Calculus from Graphical, Numerical, and Symbolic Points of View, Volume ll - 2nd edition

Summary: Ostebee and Zorn provide concrete strategies that help students understand and master concepts in calculus. This user-friendly text continues to help students interact with the main calculus objects (functions, derivatives, integrals, etc.) not only symbolically but also, where appropriate, graphically and numerically. Ostebee/Zorn strikes an appropriate balance among these points of view, without overemphasizing any of them. New exercises, examples, and much more ha ...show moreve added tremendously to this great book. NAVIGATING CALCULUS, a new CD-ROM, is being released along with the second edition. The CD contains a variety of useful tools, and resources, including a powerful graphing calculator utility, a glossary with examples, and many live activities that deepen students' encounters with calculus ideas. The CD is keyed closely to the book's table of contents. Any treatment of calculus involves many choices among competing alternatives: how and when to treat limits, which applications to include, what to prove, etc. To explain the authors' views on such matters, they've established an FAQ site at: http://www.stolaf.edu/people/zorn/ozcalc/faq/.

Benefits:

• The basic principles of the first edition remain unchanged. Conceptual understanding is still the main goal, and combining various viewpoints is still the main strategy for achieving it. The text still has an emphasis on concepts and sense making; complementing symbolic with graphical and numerical points of view; exercises of varied nature and difficulty; and a narrative aimed at student readers.
• NEW! Content changes include a new brief chapter on function approximation, centering on Taylor polynomial approximation, but also including basic discussion of Fourier polynomials.
• NEW! Many users found the previous edition short on routine exercises, so many more have been added to second edition.
• NEW! More exercises that point to specific issues and examples in the narrative have been added.
• NEW! The text now provides answers (not solutions) to odd-numbered exercises in the back of the book, in response to many user requests (from instructors, not just from students).
• NEW! To help students read the text more successfully, more examples have been added to many sections, parts of the narrative have been rewritten, and more detail and brief commentary has been included on many calculations.
• Most chapters end with one or more Interludes. These brief, project-oriented expositions with exercises are designed for independent student work and address topics or questions that are optional or out of the chapter's main stream of development.
• NEW! To make the text easier to use, changes have been made in narrative, exercises, content, emphasis, and order of presentation, based on suggestions from both teachers and students.
• NEW! The precalculus material has been compressed in order to get to the derivative idea faster. Chapter 1 now includes essentially complete coverage of the graphical point of view; derivatives now appear first in Section 1.4.
• NEW! Chapter 2 introduces and interprets the symbolic point of view, and Chapter 3 presents the combinatorial rules for calculating derivatives (e.g., the product and quotient rules).
• NEW! Differential equations provide a natural approach to scientific and engineering applications. DEs now appear earlier and appear repeatedly in subsequent sections and in exercises.
• NEW! Although DEs are emphasized more strongly, this is not a calculus/DE text. It does not cover, or even catalog, the huge variety of DEs and solution techniques. Instead, we sometimes use DEs to motivate new techniques and concepts as they develop naturally over the course.
• NEW! Slope fields now appear in Chapter 4 (they previously appeared in Chapter 12).
• NEW! Euler's method now appears in Chapter 6 (along with numerical integration methods), and separation of variables appear in Chapter 7 as an application of symbolic anti-differentiation.

Edition/Copyright: 2ND 02
Cover:
Publisher: Brooks/Cole Publishing Co.
Year Published: 2002
International: No

View Author Bio

Ostebee, Arnold : St. Olaf College

Zorn, Paul : St. Olaf College

View Table of Contents

7. USING THE INTEGRAL

Interpretations of the Integral
Areas and Volumes
Motion; Work
Probability
Separable Differential Equations

8. SYMBOLIC ANTIDIFFERENTIATION TECHNIQUES

Integration by Parts
Partial Fractions
Trigonometric Antiderivatives
Miscellaneous Antidifferentiation Exercises

9. FUNCTION APPROXIMATION

Taylor Polynomials
Taylor's Theorem
Fourier Polynomials

10. IMPROPER INTEGRALS

When Is an Integral Improper? Detecting Convergence; Estimating Limits

11. INFINITE SERIES

Sequences and Their Limits; Infinite Series, Convergence, and Divergence
Testing for Convergence; Estimating Limits
Absolute Convergence; Alternating Series
Power Series; Taylor Series
Algebra and Calculus with Power Series

12. CURVES AND VECTORS

Three-Dimensional Space
Curves and Parametric Equations
Vectors
Vector-Valued Functions, Derivatives, and Integrals
Derivatives, Antiderivatives, and Motion
The Dot Product
Lines and Planes in Three Dimensions
The Cross Product

13. DERIVATIVES

Functions of Several Variables
Partial Derivatives
Partial Derivatives and Linear Approximation
The Gradient and Directional Derivatives
Local Linearity: Theory of the Derivative
Higher Order Derivatives and Quadratic Approximation
Maxima, Minima, and Quadratic Approximation
The Chain Rule

14. INTEGRALS

Multiple Integrals and Approximating Sums
Calculating Integrals by Iteration
Double Integrals in Polar Coordinates
More on Triple Integrals; Cylindrical and Spherical Coordinates
Multiple Integrals Overviewed; Change of Variables

15. OTHER TOPICS

Linear, Circular, and Combined Motion
Using the Dot Product: More on Curves
Curvature
Lagrange Multipliers and Constrained Optimization

16. VECTOR CALCULUS

Line Integrals
More on Line Integrals; A Fundamental Theorem
Relating Line and Area Integrals: Green's Theorem
Surfaces and Their Parametrizations
Surface Integrals
Derivatives and Integrals of Vector Fields
Back to Fundamentals: Stokes' Theorem and the Divergence Theorem