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More About This Textbook
Overview
Editorial Reviews
From The Critics
This textbook for a onesemester course consists of chapters 1015 from , and covers infinite series, vectors and matrices, curves and surfaces in space, partial differentiation, multiple integrals, and vector calculus. The sixth edition integrates matrix methods with the more traditional approaches. The CDROM contains interactive examples and true false questions. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Table of Contents
Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for PositiveTerm Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations.
11. Vectors and Matrices.
Vectors in the Plane. ThreeDimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Linear Systems and Matrices. Matrix Operations. Eigenvalues and Rotated Conics.
12. Curves and Surfaces in Space.
Curves and Motion in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates.
13. Partial Differentiation.
Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Linear Approximation and Matrix Derivatives. The Multivariable Chain Rule. Directional Derivatives and Gradient Vectors. Lagrange Multipliers and Constrained Optimization. Critical Points of Multivariable Functions.
14. Multiple Integrals.
Double Integrals. Double Integrals over More General Regions. Area and Volume by Double Integration. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Integration in Cylindrical and Spherical Coordinates. Surface Area. Change of Variables in Multiple Integrals.
15. Vector Calculus.
Vector Fields. Line Integrals. The Fundamental Theorem and Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stokes' Theorem.
Appendices.
Answers.
Index.
Preface
Two entire chapters of the fifth edition have been replaced in the table of contents by two new ones; most of the remaining chapters have been extensively rewritten. Nearly 160 of the book's over 800 worked examples are new for this edition and the 1850 figures in the text include 250 new computergenerated graphics. Almost 800 of its 7250 problems are new, and these are augmented by over 330 new conceptual discussion questions that now precede the problem sets. Moreover, almost 1100 new true/false questions are included in the Study Guides on the new CDROM that accompanies this edition. In summary, almost 2200 of these 8650plus 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
Complete coverage of the calculus of transcendental functions is now fully integrated in Chapters 1 through 6—with the result that the Chapter 7 and 8 titles in the 5th edition table of contents do pot appear in this 6th edition.
A new chapter on differential equations (Chapter 8) nowappears immediately after Chapter 7 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 7) and interesting applications of both first and secondorder equations. Chapter 10 (Infinite Series) now ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of secondsemester calculus on elementary differential equations.
Linear systems and matrices, ending with an elementary treatment of eigenvalues and eigenvectors, are now introduced in Chapter 11. The subsequent coverage of multivariable calculus now integrates matrix methods and terminology with the traditional notation and approach—including (for instance) introduction and extensive application of the chain rule in matrixproduct form.
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 openended conceptual questions that can be used for either individual study or classroom discussion.
The Text CDROM. The content of the new CDROM that accompanies this text is fully integrated with the textbook material, and is designed specifically for use handinhand with study of the book itself. This CDROM features the following resources to support learning and teaching:
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 1900page Instructor's Solutions Manual (available in two 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 950page Student Solutions Manual (available in two volumes) includes a detailed solution for every oddnumbered problem in the text. The answers (alone) to most of these oddnumbered problems are included in the answers section at the back of this book.
New Technology Manuals. Each of the following manuals is available shrinkwrapped 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.
TEXT ORGANIZATION
The mean value theorem and its applications are deferred to Chapter 4. In addition, a dominant theme of Chapter 4 is the use of calculus both to construct graphs of functions and to explain and interpret graphs that have been constructed by a calculator or computer. This theme is developed in Sections 4.4 on the first derivative test and 4.6 on higher derivatives and concavity. But it may also be apparent in Sections 4.8 and 4.9 on l'Hopital's rule, which now appears squarely in the context of differential calculus and is applied here to round out the calculus of exponential and logarithmic functions.
Chapter 6 begins with a largely new section on Riemann sum approximations, with new examples centering on fluid flow and medical applications. Section 6.6 is a new treatment of centroids of plane regions and curves. Section 6.7 gives the integral approach to logarithms, and Sections 6.8 and 6.9 cover both the differential and the integral calculus of inverse trigonometric functions and of hyperbolic functions.
Chapter 7 (Techniques of Integration) is organized to accommodate those instructors who feel that methods of formal integration now require less emphasis, in view of modern techniques for both numerical and symbolic integration. Integration by parts (Section 7.3) precedes trigonometric integrals (Section 7.4). The method of partial fractions appears in Section 7.5, and trigonometric substitutions and integrals involving quadratic polynomials follow in Sections 7.6 and 7.7. Improper integrals appear in Section 7.8, with new and substantial subsections on special functions and probability and random sampling. This rearrangement of Chapter 7 makes it more convenient to stop wherever the instructor desires.
OPTIONS IN TEACHING CALCULUS
The present version of the text is accompanied by a more traditional version that treats transcendental functions later in single variable calculus and omits matrices in multivariable calculus. Both versions of the complete text are also available in twovolume split editions. By appropriate selection of first and second volumes, the instructor can therefore construct a complete text for a calculus sequence with