Calculus with Analytic Geometry / Edition 5

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This traditional text offers a balanced approach that combines the theoretical instruction of calculus with the best aspects of reform, including creative teaching and learning techniques such as the integration of technology, the use of real-life applications, and mathematical models. The Calculus with Analytic Geometry Alternate, 6/e, offers a late approach to trigonometry for those instructors who wish to introduce it later in their courses.

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Product Details

  • ISBN-13: 9780669353358
  • Publisher: Houghton Mifflin Harcourt
  • Publication date: 1/28/1994
  • Edition description: Older Edition
  • Edition number: 5
  • Pages: 1127

Meet the Author

Ron Larson received his PhD. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His Interactive Calculus (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and it was the first mainstream college textbook to be offered on the Internet.

Bob Hostetler received his PhD. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks.

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging,reading, chess, simulation baseball games, and travel.

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Table of Contents


Note: Each chapter concludes with Review Exercises. The chapter organization of this supplement is different from that of Calculus: Early Transcendental Functions; users should work by topic rather than by chapter. Correlation guidelines are available.

  • 1. The Cartesian Plane and Functions
    1.1 Real Numbers and the Real Line; 1.2 The Cartesian Plane; 1.3 Graphs of Equations; 1.4 Lines in the Plane; 1.5 Functions
    • 2. Limits and Their Properties
      2.1 An Introduction to Limits; 2.2 Techniques for Evaluating Limits; 2.3 Continuity; 2.4 Infinite Limits; 2.5 e-d Definition of Limits
      • 3. Differentiation
        3.1 The Derivative and the Tangent Line Problem; 3.2 Velocity, Acceleration, and Other Rates of Change; 3.3 Differentiation Rules for Powers, Constant Multiples, and Sums; 3.4 Differentiation Rules for Products and Quotients; 3.5 The Chain Rule; 3.6 Implicit Differentiation; 3.7 Related Rates
        • 4. Applications of Differentiation
          4.1 Extrema on an Interval; 4.2 Rolle's Theorem and the Mean Value Theorem; 4.3 Increasing and Decreasing Functions and the First Derivative Test; 4.4 Concavity and the Second Derivative Test; 4.5 Limits at Infinity; 4.6 A Summary of Curve Sketching; 4.7 Optimization Problems; 4.8 Newton's Method; 4.9 Differentials; 4.10 Business and Economics Applications
          • 5. Integration
            5.1 Antiderivatives and Indefinite Integration; 5.2 Area; 5.3 Riemann Sums and the Definite Integral; 5.4 The Fundamental Theorem of Calculus; 5.5 Integration by Substitution; 5.6 Numerical Integration
            • 6. Applications of Integration
              6.1 Area of a RegionBetween Two Curves; 6.2 Volume: The Disc Method; 6.3 Volume: The Shell Method; 6.4 Arc Length and Surfaces of Revolution; 6.5 Work; 6.6 Fluid Pressure and Fluid Force; 6.7 Moments, Centers of Mass, and Centroids
              • 7. Exponential and Logarithmic Functions
                7.1 Exponential Functions; 7.2 Differentiation and Integration of Exponential Functions; 7.3 Inverse Functions; 7.4 Logarithmic Functions; 7.5 Logarithmic Functions and Differentiation; 7.6 Logarithmic Functions and Integration; 7.7 Growth and Decay; 7.8 Indeterminate Forms and L'Hôpital's Rule
                • 8. Trigonometric Functions and Inverse Trigonometric Functions
                  8.1 Review of Trigonometric Functions; 8.2 Graphs and Limits of Trigonometric Functions; 8.3 Derivatives of Trigonometric Functions; 8.4 Integrals of Trigonometric Functions; 8.5 Inverse Trigonometric Functions and Differentiation; 8.6 Inverse Trigonometric Functions: Integration and Completing the Square; 8.7 Hyperbolic Functions
