9. Parametric Equations, Polar Coordinates, and Conic Sections**

9.1 Parametric Equations

9.2 Polar Coordinates

9.3 Graphing Polar Equations

9.4 Computing Arc Length and Area with Polar Functions

9.5 Conic Sections**Chapter Review, Self-Test, and Capstones*

**10. Vectors**

10.1 Cartesian Coordinates

10.2 Vectors

10.3 Dot Product

10.4 Cross Product

10.5 Lines in Three-Dimensional Space

10.6 Planes*Chapter Review, Self-Test, and Capstones*

**11. Vector Functions**

11.1 Vector-Valued Functions

11.2 The Calculus of Vector Functions

11.3 Unit Tangent and Unit Normal Vectors

11.4 Arc Length Parametrizations and Curvature

11.5 Motion*Chapter Review, Self-Test, and Capstones*

**Part V. Multivariable Calculus**

**12. Multivariable Functions**

12.1 Functions of Two and Three Variables

12.2 Open Sets, Closed Sets, Limits, and Continuity

12.3 Partial Derivatives

12.4 Directional Derivatives and Differentiability

12.5 The Chain Rule and the Gradient

12.6 Extreme Values

12.7 Lagrange Multipliers*Chapter Review, Self-Test, and Capstones*

**13. Double and Triple Integrals**

13.1 Double Integrals over Rectangular Regions

13.2 Double Integrals over General Regions

13.3 Double Integrals in Polar Coordinates

13.4 Applications of Double Integrals

13.5 Triple Integrals

13.6 Integration with Cylindrical and Spherical Coordinates

13.7 Jacobians and Change of Variables*Chapter Review, Self-Test, and Capstones*

**14. Vector Analysis**

14.1 Vector Fields

14.2 Line Integrals

14.3 Surfaces and Surface Integrals

14.4 Green’s Theorem

14.5 Stokes’ Theorem

14.6 The Divergence Theorem*Chapter Review, Self-Test, and Capstones*

## Authors

### Laura Taalman

**Laura Taalman**and

**Peter Kohn**are professors of mathematics at James Madison University, where they have taught calculus for a combined total of over 30 years.

**Laura Taalman**received her undergraduate degree from the University of Chicago

and master’s and Ph.D. degrees in mathematics from Duke University. Her research includes singular algebraic geometry, knot theory, and the mathematics of games and puzzles. She is a recipient of both the Alder Award and the Trevor Evans award from the Mathematical Association of America, and the author of five books on Sudoku and the mathematics of Sudoku. In her spare time, she enjoys being a geek.

**Peter Kohn**received his undergraduate degree from Antioch College, a master’s

degree from San Francisco State University, and a Ph.D. in mathematics from the University of Texas at Austin. His main areas of research are low-dimensional topology and knot theory. He has been a national judge for MathCounts since 2001. In his spare time, he enjoys hiking and riding his bicycle in the beautiful Shenandoah Valley.

### Peter Kohn

**Laura Taalman**and

**Peter Kohn**are professors of mathematics at James Madison University, where they have taught calculus for a combined total of over 30 years.

**Laura Taalman**received her undergraduate degree from the University of Chicago

and master’s and Ph.D. degrees in mathematics from Duke University. Her research includes singular algebraic geometry, knot theory, and the mathematics of games and puzzles. She is a recipient of both the Alder Award and the Trevor Evans award from the Mathematical Association of America, and the author of five books on Sudoku and the mathematics of Sudoku. In her spare time, she enjoys being a geek.

**Peter Kohn**received his undergraduate degree from Antioch College, a master’s

degree from San Francisco State University, and a Ph.D. in mathematics from the University of Texas at Austin. His main areas of research are low-dimensional topology and knot theory. He has been a national judge for MathCounts since 2001. In his spare time, he enjoys hiking and riding his bicycle in the beautiful Shenandoah Valley.

**Calculus Combo**

First Edition| 2014

Laura Taalman; Peter Kohn

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