Calculus Early Transcendentals / Edition 1

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Overview

Clear and Concise. Varberg focuses on the most critical concepts.

This popular calculus text remains the shortest mainstream calculus book available — yet covers all relevant material needed by, and appropriate to, the study of calculus at this level. It's conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish.

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Product Details

  • ISBN-13: 9780131875333
  • Publisher: Pearson
  • Publication date: 5/29/2006
  • Series: Varberg Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 880
  • Sales rank: 860,176
  • Product dimensions: 8.60 (w) x 10.90 (h) x 1.40 (d)

Table of Contents

1

PRELIMINARIES

1.1

Real Numbers, Estimation, and Logic

1.2

Inequalities and Absolute Values

1.3

The Rectangular Coordinate System

1.4

Graphs of Equations

1.5

Functions and Their Graphs

1.6

Operations on Functions

1.7

Exponential and Logarithmic Functions

1.8

The Trigonometric Functions

1.9

The Inverse Trigonometric Functions

1.10

Chapter Review

2

LIMITS

2.1

Introduction to Limits

2.2

Rigorous Study of Limits

2.3

Limit Theorems

2.4

Limits at Infinity; Infinite Limits

2.5

Limits Involving Trigonometric Functions

2.6

Natural Exponential, Natural Log, and Hyperbolic Functions

2.7

Continuity of Functions

2.8

Chapter Review

3

THE DERIVATIVE

3.1

Two Problems with One Theme

3.2

The Derivative

3.3

Rules for Finding Derivatives

3.4

Derivatives of Trigonometric Functions

3.5

The Chain Rule

3.6

Higher-Order Derivatives

3.7

Implicit Differentiation

3.8

Related Rates

3.9

Derivatives of Exponential and Logarithmic Functions

3.10

Derivatives of Hyperbolic and Inverse Trigonometric Functions

3.11

Differentials and Approximations

3.12

Chapter Review

4

APPLICATIONS OF THE DERIVATIVE

4.1

Maxima and Minima

4.2

Monotonicity and Concavity

4.3

Local Extrema and Extrema on Open Intervals

4.4

Practical Problems

4.5

Graphing Functions Using Calculus

4.6

The Mean Value Theorem for Derivatives

4.7

Solving Equations Numerically

4.8

Antiderivatives

4.9

Introduction to Differential Equations

4.10

Exponential Growth and Decay

4.11

Chapter Review

5

THE DEFINITE INTEGRAL

5.1

Introduction to Area

5.2

The Definite Integral

5.3

The 1st Fundamental Theorem of Calculus

5.4

The 2nd Fundamental Theorem of Calculus

and the Method of Substitution

5.5

The Mean Value Theorem for Integrals & the Use of Symmetry

5.6

Numerical Integration

5.7

Chapter Review

6

APPLICATIONS OF THE INTEGRAL

6.1

The Area of a Plane Region

6.2

Volumes of Solids: Slabs, Disks, Washers

6.3

Volumes of Solids of Revolution: Shells

6.4

Length of a Plane Curve

6.5

Work and Fluid Pressure

6.6

Moments and Center of Mass

6.8

Probability and Random Variables

6.8

Chapter Review

7

TECHNIQUES OF INTEGRATION &

DIFFERENTIAL EQUATIONS

7.1

Basic Integration Rules

7.2

Integration by Parts

7.3

Some Trigonometric Integrals

7.4

Rationalizing Substitutions

7.5

Integration of Rational Functions Using Partial Fractions

7.6

Strategies for Integration

7.7

First-Order Linear Differential Equations

7.8

Approximations for Differential Equations

7.9

Chapter Review

8

INDETERMINATE FORMS &

IMPROPER INTEGRALS

8.1

Indeterminate Forms of Type 0/0

8.2

Other Indeterminate Forms

8.3

Improper Integrals: Infinite Limits of Integration

8.4

Improper Integrals: Infinite Integrands

8.5

Chapter Review

9

INFINITE SERIES

9.1

Infinite Sequences

9.2

Infinite Series

9.3

Positive Series: The Integral Test

9.4

Positive Series: Other Tests

9.5

Alternating Series, Absolute Convergence,

and Conditional Convergence

9.6

Power Series

9.7

Operations on Power Series

9.8

Taylor and Maclaurin Series

9.9

The Taylor Approximation to a Function

9.10

Chapter Review

10

CONICS AND POLAR COORDINATES

10.1

The Parabola

10.2

Ellipses and Hyperbolas

10.3

Translation and Rotation of Axes

10.4

Parametric Representation of Curves in the Plane

10.5

The Polar Coordinate System

10.6

Graphs of Polar Equations

10.7

Calculus in Polar Coordinates

10.8

Chapter Review

11

GEOMETRY IN SPACE & VECTORS

11.1

Cartesian Coordinates in Three-Space

11.2

Vectors

11.3

The Dot Product

11.4

The Cross Product

11.5

Vector Valued Functions & Curvilinear Motion

11.6

Lines and Tangent Lines in Three-Space

11.7

Curvature and Components of Acceleration

11.8

Surfaces in Three Space

11.9

Cylindrical and Spherical Coordinates

11.10

Chapter Review

12

DERIVATIVES FOR FUNCTIONS OF

TWO OR MORE VARIABLES

12.1

Functions of Two or More Variables

12.2

Partial Derivatives

12.3

Limits and Continuity

12.4

Differentiability

12.5

Directional Derivatives and Gradients

12.6

The Chain Rule

12.7

Tangent Planes and Approximations

12.8

Maxima and Minima

12.9

The Method of Lagrange Multipliers

12.10

Chapter Review

13

MULTIPLE INTEGRATION

13.1

Double Integrals over Rectangles

13.2

Iterated Integrals

13.3

Double Integrals over Nonrectangular Regions

13.4

Double Integrals in Polar Coordinates

13.5

Applications of Double Integrals

13.6

Surface Area

13.7

Triple Integrals (Cartesian Coordinates)

13.8

Triple Integrals (Cyl & Sph Coordinates)

13.9

Change of Variables in Multiple Integrals

13.10

Chapter Review

14

VECTOR CALCULUS

14.1

Vector Fields

14.2

Line Integrals

14.3

Independence of Path

14.4

Green's Theorem in the Plane

14.5

Surface Integrals

14.6

Gauss's Divergence Theorem

14.7

Stokes's Theorem

14.8

Chapter Review

15

DIFFERENTIAL EQUATIONS

15.1

Linear Homogeneous Equations

15.2

Nonhomogeneous Equations

15.3

Applications of Second-Order Equations

15.4

Chapter Review

APPENDIX

A.1

Mathematical Induction

A.2

Proofs of Several Theorems

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