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by Arnold Ostebee and Paul Zorn

Cover type: PaperbackEdition: 2ND 04

Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

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Ostebee and Zorn's approach applies reform principles to a rigorous calculus text. Conceptual understanding is the main goal of the text, and looking at mathematics from many representations (graphical, symbolic, numerical) is the main strategy for achieving this type of understanding. The key strengths of the text include combining symbolic manipulation with graphical and numerical representation, exercises of a varied nature and difficulty, and explanations written to be understandable to student readers.

- A student-friendly and approachable tone, numerous examples, critical-thinking questions, and supportive details and commentary help students successfully read and use the text.
- Representation of mathematical concepts through a variety of viewpoints supports different learning styles. Students see the math worked out through multiple representations--graphically, numerically, and symbolically--to enhance conceptual understanding.
- Proofs presented at point of use contribute significantly to helping students understand rigorous calculus concepts and develop analytic skills.
- Varied exercise sets offer instructors more options for creating homework assignments. Basic Exercises, which are straightforward and focus on a single idea, help students build basic skills.
- Further Exercises are a little more ambitious and may require the synthesis of several ideas, a deeper or more sophisticated understanding of basic concepts, or the use of a computer algebra system such as Maple or Mathematica. These are available for professors to assign when they would like to challenge their students and incorporate technology into their course.
- Answers to Select Exercises can be found in the back of the text, enabling students to get immediate feedback and assess their understanding of the material.
- Interludes are brief project-oriented expositions, with related exercises, that extend the concepts presented in the chapter. Professors have the opportunity to include these topics found at the end of the chapter as independent work, group work, or as a classroom activity. The Interludes include theoretical problems and proofs intended to enhance student understanding of the key calculus concepts.

**Ostebee, Arnold : St. Olaf College**

Zorn, Paul : St. Olaf College

Note: Each chapter contains a Summary.

**11. Infinite Series**

11.1 Sequences and Their Limits

11.2 Infinite Series, Convergence, and Divergence

11.3 Testing for Convergence; Estimating Limits

11.4 Absolute Convergence; Alternating Series

11.5 Power Series

11.6 Power Series as Functions

11.7 Taylor Series

Interlude: Fourier series

**12. Curves and Vectors**

12.1 Three-Dimensional Space

12.2 Curves and Parametric Equations

12.3 Polar Coordinates and Polar Curves

12.4 Vectors

12.5 Vector-Valued Functions, Derivatives, and Integrals

12.6 Modeling Motion

12.7 The Dot Product

12.8 Lines and Planes in Three Dimensions

12.9 The Cross Product

Interlude: Beyond Free Fall

**13. Derivatives**

13.1 Functions of Several Variables

13.2 Partial Derivatives

13.3 Linear Approximation in Several Variables

13.4 The Gradient and Directional Derivatives

13.5 Higher-Order Derivatives and Quadratic Approximation

13.6 Maxima, Minima, and Quadratic Approximation

13.7 The Chain Rule

13.8 Local Linearity: Some Theory of the Derivative

**14. Integrals**

14.1 Multiple Integrals and Approximating Sums

14.2 Calculating Integrals by Iteration

14.3 Integrals over Nonrectangular Regions

14.4 Double Integrals in Polar Coordinates

14.5 Triple Integrals

14.6 More Triple Integrals; Cylindrical and Spherical Coordinates

14.7 Multiple Integrals Overviewed: Change of Variables

Interlude: Mass and Center of Mass

**15. Other Topics**

15.1 Linear, Circular, and Combined Motion

Interlude: Cycloids and Epicycloids

15.2 New Curves from Old

15.3 Curvature

15.4 Lagrange Multipliers and Constrained Optimization

15.5 Improper Multivariable Integrals

Interlude: Constructing Pedal Curves

**16. Vector Calculus**

16.1 Line Integrals

16.2 More on Line Integrals; A Fundamental Theorem

16.3 Green's Theorem: Relating Line and Area Integrals

16.4 Surfaces and Their Parameterizations

16.5 Surface Integrals

16.6 Derivatives and Integrals of Vector Fields

16.7 Back to Fundamentals: Stokes's Theorem and the Divergence Theorem

**Appendixes**

A. Matrices and Matrd Integralsix Algebra: A Crash Course

B. Theory of Multivariable Calculus: Brief Glimpses

C. Table of Derivatives

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Summary

Ostebee and Zorn's approach applies reform principles to a rigorous calculus text. Conceptual understanding is the main goal of the text, and looking at mathematics from many representations (graphical, symbolic, numerical) is the main strategy for achieving this type of understanding. The key strengths of the text include combining symbolic manipulation with graphical and numerical representation, exercises of a varied nature and difficulty, and explanations written to be understandable to student readers.

