Calculus (6° ed ) (6th Ed.)
Auteurs : Edwards C., Penney David
This book 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. KEY TOPICS: Chapter topics cover functions, graphs, and models; prelude to calculus; the derivative; additional applications of the derivative; the integral; applications of the integral; calculus of transcendental functions; techniques of integration; differential equations; polar coordinates and parametric curves; infinite series; vectors, curves, and surfaces in space; partial differentiation; multiple integrals; and vector calculus. For individuals interested in the study of calculus.
Note: This ISBN is now printed in a two volume set Part A and Part B which is shrinkwrapped together.
Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental 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 Functions 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.
Introduction. 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. Numerical Integration.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. Hyperbolic Functions.8. Techniques of Integration.
Introduction. Integral Tables and Simple Substitutions. Integration by Parts. Trigonometric Integrals. Rational Functions and Partial Fractions. Trigonometric Substitutions. Integrals Involving Quadratic Polynomials. Improper Integrals.9. Differential Equations.
Simple Equations and Models. Slope Fields and Euler's Method. Separable Equations and Applications. Linear Equations and Applications. Population Models. Linear Second-Order Equations. Mechanical Vibrations.10. Polar Coordinates and Parametric Curves.
Analytic Geometry and the Conic Sections. Polar Coordinates. Area Computations in Polar Coordinates. Parametric Curves. Integral Computations with Parametric Curves. Conic Sections and Applications.11. Infinite Series.
Introduction. Infinite Sequences. 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. Power Series Computations. Series Solutions of Differential Equations.12. Vectors, Curves, and Surfaces in Space.
Vectors in the Plane. 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.
Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Increments and Linear Approximation. The Multivariable Chain Rule. Directional Derivatives and the Gradient Vector. Lagrange Multipliers and Constrained Optimization. Critical Points of Functions of Two Variables.14. Multiple Integrals.
Double Integrals. Double Integrals over More General Regions. Area and Volume by Double I
C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students.
David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the activ
- NEW - Free CD—Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks.
- NEW - An entire chapter devoted to calculus of transcendental functions—Combines parts of two previous chapters into the new Ch. 7.
Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter.
- NEW - Expanded treatment of differential equations (New Chapter 9).
Introduces students to both direction fields and Euler's method together with the more symbolic elementary methods and applications for both first- and second-order equations.
- NEW - 1040 new True/False Questions—Available on the CD. They focus on theory and push the student to read.
- NEW - Reorganized content—Covers applied max-min problems in Ch.3 and defers related rates to Ch.4.
Offers students the opportunities to focus on and study these challenging topics in separate chapters—and test their knowledge of them in separate unit tests.
- Approximately 7000 total problems and interesting applications—Covers all ranges of difficulty, highly theoretical and computationally oriented problems.
Encourages students to learn by doing.
- Technology projects—Features icons that take users to Maple/ Mathematica/MATLAB/Calculator resources on the CD-ROM.
Gives students the opportunity to apply conceptually based technology following key sections of the text.
- 320 Section-ending Concepts: Questions & Discussion.
Serves students with a basis for either writing assignments or class discussion.
- Small optional section of matrix terminology and notation in the multivariable portion of the text.
Date de parution : 06-2002
Ouvrage de 1080 p.
21x27.5 cm