by Arnold Ostebee and Paul Zorn
List price: $116.95
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 have 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:
Author Bio
Ostebee, Arnold : St. Olaf College
Zorn, Paul : St. Olaf College
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
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 have 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:
Author Bio
Ostebee, Arnold : St. Olaf College
Zorn, Paul : St. Olaf College
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