                  • 9. Integration Techniques and Improper Integrals
                    9.1 Basic Integration Formulas; 9.2 Integration by Parts; 9.3 Trigonometric Integrals; 9.4 Trigonometric Substitution; 9.5 Partial Fractions; 9.6 Integration by Tables and Other Integration Techniques; 9.7 Improper Integrals
                    • 10. Infinite Series
                      10.1 Sequences; 10.2 Series and Convergence; 10.3 The Integral Test and p-Series; 10.4 Comparisons of Series; 10.5 Alternating Series; 10.6 The Ratio and Root Tests; 10.7 Taylor Polynomials and Approximations; 10.8 Power Series; 10.9 Representation of Functions by Power Series; 10.10 Taylor and Maclaurin Series
                      • 11. Conic Sections
                        11.1 Parabolas; 11.2 Ellipses; 11.3 Hyperbolas; 11.4 Rotation and the General Second-Degree Equation
                        • 12. Plane Curves, Parametric Equations, and Polar Coordinates
                          12.1 Plane Curves and Parametric Equations; 12.2 Parametric Equations and Calculus; 12.3 Polar Coordinates and Polar Graphs; 12.4 Tangent Lines and Curve Sketching in Polar Coordinates; 12.5 Area and Arc Length in Polar Coordinates; 12.6 Polar Equations for Conics and Kepler's Laws
                          • 13. Vectors and Curves in the Plane
                            13.1 Vectors in the Plane; 13.2 The Dot Product of Two Vectors; 13.3 Vector-Valued Functions; 13.4 Velocity and Acceleration; 13.5 Tangent Vectors and Normal Vectors; 13.6 Arc Length and Curvature
                            • 14. Solid Analytic Geometry and Vectors in Space
                              14.1 Space Coordinates and Vectors in Space; 14.2 The Cross Product of Two Vectors in Space; 14.3 Lines and Planes in Space; 14.4 Surfaces in Space; 14.5 Curves and Vector-Valued Functions in Space; 14.6 Tangent Vectors, Normal Vectors, and Curvature in Space
                              • 15. Functions of Several Variables
                                15.1 Introduction to Functions of Several Variables; 15.2 Limits and Continuity; 15.3 Partial Derivatives; 15.4 Differentials; 15.5 Chain Rules for Functions of Several Variables; 15.6 Directional Derivatives and Gradients; 15.7 Tangent Planes and Normal Lines; 15.8 Extrema of Functions of Two Variables; 15.9 Applications of Extrema of Functions of Two Variables; 15.10 Lagrange Multipliers
                                • 16. Multiple Integration
                                  16.1 Iterated Integrals and Area in the Plane; 16.2 Double Integrals and Volume; 16.3 Change of Variables: Polar Coordinates; 16.4 Center of Mass and Moments of Inertia; 16.5 Surface Area; 16.6 Triple Integrals and Applications; 16.7 Cylindrical and Spherical Coordinates; 16.8 Triple Integrals in Cylindrical and Spherical Coordinates; 16.9 Change of Variables: Jacobians
                                  • 17. Vector Analysis
                                    17.1 Vector Fields; 17.2 Line Integrals; 17.3 Conservative Vector Fields and Independence of Path; 17.4 Green's Theorem; 17.5 Parametric Surfaces; 17.6 Surface Integrals; 17.7 Divergence Theorem; 17.8 Stokes's Theorem
                                    • 18. Differential Equations
                                      18.1 Definitions and Basic Concepts; 18.2 Separation of Variables in First-Order Equations; 18.3 Exact First-Order Equations; 18.4 First-Order Linear Differential Equations; 18.5 Second-Order Homogeneous Linear Equations; 18.6 Second-Order Nonhomogeneous Linear Equations; 18.7 Series Solutions of Differential Equations
                                      • Appendixes: A. Proofs of Selected Theorems; B. Basic Differentiation Rules for Elementary Functions; C. Integration Tables
                                      • Answers to Odd-Numbered Exercises
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