- A student-friendly and approachable tone, numerous examples, critical-thinking questions, and supportive details and commentary help students successfully read and use the text.
- Representation of mathematical concepts through a variety of viewpoints supports different learning styles. Students see the math worked out through multiple representations--graphically, numerically, and symbolically--to enhance conceptual understanding.
- Proofs presented at point of use contribute significantly to helping students understand rigorous calculus concepts and develop analytic skills.
- Varied exercise sets offer instructors more options for creating homework assignments. Basic Exercises, which are straightforward and focus on a single idea, help students build basic skills.
- Further Exercises are a little more ambitious and may require the synthesis of several ideas, a deeper or more sophisticated understanding of basic concepts, or the use of a computer algebra system such as Maple or Mathematica. These are available for professors to assign when they would like to challenge their students and incorporate technology into their course.
- Answers to Select Exercises can be found in the back of the text, enabling students to get immediate feedback and assess their understanding of the material.
- Interludes are brief project-oriented expositions, with related exercises, that extend the concepts presented in the chapter. Professors have the opportunity to include these topics found at the end of the chapter as independent work, group work, or as a classroom activity. The Interludes include theoretical problems and proofs intended to enhance student understanding of the key calculus concepts.

Author Bio

**Ostebee, Arnold : St. Olaf College**

Zorn, Paul : St. Olaf College

Table of Contents

Note: Each chapter contains a Summary.

**11. Infinite Series**

11.1 Sequences and Their Limits

11.2 Infinite Series, Convergence, and Divergence

11.3 Testing for Convergence; Estimating Limits

11.4 Absolute Convergence; Alternating Series

11.5 Power Series

11.6 Power Series as Functions

11.7 Taylor Series

Interlude: Fourier series

**12. Curves and Vectors**

12.1 Three-Dimensional Space

12.2 Curves and Parametric Equations

12.3 Polar Coordinates and Polar Curves

12.4 Vectors

12.5 Vector-Valued Functions, Derivatives, and Integrals

12.6 Modeling Motion

12.7 The Dot Product

12.8 Lines and Planes in Three Dimensions

12.9 The Cross Product

Interlude: Beyond Free Fall

**13. Derivatives**

13.1 Functions of Several Variables

13.2 Partial Derivatives

13.3 Linear Approximation in Several Variables

13.4 The Gradient and Directional Derivatives

13.5 Higher-Order Derivatives and Quadratic Approximation

13.6 Maxima, Minima, and Quadratic Approximation

13.7 The Chain Rule

13.8 Local Linearity: Some Theory of the Derivative

**14. Integrals**

14.1 Multiple Integrals and Approximating Sums

14.2 Calculating Integrals by Iteration

14.3 Integrals over Nonrectangular Regions

14.4 Double Integrals in Polar Coordinates

14.5 Triple Integrals

14.6 More Triple Integrals; Cylindrical and Spherical Coordinates

14.7 Multiple Integrals Overviewed: Change of Variables

Interlude: Mass and Center of Mass

**15. Other Topics**

15.1 Linear, Circular, and Combined Motion

Interlude: Cycloids and Epicycloids

15.2 New Curves from Old

15.3 Curvature

15.4 Lagrange Multipliers and Constrained Optimization

15.5 Improper Multivariable Integrals

Interlude: Constructing Pedal Curves

**16. Vector Calculus**

16.1 Line Integrals

16.2 More on Line Integrals; A Fundamental Theorem

16.3 Green's Theorem: Relating Line and Area Integrals

16.4 Surfaces and Their Parameterizations

16.5 Surface Integrals

16.6 Derivatives and Integrals of Vector Fields

16.7 Back to Fundamentals: Stokes's Theorem and the Divergence Theorem

**Appendixes**

A. Matrices and Matrd Integralsix Algebra: A Crash Course

B. Theory of Multivariable Calculus: Brief Glimpses

C. Table of Derivatives

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

Ostebee and Zorn's approach applies reform principles to a rigorous calculus text. Conceptual understanding is the main goal of the text, and looking at mathematics from many representations (graphical, symbolic, numerical) is the main strategy for achieving this type of understanding. The key strengths of the text include combining symbolic manipulation with graphical and numerical representation, exercises of a varied nature and difficulty, and explanations written to be understandable to student readers.

