Calculus with Analytic Geometry / Edition 5

ISBN-10: 0669353353

ISBN-13: 9780669353358

Pub. Date: 01/28/1994

Publisher: Houghton Mifflin Harcourt

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

Overview

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.

Product Details

ISBN-13:
9780669353358
Publisher:
Houghton Mifflin Harcourt
Publication date:
01/28/1994
Edition description:
Older Edition
Pages:
1127
Product dimensions:
9.06(w) x 11.02(h) x (d)

Related Subjects

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