Calculus
2nd Edition
Published on 19. May 2000
Book
Paperback/Softback
816 pages
978-0-201-44138-3 (ISBN)
Description
Written by an experienced author team with expertise in the use of technology and NCTM guidelines, this text provides an emphasis on multiple representations of concepts and an abundance of worked examples. Calculus is explored through the interpretation of graphs and tables as well as through the application of analytical methods. Rich exercises include graphical and data-based problems, and interesting real-life applications in biology, business, chemistry, economics, engineering, finance, physics, the social sciences and statistics. Stepped Explorations throughout the text provide guided investigations of key concepts and help students build problem-solving skills. A grapher is required.
More details
Edition
2nd edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 260 mm
Width: 210 mm
Thickness: 40 mm
Weight
1682 gr
ISBN-13
978-0-201-44138-3 (9780201441383)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
(Each chapter ends with Key Terms and Review Exercises.)
Prerequisites for Calculus.
Lines.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
Limits and Continuity.
Rates of Change and Limits.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
Derivatives.
Derivative of a Function.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus at Work.
Applications of Derivatives.
Extreme Values of Functions.
Mean Value Theorem.
Connecting f' and f' with the Graph of f.
Modeling and Optimization.
Linearization and Newton's Method.
Related Rates.
The Definite Integral.
Estimating with Finite Sums.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Key Terms.
Calculus At Work.
Differential Equations and Mathematical Modeling.
Antiderivatives and Slope Fields.
Integration by Substitution.
Integration by Parts.
Exponential Growth and Decay.
Population Growth.
Numerical Methods.
Calculus At Work.
Applications of Definite Integrals.
Integral as Net Change.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus at Work.
L'Hopital's Rule, Improper Integrals, and Partial Fractions.
L'Hopital's Rule.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
Infinite Series.
Power Series.
Taylor Series.
Taylor's Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus at Work.
Parametric, Vector, and Polar Functions.
Parametric Functions.
Vectors in the Plane.
Vector-valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
Cumulative Review.
Appendices.
Formulas from Precalculus Mathematics.
Mathematical Induction.
Using the Limit Definition.
Proof of the Chain Rule.
Conic Sections.
Hyperbolic Functions.
Brief Table of Integrals.
Glossary.
Selected Answers/Solutions.
Applications Index.
Index.
Prerequisites for Calculus.
Lines.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
Limits and Continuity.
Rates of Change and Limits.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
Derivatives.
Derivative of a Function.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus at Work.
Applications of Derivatives.
Extreme Values of Functions.
Mean Value Theorem.
Connecting f' and f' with the Graph of f.
Modeling and Optimization.
Linearization and Newton's Method.
Related Rates.
The Definite Integral.
Estimating with Finite Sums.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Key Terms.
Calculus At Work.
Differential Equations and Mathematical Modeling.
Antiderivatives and Slope Fields.
Integration by Substitution.
Integration by Parts.
Exponential Growth and Decay.
Population Growth.
Numerical Methods.
Calculus At Work.
Applications of Definite Integrals.
Integral as Net Change.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus at Work.
L'Hopital's Rule, Improper Integrals, and Partial Fractions.
L'Hopital's Rule.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
Infinite Series.
Power Series.
Taylor Series.
Taylor's Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus at Work.
Parametric, Vector, and Polar Functions.
Parametric Functions.
Vectors in the Plane.
Vector-valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
Cumulative Review.
Appendices.
Formulas from Precalculus Mathematics.
Mathematical Induction.
Using the Limit Definition.
Proof of the Chain Rule.
Conic Sections.
Hyperbolic Functions.
Brief Table of Integrals.
Glossary.
Selected Answers/Solutions.
Applications Index.
Index.