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Calculus From Graphical, Numerical and Symbolic Points of View

Calculus From Graphical, Numerical and Symbolic Points of View - 97 edition

ISBN13: 978-0030195877

Cover of Calculus From Graphical, Numerical and Symbolic Points of View 97 (ISBN 978-0030195877)
ISBN13: 978-0030195877
ISBN10: 003019587X
Cover type:
Edition/Copyright: 97
Publisher: Saunders College Division
Published: 1997
International: No

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Calculus From Graphical, Numerical and Symbolic Points of View - 97 edition

ISBN13: 978-0030195877

Arnold Ostebee and Paul Zorn

ISBN13: 978-0030195877
ISBN10: 003019587X
Cover type:
Edition/Copyright: 97
Publisher: Saunders College Division

Published: 1997
International: No
Summary

Unlike traditional calculus texts that emphasize only an algebraic (symbolic) approach to learning the concepts, Ostebee/Zorn balances the symbolic approach with numerical and graphical ones. These three viewpoints give students a richer understanding of the fundamental concepts. Because important theorems and proofs are included, this text is appropriate for math and physical science majors. Technology (graphing calculators or computers) has a supporting role as an exploratory tool, rather than as an end in itself. Among the text's other distinctive features are the unusual variety of exercises, many which are graphical in nature; the informal, reader-friendly exposition; the attention to careful definitions and theorem statements; and the seamless integration of text and graphics in the exposition.

Table of Contents

Volume 1 contains Chapters 1 through 6 and the Appendixes.

Volume 2 contains Chapters 6 through 14 and selections from Chapters 3 and 4. Most chapters end with a Chapter Summary.

1. Functions in Calculus

Functions, calculus Style
Graphs
Machine Graphics
What is a Function?
A Field Guide to Elementary Functions
New Functions from Old
Modeling with Elementary Functions

2. The Derivative

Amount of Functions and Rate Functions: The Idea of the Derivative
Estimating Derivatives: A Closer Look
The Geometry of Derivatives
The Geometry of Higher-Order Derivatives
Average and Instantaneous Rates: Defining the Derivative
Limits and Continuity
Limits Involving Infinity; New Limits from Old

3. Derivatives of Elementary Functions

Derivatives of Power Functions and Polynomials
Using Derivative and Antiderivative Formulas
Derivatives of Exponential and Logarithmic Functions
Derivatives of Trigonometric Functions
New Derivatives From Old: The Product and Quotient Rules
New Derivatives Form Old: The Chain Rule
Implicit Differentiation
Inverse Trigonometric Functions and Their Derivatives

4. Applications of the Derivative

Differential Equations and Their Solutions
More Differential Equations: Modeling Growth
Linear and Quadratic Approximation; Taylor Polynomials
Newton's Method: Finding Roots
Splines: Connecting the Dots
Optimization
Calculus for Money: Derivatives in Economics
Related Rates
Parametric Equations, Parametric Curves
Why Continuity Matters
Why Differentiability Matters; The Mean Value Theorem

5. The Integral

Areas And Integrals
The Area Function
The Fundamental Theorem of Calculus
Approximating Sums: The Integral as a Limit
Approximating Sums: Interpretations and Applications

6. Finding Antiderivatives

Antiderivatives: The Idea
Antidifferentiation by Substitution
Integral Aids: Tables and Computers

7. Numerical Integration

The Idea of Approximation
More on Error: Left and Right Sums and the First Derivative
Trapezoid Sums, Midpoint Sums, and the Second Derivative
Simpson's Rule

8. Using the Definite Integral

Introduction
Finding Volumes by Integration
Arclength
Work
Present Value
Fourier Polynomials

9. More Antidifferentiation Techniques

Integration by Parts
Partial Fractions
Trigonometric Antiderivatives
Miscellaneous Exercises

10. Improper Integrals

When Is an Integral Improper?
Detecting Convergence, Estimating Limits
Improper Integrals and Probability
l'Hôpital's Rule: Comparing Rates

11. Infinite Series

Sequences and Their Limits
Infinite Series, Convergence, and Divergence
Testing for Convergence; Estimating Limits
Absolute Convergence; Alternating Series
Power Series
Power Series as Functions
Maclaurin and Taylor Series

12. Differential Equations

Differential Equations: The Basics
Slope Fields: Solving DE's Graphically
Euler's Method: Solving DE's Numerically
Separating Variables: Solving DE's Symbolically

13. Polar Coordinates

Polar Coordinates and Polar Curves
Calculus in Polar Coordinates

14. Multivariable Calculus: A First Look

Three-Dimensional Space
Functions of Several Variables
Partial Derivatives
Optimization and Partial Derivatives: A First Look
Multiple Integrals and Approximating Sums
Calculating Integrals by Iteration
Double Integrals in Polar Coordinates

Appendices:

Real Numbers and The Coordinate Plane
Lines and Linear Functions
Polynomial Algebra: A Brisk Review
Real-World Calculus: From Words to Mathematics
Linear, Polynomial, and Rational Functions
Algebra of Exponentials
Algebra of Logarithms
Trigonometric Functions
Selected Proofs
A Graphical Glossary of Functions

Index

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