ISBN13:978-0618247875 ISBN10: 0618247874 This edition has also been released as: ISBN13: 978-0030256769 ISBN10: 0030256763
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/.
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.
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
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
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
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