Single Variable Calculus, Books a la Carte Edition

by Briggs, Bill; Cochran, Lyle; Gillett, Bernard; Schulz, Eric

• ISBN13: 9780321694218
• ISBN10: 032169421X
• Edition: 1st
• Format: Loose-leaf
• Copyright: 2010-03-09
• Publisher: Pearson

Summary

This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books agrave; la Carte also offer a great valuethis format costs significantly less than a new textbook. Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacherrs"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 readersrs" 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.

Table of Contents

Chapter 1: Functions

1.1 Review of Functions

1.2 Representing Functions

1.3 Trigonometric Functions and Their Inverses

 

Chapter 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

 

Chapter 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 Inverse Trigonometric Functions

3.9 Related Rates

 

Chapter 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 Antiderivatives

 

Chapter 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

 

Chapter 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 Physical Applications

6.7 Logarithmic and Exponential Functions Revisited

6.8 Exponential Models

 

Chapter 7: Logarithmic and Exponential Functions

7.1 A Short Review

7.2 Inverse Functions

7.3 The Natural Logarithm

7.4 The Exponential Function

7.5 Exponential Models

7.6 Inverse Trigonometric Functions

7.7 L’Hôpital’s Rule Revisited and Growth Rates of Functions

 

Chapter 8: Integration Techniques

8.1 Integration by Parts

8.2 Trigonometric Integrals

8.3 Trigonometric Substitutions

8.4 Partial Fractions

8.5 Other Integration Strategies

8.6 Numerical Integration

8.7 Improper Integrals

8.8 Introduction to Differential Equations

 

Chapter 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 and Comparison Tests

9.6 Alternating Series

Review

 

Chapter 10: Power Series

10.1 Approximating Functions with Polynomials

10.2 Power Series

10.3 Taylor Series

10.4 Working with Taylor Series

 

Chapter 11: Parametric and Polar Curves

11.1 Parametric Equations

11.2 Polar Coordinates

11.3 Calculus in Polar Coordinates

11.4 Conic Sections

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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