Single Variable Calculus Concepts and Contexts (with CD)

by Stewart, James

• ISBN13: 9780534378622
• ISBN10: 0534378625
• Format: Hardcover
• Copyright: 2000-12-13
• Publisher: Brooks Cole

Summary

James Stewart's well-received SINGLE VARIABLE CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

Table of Contents

Functions And Models

Four Ways to Represent a Function

Mathematical Models

New Functions from Old Functions

Graphing Calculators and Computers

Exponential Functions

Inverse Functions and Logarithms

Parametric Curves

Review

Principles of Problem Solving

Limits And Derivatives

The Tangent and Velocity Problems

The Limit of a Function

Calculating Limits Using the Limit Laws

Continuity

Limits Involving Infinity

Tangents, Velocities, and Other Rates of Change

Derivatives

The Derivative as a Function

Linear Approximations

What does f' say about f?

Review

Focus on Problem Solving

Differentiation Rules

Derivatives of Polynomials and Exponential Functions

The Product and Quotient Rules

Rates of Change in the Natural and Social Sciences

Derivatives of Trigonometric Functions

The Chain Rule

Implicit Differentiation

Derivatives of Logarithmic Functions

Linear Approximations and Differentials

Review

Focus on Problem Solving

Applications Of Differentiation

Related Rates

Maximum and Minimum Values

Derivatives and the Shapes of Curves

Graphing with Calculus and Calculators

Indeterminate Forms and l'Hospital's Rule

Optimization Problems

Applications to Economics

Newton's Method

Antiderivatives

Review

Focus on Problem Solving

Integrals

Areas and Distances

The Definite Integral

Evaluating Definite Integrals

The Fundamental Theorem of Calculus

The Substitution Rule

Integration by Parts

Additional Techniques of Integration

Integration Using Tables and Computer Algebra Systems

Approximate Integration

Improper Integrals

Review

Focus on Problem Solving

Applications Of Integration

More about Areas

Volumes

Arc Length

Average Value of a Function

Applications to Physics and Engineering

Applications to Economics and Biology

Probability

Review

Focus on Problem Solving

Differential Equations

Modeling with Differential Equations

Direction Fields and Euler's Method

Separable Equations

Exponential Growth and Decay

The Logistic Equation

Predator-Prey Systems

Review

Focus on Problem Solving

Infinite Sequences And Series

Sequences

Series

The Integral and Comparison Tests; Estimating Sums

Other Convergence Tests

Power Series

Representation of Functions as Power Series

Taylor and Maclaurin Series

The Binomial Series

Applications of Taylor Polynomials

Using Series to Solve Differential Equations

Appendices

Intervals, Inequalities, And Absolute Values

Coordinate Geometry

Trigonometry

Precise Definitions Of Limits

A Few Proofs

Sigma Notation

Integration Of Rational Functions By Partial Fractions

Polar Coordinates

Complex Numbers

Answers To Odd-Numbered Exercises

Index

Table of Contents provided by Publisher. All Rights Reserved.