## Description

**For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors.**

**Briggs/Cochran** is the most successful new calculus series published in the last two decades. The authors’ decades of teaching experience resulted in a text that reflects how students generally use a textbook—i.e., they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows.

To further support student learning, the MyMathLab course features an eBook with 700 Interactive Figures that can be manipulated to shed light on key concepts. In addition, the *Instructor’s Resource Guide and Test Bank* features quizzes, test items, lecture support, guided projects, and more.

*This book is a special version of*Calculus: Early Transcendentals

*by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections. See the “Features” section for more details.*

## Table of Contents

**1. Functions **

1.1 Review of functions

1.2 Representing functions

1.3 Inverse, exponential, and logarithmic functions

1.4 Trigonometric functions and their inverses

**2. Limits**

2.1 The idea of limits

2.2 Definitions of limits

2.3 Techniques for computing limits

2.4 Infinite limits

2.5 Limits at infinity

2.6 Continuity

2.7 Precise definitions of limits

**3. Derivatives**

3.1 Introducing the derivative

3.2 Rules of differentiation

3.3 The product and quotient rules

3.4 Derivatives of trigonometric functions

3.5 Derivatives as rates of change

3.6 The Chain Rule

3.7 Implicit differentiation

3.8 Derivatives of logarithmic and exponential functions

3.9 Derivatives of inverse trigonometric functions

3.10 Related rates

**4. Applications of the Derivative**

4.1 Maxima and minima

4.2 What derivatives tell us

4.3 Graphing functions

4.4 Optimization problems

4.5 Linear approximation and differentials

4.6 Mean Value Theorem

4.7 L’Hôpital’s Rule

4.8 Newton’s Method

4.9 Antiderivatives

**5. Integration**

5.1 Approximating areas under curves

5.2 Definite integrals

5.3 Fundamental Theorem of Calculus

5.4 Working with integrals

5.5 Substitution rule

**6. Applications of Integration**

6.1 Velocity and net change

6.2 Regions between curves

6.3 Volume by slicing

6.4 Volume by shells

6.5 Length of curves

6.6 Surface area

6.7 Physical applications

6.8 Logarithmic and exponential functions revisited

6.9 Exponential models

6.10 Hyperbolic functions

**7. Integration Techniques**

7.1 Integration Strategies

7.2 Integration by parts

7.3 Trigonometric integrals

7.4 Trigonometric substitutions

7.5 Partial fractions

7.6 Other integration strategies

7.7 Numerical integration

7.8 Improper integrals

**8. Differential Equations **

8.1 Basic ideas

8.2 Direction fields and Euler’s method

8.3 Separable differential equations

8.4 Special first-order differential equations

8.5 Modeling with differential equations

**9. Sequences and Infinite Series**

9.1 An overview

9.2 Sequences

9.3 Infinite series

9.4 The Divergence and Integral Tests

9.5 The Ratio, Root, and Comparison Tests

9.6 Alternating series

**10. Power Series**

10.1 Approximating functions with polynomials

10.2 Properties of Power series

10.3 Taylor series

10.4 Working with Taylor series

**11. Parametric and Polar Curves **

11.1 Parametric equations

11.2 Polar coordinates

11.3 Calculus in polar coordinates

11.4 Conic sections

**12. Vectors and Vector-Valued Functions**

12.1 Vectors in the plane

12.2 Vectors in three dimensions

12.3 Dot products

12.4 Cross products

12.5 Lines and curves in space

12.6 Calculus of vector-valued functions

12.7 Motion in space

12.8 Length of curves

12.9 Curvature and normal vectors

**13. Functions of Several Variables**

13.1 Planes and surfaces

13.2 Graphs and level curves

13.3 Limits and continuity

13.4 Partial derivatives

13.5 The Chain Rule

13.6 Directional derivatives and the gradient

13.7 Tangent planes and linear approximation

13.8 Maximum/minimum problems

13.9 Lagrange multipliers

**14. Multiple Integration**

14.1 Double integrals over rectangular regions

14.2 Double integrals over general regions

14.3 Double integrals in polar coordinates

14.4 Triple integrals

14.5 Triple integrals in cylindrical and spherical coordinates

14.6 Integrals for mass calculations

14.7 Change of variables in multiple integrals

**15. Vector Calculus**

15.1 Vector fields

15.2 Line integrals

15.3 Conservative vector fields

15.4 Green’s theorem

15.5 Divergence and curl

15.6 Surface integrals

15.6 Stokes’ theorem

15.8 Divergence theorem

* *

Appendix A. Algebra Review

Appendix B. Proofs of Selected Theorems## Purchase Info ?

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Calculus for Scientists and Engineers: Early Transcendentals, CourseSmart eTextbook

Format: Safari Book

$108.99 | ISBN-13: 978-0-321-78547-3