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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/.
1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW
Functions, Calculus Style
Graphs
A Field Guide to Elementary Functions
Amount Functions and Rate Functions: The Idea of the Derivative
Estimating Derivatives: A Closer Look
The Geometry of Derivatives
The Geometry of Higher-Order Derivatives
Chapter Summary
Interlude: Zooming in on Differences
2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW
Defining the Derivative
Derivatives of Power Functions ad Polynomials
Limits
Derivatives, Antiderivatives, and Their Uses
Differential Equations; Modeling Motion
Derivatives of Exponential and Logarithm Functions; Modeling Growth
Derivatives of Trigonometric Functions; Modeling Oscillation
Chapter Summary
Interlude: Tangent Lines in History
Interlude: Limit--the Formal Definition
3. NEW DERIVATIVES FROM OLD
Algebraic Combinations: The Product and Quotient Rules
Composition and the Chain Rule
Implicit Functions and Implicit Differentiation
Inverse Functions and their Derivatives; Inverse Trigonometric Functions
Miscellaneous Derivatives and Antiderivatives
Chapter Summary
Interlude: Vibrations--Simple and Damped
Interlude: Hyperbolic Functions
4. USING THE DERIVATIVE
Direction Fields; More on Growth and Motion
Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates
More on Optimization
Parametric Equations
Related Rates
Newton's Method
Linear Approximation and Taylor Polynomials
Continuity
The Mean Value Theorem
Chapter Summary
Interlude: Growth with Interest
Interlude: Logistic Growth
Interlude: Digging Deeper for Roots (More on Newton's Method)
5. THE INTEGRAL
Areas and Integrals
The Area Function
The Fundamental Theorem of Calculus
Finding Antiderivatives by Substitution
Finding Antiderivatives Using Tables and Computers
Approximating Sums: The Integral as a Limit
Working with Approximating Sums
Chapter Summary
Interlude: Mean Value Theorems and Integrals
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/.
Table of Contents
1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW
Functions, Calculus Style
Graphs
A Field Guide to Elementary Functions
Amount Functions and Rate Functions: The Idea of the Derivative
Estimating Derivatives: A Closer Look
The Geometry of Derivatives
The Geometry of Higher-Order Derivatives
Chapter Summary
Interlude: Zooming in on Differences
2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW
Defining the Derivative
Derivatives of Power Functions ad Polynomials
Limits
Derivatives, Antiderivatives, and Their Uses
Differential Equations; Modeling Motion
Derivatives of Exponential and Logarithm Functions; Modeling Growth
Derivatives of Trigonometric Functions; Modeling Oscillation
Chapter Summary
Interlude: Tangent Lines in History
Interlude: Limit--the Formal Definition
3. NEW DERIVATIVES FROM OLD
Algebraic Combinations: The Product and Quotient Rules
Composition and the Chain Rule
Implicit Functions and Implicit Differentiation
Inverse Functions and their Derivatives; Inverse Trigonometric Functions
Miscellaneous Derivatives and Antiderivatives
Chapter Summary
Interlude: Vibrations--Simple and Damped
Interlude: Hyperbolic Functions
4. USING THE DERIVATIVE
Direction Fields; More on Growth and Motion
Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates
More on Optimization
Parametric Equations
Related Rates
Newton's Method
Linear Approximation and Taylor Polynomials
Continuity
The Mean Value Theorem
Chapter Summary
Interlude: Growth with Interest
Interlude: Logistic Growth
Interlude: Digging Deeper for Roots (More on Newton's Method)
5. THE INTEGRAL
Areas and Integrals
The Area Function
The Fundamental Theorem of Calculus
Finding Antiderivatives by Substitution
Finding Antiderivatives Using Tables and Computers
Approximating Sums: The Integral as a Limit
Working with Approximating Sums
Chapter Summary
Interlude: Mean Value Theorems and Integrals