Calculus Of A Single Variable

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  • Edition: 8th
  • Format: Hardcover
  • Copyright: 1/19/2005
  • Publisher: Brooks Cole
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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
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
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
Series and Convergence Section Project: Cantor\'s Disappearing Table
The Integral Test and p-Series Section Project: The Harmonic Series
Table of Contents provided by Publisher. All Rights Reserved.

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