by Arnold Ostebee and Paul Zorn
List price: $111.56
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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.
Author Bio
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
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.
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