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Calculus - With Analytic Geometry - Text Only

Calculus - With Analytic Geometry - Text Only - 7th edition

ISBN13: 978-0618141807

Cover of Calculus - With Analytic Geometry - Text Only 7TH 02 (ISBN 978-0618141807)
ISBN13: 978-0618141807
ISBN10: 0618141804
Cover type:
Edition/Copyright: 7TH 02
Publisher: Houghton Mifflin Harcourt
Published: 2002
International: No

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Calculus - With Analytic Geometry - Text Only - 7TH 02 edition

ISBN13: 978-0618141807

Ron Larson, Robert P. Hostetler and Bruce H. Edwards

ISBN13: 978-0618141807
ISBN10: 0618141804
Cover type:
Edition/Copyright: 7TH 02
Publisher: Houghton Mifflin Harcourt

Published: 2002
International: No
Summary

Author Bio

Larson, Ron : The Pennsylvania State University, The Behrend College


Hostetler, Robert P. : The Pennsylvania State University, The Behrend College


Edwards, Bruce H. : University of Florida

Table of Contents

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

P.S. Problem Solving


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
P.S. Problem Solving
2. Differentiation

2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 The 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

P.S. Problem Solving
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

P.S. Problem Solving
4. Integration

4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Reimann 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

P.S. Problem Solving
5. Logarithmic, Exponential, and Other Transcendental Functions

5.1 The Natural Logarithmic Function and Differentiation
5.2 The Natural Logarithmic Function and 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 Differential Equations: Growth and Decay
5.7 Differential Equations: Separation of Variables
5.8 Inverse Trigonometric Functions and Differentiation
5.9 Inverse Trigonometric Functions and Integration
5.10 Hyperbolic Functions

Section Project: St. Louis Arch
P.S. Problem Solving
6. Applications of Integration

6.1 Area of a Region Between Two Curves
6.2 Volume: The Disc Method
6.3 Volume: The Shell Method

Section Project: Saturn's Oblateness

6.4 Arc Length and Surfaces of Revolution
6.5 Work

Section Project: Tidal Energy

6.6 Moments, Centers of Mass, and Centroids
6.7 Fluid Pressure and Fluid Force

P.S. Problem Solving
7. Integration Techniques, L'Hôpital's Rule, and Improper Integrals

7.1 Basic Integration Rules
7.2 Integration by Parts
7.3 Trigonometric Integrals

Section Project: Power Lines

7.4 Trigonometric Substitution
7.5 Partial Fractions
7.6 Integration by Tables and Other Integration Techniques
7.7 Indeterminant Forms and L'Hôpital's Rule
7.8 Improper Integrals

P.S. Problem Solving
8. Infinite Series

8.1 Sequences
8.2 Series and Convergence

Section Project: Cantor's Disappearing Table

8.3 The Integral Test and p-Series

Section Project: The Harmonic Series

8.4 Comparisons of Series

Section Project: Solera Method

8.5 Alternating Series
8.6 The Ratio and Root Tests
8.7 Taylor Polynomials and Approximations
8.8 Power Series
8.9 Representation of Functions by Power Series
8.10 Taylor and Maclaurin Series

P.S. Problem Solving
9. Conics, Parametric Equations, and Polar Coordinates

9.1 Conics and Calculus
9.2 Plane Curves and Parametric Equations

Section Project

9.3 Parametric Equations and Calculus
9.4 Polar Coordinates and Polar Graphs

Section Project

9.5 Area and Arc Length in Polar Coordinates
9.6 Polar Equations of Conics and Kepler's Laws

P.S. Problem Solving
10. Vectors and the Geometry of Space

10.1 Vectors in the Plane
10.2 Space Coordinates and Vectors in Space
10.3 The Dot Product of Two Vectors
10.4 The Cross Product of Two Vectors in Space
10.5 Lines and Planes in Space

Section Project

10.6 Surfaces in Space
10.7 Cylindrical and Spherical Coordinates

Section Project
P.S. Problem Solving
11. Vector-Valued Functions

11.1 Vector-Valued Functions

Section Project

11.2 Differentiation and Integration of Vector-Valued Functions
11.3 Velocity and Acceleration

Section Project

11.4 Tangent Vectors and Normal Vectors
11.5 Arc Length and Curvature

P.S. Problem Solving
12. Functions of Several Variables

12.1 Introduction to Functions of Several Variables
12.2 Limits and Continuity
12.3 Partial Derivatives

Section Project

12.4 Differentials
12.5 Chain Rules for Functions of Several Variables
12.6 Directional Derivatives and Gradients
12.7 Tangent Planes and Normal Lines

Section Project

12.8 Extrema of Functions of Two Variables
12.9 Applications of Extrema of Functions of Two Variables

Section Project

12.10 Lagrange Multipliers

P.S. Problem Solving
13. Multiple Integration

13.1 Iterated Integrals and Area in the Plane
13.2 Double Integrals and Volume
13.3 Change of Variables: Polar Coordinates
13.4 Center of Mass and Moments of Inertia

Section Project

13.5 Surface Area

Section Project

13.6 Triple Integrals and Applications
13.7 Triple Integrals in Cylindrical and Spherical Coordinates

Section Project

13.8 Change of Variables: Jacobians

P.S. Problem Solving
14. Vector Analysis

14.1 Vector Fields
14.2 Line Integrals
14.3 Conservative Vector Fields and Independence of Path
14.4 Green's Theorem
14.5 Parametric Surfaces
14.6 Surface Integrals
14.7 Divergence Theorem
14.8 Stoke's Theorem

P.S. Problem Solving

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