by Arnold Ostebee and Paul Zorn

ISBN13: 978-0030256813

ISBN10: 003025681X

Cover type:

Edition/Copyright: 2ND 02

Publisher: Houghton Mifflin Harcourt

Published: 2002

International: No

ISBN10: 003025681X

Cover type:

Edition/Copyright: 2ND 02

Publisher: Houghton Mifflin Harcourt

Published: 2002

International: No

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**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.

**6. NUMERICAL INTEGRATION. **

Approximating Integrals: The Idea and Basic Methods.

Euler's Method for Differential Equations.

Error Bounds.

**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.

**V.VECTORS AND POLAR COORDINATES. **

Vectors.

Polar Coordinates and Polar Curves.

Calculus in Polar Coordinates.

**M. MULTIVARIABLE CALCULUS: A FIRST LOOK. **

Three-dimensional Space.

Functions of Several Variables.

Partial Derivatives.

Optimization and Partial Derivatives.

Multiple Integrals and Approximating Sums.

Calculating Multiple Integrals by Iteration.

Summary and Review.

**APPENDICES. **

Machine Graphics.

Real Numbers and the Coordinate Plane.

Lines and Linear Functions.

Polynomials and Rational Functions.

Exponential and Logarithm Functions.

Trigonometric Functions.

Real-World Calculus: From Words to Mathematics.

Selected Proofs.

A Graphical Glossary of Functions.

Complex Numbers.

Matrices and Matrix Algebra: A Crash Course.

Formulas, Identities, and Table of Integrals.

ISBN10: 003025681X

Cover type:

Edition/Copyright: 2ND 02

Publisher: Houghton Mifflin Harcourt

Published: 2002

International: No

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.

**6. NUMERICAL INTEGRATION. **

Approximating Integrals: The Idea and Basic Methods.

Euler's Method for Differential Equations.

Error Bounds.

**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.

**V.VECTORS AND POLAR COORDINATES. **

Vectors.

Polar Coordinates and Polar Curves.

Calculus in Polar Coordinates.

**M. MULTIVARIABLE CALCULUS: A FIRST LOOK. **

Three-dimensional Space.

Functions of Several Variables.

Partial Derivatives.

Optimization and Partial Derivatives.

Multiple Integrals and Approximating Sums.

Calculating Multiple Integrals by Iteration.

Summary and Review.

**APPENDICES. **

Machine Graphics.

Real Numbers and the Coordinate Plane.

Lines and Linear Functions.

Polynomials and Rational Functions.

Exponential and Logarithm Functions.

Trigonometric Functions.

Real-World Calculus: From Words to Mathematics.

Selected Proofs.

A Graphical Glossary of Functions.

Complex Numbers.

Matrices and Matrix Algebra: A Crash Course.

Formulas, Identities, and Table of Integrals.

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