Calculus of A Single Variable / Edition 7

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Overview

Ideal for the single-variable, one-, or two-semester calculus course, Calculus of a Single Variable, 8/e, contains the first 9 chapters of Calculus, 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-semester Calculus I with Precalculus text. 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 allcalculus 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.
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Product Details

  • ISBN-13: 9780618149162
  • Publisher: Cengage Learning
  • Publication date: 7/13/2001
  • Edition description: Older Edition
  • Edition number: 7
  • Pages: 880
  • Product dimensions: 8.70 (w) x 10.70 (h) x 1.30 (d)

Meet the Author

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.

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Table of Contents

Contents

Note: Each chapter contains Review Exercises and Problem Solving.

  • P. Preparation for Calculus
    P.1 Graphs and Models
    P.2 Linear Models and Rates of Change
    P.3 Functions and Their Graphs
    P.4 Fitting Models to Data
    • 1. Limits and Their Properties
      1.1 A Preview of Calculus
      1.2 Finding Limits Graphically and Numerically
      1.3 Evaluating Limits Analytically
      1.4 Continuity and One-Sided Limits
      1.5 Infinite Limits
      Section Project: Graphs and Limits of Trigonometric Functions
      • 2. Differentiation
        2.1 The Derivative and the Tangent Line Problem
        2.2 Basic Differentiation Rules and Rates of Change
        2.3 Product and Quotient Rules and Higher-Order Derivatives
        2.4 The Chain Rule
        2.5 Implicit Differentiation
        Section Project: Optical Illusions
        2.6 Related Rates
        • 3. Applications of Differentiation
          3.1 Extrema on an Interval
          3.2 Rolle's Theorem and the Mean Value Theorem
          3.3 Increasing and Decreasing Functions and the First Derivative Test
          Section Project: Rainbows
          3.4 Concavity and the Second Derivative Test
          3.5 Limits at Infinity
          3.6 A Summary of Curve Sketching
          3.7 Optimization Problems
          Section Project: Connecticut River
          3.8 Newton's Method
          3.9 Differentials
          • 4. Integration
            4.1 Antiderivatives and Indefinite Integration
            4.2 Area
            4.3 Riemann Sums and Definite Integrals
            4.4 The Fundamental Theorem of Calculus
            Section Project: Demonstrating the Fundamental Theorem
            4.5 Integration by Substitution
            4.6 Numerical Integration
            • 5. Logarithmic, Exponential, and Other Transcendental Functions
              5.1 The Natural Logarithmic Function: Differentiation
              5.2 The Natural Logarithmic Function: Integration
              5.3 Inverse Functions
              5.4 Exponential Functions: Differentiation and Integration
              5.5 Bases Other Than e and Applications
              Section Project: Using Graphing Utilities to Estimate Slope
              5.6 Inverse Trigonometric Functions: Differentiation
              5.7 Inverse Trigonometric Functions: Integration
              5.8 Hyperbolic Functions
              Section Project: St. Louis Arch
              • 6. Differential Equations
                6.1 Slope Fields and Euler's Method
                6.2 Differential Equations: Growth and Decay
                6.3 Separation of Variables and the Logistic Equation
                6.4 First-Order Linear Differential Equations
                Section Project: Weight Loss
                • 7. Applications of Integration
                  7.1 Area of a Region Between Two Curves
                  7.2 Volume: The Disk Method
                  7.3 Volume: The Shell Method
                  Section Project: Saturn
                  7.4 Arc Length and Surfaces of Revolution
                  7.5 Work
                  Section Project: Tidal Energy
                  7.6 Moments, Centers of Mass, and Centroids
                  7.7 Fluid Pressure and Fluid Force
                  • 8. Integration Techniques, L'Hôpital's Rule, and Improper Integrals
                    8.1 Basic Integration Rules
                    8.2 Integration by Parts
                    8.3 Trigonometric Integrals
                    Section Project: Power Lines
                    8.4 Trigonometric Substitution
                    8.5 Partial Fractions
                    8.6 Integration by Tables and Other Integration Techniques
                    8.7 Indeterminate Forms and L'Hôpital's Rule
                    8.8 Improper Integrals
                    • 9. Infinite Series
                      9.1 Sequences
                      9.2 Series and Convergence
                      Section Project: Cantor's Disappearing Table
                      9.3 The Integral Test and p-Series
                      Section Project: The Harmonic Series
                      9.4 Comparisons of Series
                      Section Project: Solera Method
                      9.5 Alternating Series
                      9.6 The Ratio and Root Tests
                      9.7 Taylor Polynomials and Approximations
                      9.8 Power Series
                      9.9 Representation of Functions by Power Series
                      9.10 Taylor and Maclaurin Series
                      • 10. Conics, Parametric Equations, and Polar Coordinates
                        10.1 Conics and Calculus
                        10.2 Plane Curves and Parametric Equations
                        Section Project: Cycloids
                        10.3 Parametric Equations and Calculus
                        10.4 Polar Coordinates and Polar Graphs
                        Section Project: Anamorphic Art
                        10.5 Area and Arc Length in Polar Coordinates
                        10.6 Polar Equations of Conics and Kepler's Laws
                        • Appendices
                          A. Proofs of Selected Theorems
                          B. Integration Tables
                          C. Additional Topics in Differential Equations (Web and CD-ROM only)
                          D. Precalculus Review (Web and CD-ROM only)
                          E. Rotation and the General Second-Degree Equation (Web and CD-ROM only)
                          F. Complex Numbers (Web and CD-ROM only)
                          G. Business and Economic Applications (Web only)
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