- A student-friendly and approachable tone, numerous examples, critical-thinking questions, and supportive details and commentary help students successfully read and use the text.
- Representation of mathematical concepts through a variety of viewpoints supports different learning styles. Students see the math worked out through multiple representations--graphically, numerically, and symbolically--to enhance conceptual understanding.
- Proofs presented at point of use contribute significantly to helping students understand rigorous calculus concepts and develop analytic skills.
- Varied exercise sets offer instructors more options for creating homework assignments. Basic Exercises, which are straightforward and focus on a single idea, help students build basic skills.
- Further Exercises are a little more ambitious and may require the synthesis of several ideas, a deeper or more sophisticated understanding of basic concepts, or the use of a computer algebra system such as Maple or Mathematica. These are available for professors to assign when they would like to challenge their students and incorporate technology into their course.
- Answers to Select Exercises can be found in the back of the text, enabling students to get immediate feedback and assess their understanding of the material.
- Interludes are brief project-oriented expositions, with related exercises, that extend the concepts presented in the chapter. Professors have the opportunity to include these topics found at the end of the chapter as independent work, group work, or as a classroom activity. The Interludes include theoretical problems and proofs intended to enhance student understanding of the key calculus concepts.

**Ostebee, Arnold : St. Olaf College**

Zorn, Paul : St. Olaf College

Note: Each chapter contains a Summary.

**11. Infinite Series**

11.1 Sequences and Their Limits

11.2 Infinite Series, Convergence, and Divergence

11.3 Testing for Convergence; Estimating Limits

11.4 Absolute Convergence; Alternating Series

11.5 Power Series

11.6 Power Series as Functions

11.7 Taylor Series

Interlude: Fourier series

**12. Curves and Vectors**

12.1 Three-Dimensional Space

12.2 Curves and Parametric Equations

12.3 Polar Coordinates and Polar Curves

12.4 Vectors

12.5 Vector-Valued Functions, Derivatives, and Integrals

12.6 Modeling Motion

12.7 The Dot Product

12.8 Lines and Planes in Three Dimensions

12.9 The Cross Product

Interlude: Beyond Free Fall

**13. Derivatives**

13.1 Functions of Several Variables

13.2 Partial Derivatives

13.3 Linear Approximation in Several Variables

13.4 The Gradient and Directional Derivatives

13.5 Higher-Order Derivatives and Quadratic Approximation

13.6 Maxima, Minima, and Quadratic Approximation

13.7 The Chain Rule

13.8 Local Linearity: Some Theory of the Derivative

**14. Integrals**

14.1 Multiple Integrals and Approximating Sums

14.2 Calculating Integrals by Iteration

14.3 Integrals over Nonrectangular Regions

14.4 Double Integrals in Polar Coordinates

14.5 Triple Integrals

14.6 More Triple Integrals; Cylindrical and Spherical Coordinates

14.7 Multiple Integrals Overviewed: Change of Variables

Interlude: Mass and Center of Mass

**15. Other Topics**

15.1 Linear, Circular, and Combined Motion

Interlude: Cycloids and Epicycloids

15.2 New Curves from Old

15.3 Curvature

15.4 Lagrange Multipliers and Constrained Optimization

15.5 Improper Multivariable Integrals

Interlude: Constructing Pedal Curves

**16. Vector Calculus**

16.1 Line Integrals

16.2 More on Line Integrals; A Fundamental Theorem

16.3 Green's Theorem: Relating Line and Area Integrals

16.4 Surfaces and Their Parameterizations

16.5 Surface Integrals

16.6 Derivatives and Integrals of Vector Fields

16.7 Back to Fundamentals: Stokes's Theorem and the Divergence Theorem

**Appendixes**

A. Matrices and Matrd Integralsix Algebra: A Crash Course

B. Theory of Multivariable Calculus: Brief Glimpses

C. Table of Derivatives