Calculus Of A Single Variable

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618503032
• ISBN10: 061850303X
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-01-19
• Publisher: Brooks Cole

Summary

Ideal for the single-variable, one-, or two-semester calculus course,Calculus of a Single Variable,8/e, contains the first 9 chapters ofCalculus,8/e. The text continues to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer a two-semesterCalculus I with Precalculustext. Every edition of the series has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best. The explanations, theorems, and definitions have been thoroughly and critically reviewed. Additionally, the exercise sets have been carefully and extensively examined to ensure they cover all calculus topics appropriately. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank. The Eduspace online resources have been integrated into a comprehensive learning system that combines numerous dynamic calculus resources with online homework and testing materials. Eduspace with eSolutions combines all the features of Eduspace with an electronic version of the textbook exercises and the complete solutions to the odd-numbered text exercises, providing students with a convenient and comprehensive way to do homework and view the course materials. The Integrated Learning System addresses the changing needs of today's instructors and students. Recognizing that the calculus course is presented in a variety of teaching and learning environments, the program resources are available in print, CD-ROM, and online formats. SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.

Table of Contents

Preparation for Calculus

Graphs and Models

Linear Models and Rates of Change

Functions and Their Graphs

Fitting Models to Data

Limits and Their Properties

A Preview of Calculus

Finding Limits Graphically and Numerically

Evaluating Limits Analytically

Continuity and One-Sided Limits

Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions

Differentiation

The Derivative and the Tangent Line Problem

Basic Differentiation Rules and Rates of Change

Product and Quotient Rules and Higher-Order Derivatives

The Chain Rule

Implicit Differentiation Section Project: Optical Illusions

Related Rates

Applications of Differentiation

Extrema on an Interval

Rolle\'s Theorem and the Mean Value Theorem

Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows

Concavity and the Second Derivative Test

Limits at Infinity

A Summary of Curve Sketching

Optimization Problems Section Project: Connecticut River

Newton\'s Method

Differentials

Integration

Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals

The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem

Integration by Substitution

Numerical Integration

Logarithmic, Exponential, and Other Transcendental Functions

The Natural Logarithmic Function: Differentiation

The Natural Logarithmic Function: Integration

Inverse Functions

Exponential Functions: Differentiation and Integration

Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope

Inverse Trigonometric Functions: Differentiation

Inverse Trigonometric Functions: Integration

Hyperbolic Functions Section Project: St. Louis Arch

Differential Equations

Slope Fields and Euler\'s Method

Differential Equations: Growth and Decay

Separation of Variables and the Logistic Equation

First-Order Linear Differential Equations Section Project: Weight Loss

Applications of Integration

Area of a Region Between Two Curves

Volume: The Disk Method

Volume: The Shell Method Section Project: Saturn

Arc Length and Surfaces of Revolution

Work Section Project: Tidal Energy

Moments, Centers of Mass, and Centroids

Fluid Pressure and Fluid Force

Integration Techniques, L\'H?pital\'s Rule, and Improper Integrals

Basic Integration Rules

Integration by Parts

Trigonometric Integrals Section Project: Power Lines

Trigonometric Substitution

Partial Fractions

Integration by Tables and Other Integration Techniques

Indeterminate Forms and L\'H?pital\'s Rule 8.8 Improper Integrals

Infinite Series

Sequences

Series and Convergence Section Project: Cantor\'s Disappearing Table

The Integral Test and p-Series Section Project: The Harmonic Series

C

Table of Contents provided by Publisher. All Rights Reserved.