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For three-semester undergraduate-level courses in Calculus.
This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations.
Contemporary calculus instructors and students face traditional challenges as well as new ones that result from changes in the role and practice of mathematics by scientists and engineers in the world at large. As a consequence, this sixth edition of our calculus textbook is its most extensive revision since the first edition appeared in 1982.
Two chapters of the fifth edition have been combined in a single more tightly organized one. An entirely new chapter now appears in the table of contents, and most of the remaining chapters have been extensively rewritten. About 125 of the book's over 750 worked examples are new for this edition and the 1825 figures in the text include 225 new computer-generated graphics. About 600 of its over 7000 problems are new, and these are augmented by 320 new conceptual discussion questions that now precede the problem sets. Moreover, 1050 new true/false questions are included in the Study Guides on the new CD-ROM that accompanies this edition. In summary, almost 2000 of these 8400-plus problems and questions are new, and the text discussion and explanations have undergone corresponding alteration and improvement.
PRINCIPAL NEW FEATURES
The current revision of the text features
The new chapter on differential equations now appears immediately after Chapter 8 on techniques of integration. It includes both direction fields and Eider's method together with the more elementary symbolic methods (which exploit techniques from Chapter 8) and interesting applications of both first- and second-order equations. Chapter 11 (Infinite Series) now ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of second-semester calculus on elementary differential equations.
NEW LEARNING RESOURCES
Conceptual Discussion Questions: The set of problems that concludes each section is now preceded by a brief Concepts: Questions and Discussion set consisting of several open-ended conceptual questions that can be used for either individual study or classroom discussion.
The Text CD-ROM: The content of the new CD-ROM that accompanies this text is fully integrated with the textbook material, and is designed specifically for use hand-in-hand with study of the book itself. This CD-ROM features the following resources to support learning and teaching:
PH Grade Assist (Computerized Homework Grading System)-About 2000 of the textbook problems are incorporated in an automated grading system that is now available. Each problem solution in the system is structured algorithmically so that students can work in a computer lab setting to submit homework assignments for automatic grading. (There is a small annual fee per participating student.)
New Solutions Manuals: The entirely new 1810-page Instructor's Solutions Manual (available in three volumes) includes a detailed solution for every problem in the book. These solutions were written exclusively by the authors and have been checked independently by others.
The entirely new 930-page Student Solutions Manual (available in two volumes) includes a detailed solution for every odd-numbered problem in the text. The answers (alone) to most of these odd-numbered problems are included in the answers section at the back of this book.
New Technology manuals: Each of the following manuals is available shrink-wrapped with any version of the text for half the normal price of the manual (all of which are inexpensive):
THE TEXT IN MORE DETAIL...
In preparing this edition, we have taken advantage of many valuable comments and suggestions from users of the first five editions. This revision was so pervasive that the individual changes are too numerous to be detailed in a preface, but the following paragraphs summarize those that may be of widest interest.
OPTIONS IN TEACHING CALCULUS
The Calculus Sequence--The present version of the text is accompanied by a less traditional version that treats transcendental functions earlier in single-variable calculus and includes matrices for use in multivariable calculus. Both versions of the complete text are also available in two-volume split editions. By appropriate selection of first and second volumes, the instructor can therefore construct a complete text for a calculus sequence with
Maximum-Minimum Problems--The text includes first coverage of maximum-minimum problems in Chapter 3 (Sections 3.5 and 3.6) to provide early motivation in the form of concrete applications of the derivative, and then returns with the first- and
Edwards, C. Henry :
Penney, David E. : University of Georgia
1. Functions, Graphs, and Models
Functions and Mathematical Modeling
Graphs of Equations and Functions
Polynomials and Algebraic Functions
Preview: What Is Calculus?
2. Prelude to Calculus
Tangent Lines and Slope Predictors
The Limit Concept
More about Limits
The Concept of Continuity
3. The Derivative
The Derivative and Rates of Change
Basic Differentiation Rules
The Chain Rule
Derivatives of Algebraic Functions
Maxima and Minima of Functions on Closed Intervals
Applied Optimization Problems
Derivatives of Trigonometric Functions
Successive Approximations and Newton's Method
4. Additional Applications of the Derivative
Implicit Differentiation and Related Rates
Increments, Differentials, and Linear Approximation
Increasing and Decreasing Functions and the Mean Value Theorem
The First Derivative Test and Applications
Simple Curve Sketching
Higher Derivatives and Concavity
Curve Sketching and Asymptotes
5. The Integral
Antiderivatives and Initial Value Problems
Elementary Area Computations
Riemann Sums and the Integral
Evaluation of Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Areas of Plane Regions
6. Applications of the Integral
Riemann Sum Approximations
Volumes by the Method of Cross Sections
Volumes by the Method of Cylindrical Shells
Arc Length and Surface Area of Revolution
Force and Work
Centroids of Plane Regions and Curves
7. Calculus of Transcendental Functions
Exponential and Logarithmic Functions
Indeterminate Forms and L'Hopîtal's Rule
More Indeterminate Forms
The Logarithm as an Integral
Inverse Trigonometric Functions
8. Techniques of Integration
Integral Tables and Simple Substitutions
Integration by Parts
Rational Functions and Partial Fractions
Integrals Involving Quadratic Polynomials
9. Differential Equations
Simple Equations and Models
Slope Fields and Euler's Method
Separable Equations and Applications
Linear Equations and Applications
Linear Second-Order Equations
10. Polar Coordinates and Parametric Curves
Analytic Geometry and the Conic Sections
Area Computations in Polar Coordinates
Integral Computations with Parametric Curves
Conic Sections and Applications
11. Infinite Series
Infinite Series and Convergence
Taylor Series and Taylor Polynomials
The Integral Test
Comparison Tests for Positive-Term Series
Alternating Series and Absolute Convergence
Power Series Computations
Series Solutions of Differential Equations
12. Vectors, Curves, and Surfaces in Space
Vectors in the Plane
Rectangular Coordinates and Three-Dimensional Vectors
The Cross Product of Vectors
Lines and Planes in Space
Curves and Motions in Space
Curvature and Acceleration
Cylinders and Quadric Surfaces
Cylindrical and Spherical Coordinates
13. Partial Differentiation
Functions of Several Variables
Limits and Continuity
Multivariable Maxima and Minima
Increments and Linear Approximation
The Multivariable Chain Rule
Directional Derivatives and Gradient Vectors
Lagrange Multipliers and Constrained Optimization
Critical Points of Multivariable Functions
14. Multiple Integrals
Double Integrals over More General Regions
Area and Volume by Double Integration
Double Integrals in Polar Coordinates
Applications of Double Integrals
Integration in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals
15. Vector Calculus
The Fundamental Theorem and Independence of Path
The Divergence Theorem
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