9780134766850

Calculus, Single Variable: Early Transcendentals

Bernard Gillett, Eric Schulz, Lyle Cochran, William L. Briggs

3rd Edition

For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. T he most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs' Calculus Series retains its hallmark features while introducing important advances and refinements. Bri

2.1

The Idea of Limits

Exercises

p.61

2.2

Definitions of Limits

Exercises

p.67

2.3

Techniques for Computing Limits

Exercises

p.79

2.4

Infinite Limits

Exercises

p.88

2.5

Limits at Infinity

Exercises

p.100

2.6

Continuity

Exercises

p.112

2.7

Precise Definitions of Limits

Exercises

p.124

Review Exercises

p.128

3.1

Introducting the Derivative

Exercises

p.137

3.2

Working with Derivatives

Exercises

p.148

3.3

Rules of Differentiation

Exercises

p.159

3.4

The Product and Quotient Rules

Exercises

p.168

3.5

Derivatives of Trigonmetric Functions

Exercises

p.175

3.6

Derivatives as Rates of Change

Exercises

p.186

3.7

The Chain Rule

Exercises

p.196

3.8

Implicit Differentiation

Exercises

p.205

3.9

Derivatives of Logarithmic and Exponential Functions

Exercises

p.215

3.10

Derivatives of Inverse Trigonometric Functions

Exercises

p.225

3.11

Related Rates

Exercises

p.231

Review Exercises

p.236

4.1

Maxima and Minima

Exercises

p.247

4.2

Mean Value Theorem

Exercises

p.254

4.3

What Derivatives Tell Us

Exercises

p.267

4.4

Graphing Functions

Exercises

p.277

4.5

Optimization Problems

Exercises

p.284

4.6

Linear Approximation of Differentials

Exercises

p.298

4.7

L'Hopital's Rule

Exercises

p.310

4.8

Newton's Methods

Exercises

p.318

4.9

Antiderivatives

Exercises

p.331

Review Exercises

p.334

8.1

Basic Approaches

Exercises

p.523

8.2

Integration by Parts

Exercises

p.529

8.3

Trignometric Integrals

Exercises

p.536

8.4

Trignometric Substitutions

Exercises

p.543

8.5

Partial Fractions

Exercises

p.554

8.6

Integration Strategies

Exercises

p.560

8.7

Other Methods of Integration

Exercises

p.565

8.8

Numerical Integration

Exercises

p.578

8.9

Improper Integrals

Exercises

p.590

Review Exercises

p.593

10.1

An Overview

Exercises

p.647

10.2

Sequences

Exercises

p.659

10.3

Infinite Series

Exercises

p.668

10.4

The Divergence and Integral Tests

Exercises

p.680

10.5

Comparison Tests

Exercises

p.687

10.6

Alternating Series

Exercises

p.694

10.7

The Ratio and Root Tests

Exercises

p.699

10.8

Choosing a Convergence Test

Exercises

p.703

Review Exercises

p.704

15.1

Graphs and Level Curves

Exercises

p.927

15.2

Limits and Continuity

Exercises

p.937

15.3

Partial Derivatives

Exercises

p.948

15.4

The Chain Rule

Exercises

p.957

15.5

Directional Derivatives and the Gradient

Exercises

p.970

15.6

Tangent Planes and Linear Approximation

Exercises

p.980

15.7

Maximum/Minimum Problems

Exercises

p.993

15.8

Lagrange Multipliers

Exercises

p.1002

Review Exercises

p.1005

16.1

Double Integrals over Rectangular Regions

Exercises

p.1015

16.2

Double Integrals over General Regions

Exercises

p.1024

16.3

Double Integrals in Polar Coordinates

Exercises

p.1033

16.4

Triple Integrals

Exercises

p.1043

16.5

Triple Integrals in Cyclindrical and Spherical Coordinates

Exercises

p.1059

16.6

Integrals for Mass Calculations

Exercises

p.1070

16.7

Change of Variables in Multiple Integrals

Exercises

p.1082

Review Exercises

p.1084

17.1

Vector Fields

Exercises

p.1096

17.2

Line Integrals

Exercises

p.1110

17.3

Conservative Vector Fields

Exercises

p.1121

17.4

Green's Theorem

Exercises

p.1133

17.5

Divergence and Curl

Exercises

p.1143

17.6

Surface Integrals

Exercises

p.1159

17.7

Stoke's Theorem

Exercises

p.1169

17.8

Divergence Theorem

Exercises

p.1179

Review Exercises

p.1182