## Description

Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher’s voice beyond the classroom. That voice—evident in the narrative, the figures, and the questions interspersed in the narrative—is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers’ geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope. This book covers chapters single variable topics (chapters 1—10) of **Calculus for Scientists and Engineers: Early Transcendentals**, which is an expanded version of **Calculus: Early Transcendentals** by the same authors.

## 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

This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course.

Package ISBN-13: 9780321956170

Includes this title packaged with:

- Maple Student Access Code Package

. Waterloo Maple, Inc. - MyLab Math -- Valuepack Access Card, 6th Edition

. . Pearson Education

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Package ISBN-13: 9780321929952

Includes this title packaged with:

- MyLab Math -- Valuepack Access Card, 6th Edition

. . Pearson Education - Student Solutions Manual for Calculus for Scientists and Engineers: Early Transcendentals, Single Variable

William L. Briggs, Lyle Cochran, Bernard Gillett

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