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Once again keeping a keen ear to the needs of the evolving calculus community, Stewart created this text at the suggestion and with the collaboration of professors in the mathematics department at Texas A&M University. With an early introduction to vectors and vector functions, the approach is ideal for engineering students who use vectors early in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and… More integrals of vector functions are interwoven throughout the subsequent chapters. As with the other texts in his Calculus series, in Early Vectors Stewart makes us of heuristic examples to reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject. This heuristic or discovery approach in the examples give students an intuitive feeling for analysis.Less

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Book details

List price: $269.95 Copyright year: 1999 Publisher: Brooks/Cole Publication date: 5/9/2003 Binding: Hardcover Pages: 1120 Size: 8.50" wide x 10.00" long x 2.00" tall Weight: 5.082 Language: English

AuthorTable of Contents

Review and Preview

Functions and Their Graphs

Types of Functions

Shifting and Scaling

Graphing Calculators and Computers

Principles of Problem Solving

A Preview of Calculus

Introduction to Vectors and Vector Functions

Vectors

The Dot Product

Vector Functions

Review

Limits and Rates of Change

The Tangent and Velocity Problems

The Limit of a Function

Calculating Limits Using the Limit Law

The Precise Definition of a Limit

Continuity

Limits at Infinity

Horizontal Asymptotes

Tangents, Velocities, and Other Rates of Change

Review

Derivatives

Derivatives

Differentiation Formulas

Rates of Change in the Natural and Social Sciences

Derivatives of Trigonometric Functions

The Chain Rule

Implicit Differentiation

Derivatives of Vector Functions

Higher Derivatives

Slopes and Tangents of Parametric Curves

Related Rates

Differentials; Linear and Quadratic Approximations

Newton's Method

Review

Problems Plus

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Exponential Functions and Their Derivatives

Inverse Functions

Logarithmic Functions

Derivatives of Logarithmic Functions

Exponential Growth and Decay

Inverse Trigonometric Functions

Hyperbolic Functions

Indeterminate Forms and L'Hospital's Rule

Review

Applications Plus

Applications of Differentiation

What does f Say about f?

Maximum and Minimum Values

Derivatives and the Shapes of Curves

Graphing with Calculus and Calculators

Applied Maximum and Minimum Problems

Applications to Economics

Antiderivatives

Review

Problems Plus

Integrals

Sigma Notation

Area

The Definite Integral

The Fundamental Theorem of Calculus

The Substitution Rule

The Logarithm Defined as an Integral

Review

Applications Plus

Applications of Integration

Areas between Curves

Volume

Volumes by Cylindrical Shells

Work

Average Value of a Function

Review

Problems Plus

Techniques of Integration

Integration by Parts

Trigonometric Integrals

Trigonometric Substitution

Integration of Rational Functions by Partial Fractions

Rationalizing Substitutions

Strategy for Integration

Using Tables of Integrals and Computer Algebra Systems

Approximate Integration

Improper Integrals

Review

Applications Plus

Further Applications of Integration

Differential Equations

First-Order Linear Equations

Arc Length

Area of Surface of Revolution

Moments and Centers of Mass

Hydrostatic Pressure and Force

Applications to Economics and Biology

Review

Problems Plus

Infinite Sequences and Series

Sequences

Series

The Integral Test and Comparison Tests

Other Convergence Tests

Power Series

Representation of Functions as Power Series

Taylor and Maclaurin Series

The Binomial Series

Writing Project: How Newton Discovered the Binomial Series

Applications of Taylor Polynomials

Review

Applications Plus

Three-Dimensional Analytic Geometry and Vectors

Three-Dimensional Coordinate Systems

Vectors and the Dot Product in Three Dimension

The Cross Product

Equations of Lines and Planes

Quadric Surfaces

Vector Functions and Space Curves

Arc Length and Curvature

Motion in Space

Review

Applications Plus

Partial Derivatives

Functions of Several Variables

Limits and Continuity

Partial Derivatives

Tangent Planes and Differentials

The Chain Rule

Directional Derivatives and the Gradient Vector

Maximum and Minimum Values

Lagrange Multipliers

Review

Problems Plus

Multiple Integrals

Double Integrals over Rectangles

Iterated Integrals

Double Integrals over General Regions

Polar Coordinates

Applications of Double Integrals

Surface Area

Triple Integrals

Cylindrical and Spherical Coordinates

Triple Integrals in Cylindrical and Spherical Coordinates

Change of Variables in Multiple Integrals

Review

Applications Plus

Vector Calculus

Vector Fields

Line Integrals

The Fundamental Theorem for Line Integrals

Green's Theorem

Curl and Divergence

Parametric Surfaces and their Areas

Surface Integrals

Stoke's Theorem

The Divergence Theorem

Summary

Review

Problems Plus

Second-Order Differential Equations

Second-Order Linear Equations

Nonhomogeneous Linear Equations

Applications of Second-Order Differential Equations

Using Series to Solve Differential Equations

Review

Problems Plus

Numbers, Inequalities, and Absolute Values

Coordinate Geometry and Lines

Graphs of Second-Degree Equations

Trigonometry

Mathematical Induction

Proofs of Theorems

Lies My Calculator and Computer Told Me

Complex Numbers

Conic Sections

Conic Sections in Polar Coordinates

Answers to Odd-Numbered Exercises

Index

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