ISBN-10:
0618226869
ISBN-13:
9780618226863
Pub. Date:
02/28/2002
Publisher:
Houghton Mifflin Company College Division
Calculus: Early Transcendental Functions / Edition 3

Calculus: Early Transcendental Functions / Edition 3

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Overview

Calculus: Early Transcendental Functions / Edition 3

Designed for the three-semester engineering calculus course, Calculus: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of 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 save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the fourth of Calculus: Early Transcendental Functions, 4/e 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 Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

Product Details

ISBN-13: 9780618226863
Publisher: Houghton Mifflin Company College Division
Publication date: 02/28/2002
Edition description: Older Edition
Pages: 1091
Product dimensions: 8.70(w) x 10.80(h) x 1.80(d)

About 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.

The Pennsylvania State University, The Behrend College Bio: Robert P. Hostetler received his Ph.D. 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 graphingcalculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.

Table of Contents

Note: Each

Chapter includes Review Exercises and P.S. Problem Solving.
1.Preparation for Calculus
1.1 Graphs and Models
1.2 Linear Models and Rates of Change
1.3 Functions and Their Graphs
1.4 Fitting Models to Data
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
2.Limits and Their Properties
2.1 A Preview of Calculus
2.2 Finding Limits Graphically and Numerically
2.3 Evaluating Limits Analytically
2.4 Continuity and One-Sided Limits
2.5 Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions
3.Differentiation
3.1 The Derivative and the Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 Product and Quotient Rules and Higher-Order Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation Section Project: Optical Illusions
3.6 Derivatives of Inverse Functions
3.7 Related Rates
3.8 Newton's Method
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 Section Project: Rainbows
4.4 Concavity and the Second Derivative Test
4.5 Limits at Infinity
4.6 A Summary of Curve Sketching
4.7 Optimization Problems Section Project: Connecticut River
4.8 Differentials
5.Integration
5.1 Antiderivatives and Indefinite Integration
5.2 Area
5.3 Riemann Sums and Definite Integrals
5.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem
5.5 Integration by Substitution
5.6 Numerical Integration
5.7 The Natural Logarithmic Function:Integration
5.8 Inverse Trigonometric Functions: Integration
5.9 Hyperbolic Functions Section Project: St. Louis Arch
6.Differential Equations
6.1 Slope Fields and Euler's Method
6.4 Differential Equations: Growth and Decay
6.5 Differential Equations: Separation of Variables
6.4 The Logistic Equation
6.5 First-Order Linear Differential Equations Section Project: Weight Loss
6.6 Predator-Prey Differential Equations
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 Projects: 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
11.Vectors and the Geometry of Space
11.1 Vectors in the Plane
11.2 Space Coordinates and Vectors in Space
11.3 The Dot Product of Two Vectors
11.4 The Cross Product of Two Vectors in Space
11.5 Lines and Planes in Space Section Project: Distances in Space
11.6 Surfaces in Space
11.7 Cylindrical and Spherical Coordinates
12.Vector-Valued Functions
12.1 Vector-Valued Functions Section Project: Witch of Agnesi
12.2 Differentiation and Integration of Vector-Valued Functions
12.3 Velocity and Acceleration
12.4 Tangent Vectors and Normal Vectors
12.5 Arc Length and Curvature
13.Functions of Several Variables
13.1 Introduction to Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives Section Project: Moire Fringes
13.4 Differentials
13.5 Chain Rules for Functions of Several Variables
13.6 Directional Derivatives and Gradients
13.7 Tangent Planes and Normal Lines Section Project: Wildflowers
13.8 Extrema of Functions of Two Variables
13.9 Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline
13.10 Lagrange Multipliers
14.Multiple Integration
14.1 Iterated Integrals and Area in the Plane
14.2 Double Integrals and Volume
14.3 Change of Variables: Polar Coordinates
14.4 Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail
14.5 Surface Area Section Project: Capillary Action
14.6 Triple Integrals and Applications
14.7 Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres
14.8 Change of Variables: Jacobians
15.Vector Analysis
15.1 Vector Fields
15.2 Line Integrals
15.3 Conservative Vector Fields and Independence of Path
15.4 Green's Theorem Section Project: Hyperbolic and Trigonometric Functions
15.5 Parametric Surfaces
15.6 Surface Integrals Section Project: Hyperboloid of One Sheet
15.7 Divergence Theorem
15.8 Stoke's Theorem Section Project: The Planimeter Appendices

Appendix A Proofs of Selected Theorems

Appendix B Integration Tables

Appendix C Business and Economic Applications Additional Appendices The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM:

Appendix D Precalculus Review

Appendix E Rotation and General Second-Degree Equation

Appendix F Complex Numbers

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