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by Schaum, Frank Jr. Ayres and Elliott Eds. Mendelson

Edition: 4TH 99Copyright: 1999

Publisher: McGraw-Hill Publishing Company

Published: 1999

International: No

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Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­more than104,000 copies were bought of the prior edition!­­includes problems and examples using graphing calculators.

Linear Coordinate Systems.

Absolute Value.

Inequalities.

Rectangular Coordinate Systems.

Lines.

Circles.

Equations and Their Graphs.

Functions.

Limits.

Continuity.

The Derivative.

Rules for Differentiating Functions.

Implicit Differentiation.

Tangent and Normal Lines.

Law of the Mean.

Increasing and Decreasing Functions.

Maximum and Minimum Values.

Curve Sketching.

Concavity.

Symmetry.

Review of Trigonometry.

Differentiation of Trigonometric Functions.

Inverse Trigonometric Functions.

Rectilinear and Circular Motion.

Related Rates.

Differentials.

Newton's Method.

Antiderivatives.

The Definite Integral.

Area Under a Curve.

The Fundamental Theorem of Calculus.

The Natural Logarithm.

Exponential and Logarithmic Functions.

L'Hopital's Rule.

Exponential Growth and Decay.

Applications of Integration I: Area and Arc Length.

Applications of Integration II: Volume.

Techniques of Integration I: Integration by Parts.

Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions.

Techniques of Integration III: Integration by Partial Fractions.

Miscellaneous Substitutions.

Improper Integrals.

Applications of Integration II: Area of A Surface of Revolution.

Parametric Representation of Curves.

Curvature. Plane Vectors.

Curvilinear Motion.

Polar Coordinates.

Infinite Sequences.

Infinite Series.

Series with Positive Terms.

The Integral Test.

Comparison Tests.

Alternating Series.

Absolute and Conditional Convergence.

The Ratio Test. Power Series.

Taylor and Maclaurin Series.

Taylor's Formual with Remainder.

Partial Derivatives.

Total Differential.

Differentiability. Chain Rules.

Space Vectors.

Surface and Curves in Space.

Directional Derivatives.

Maximum and Minimum Values.

Vector Differentiation and Integration.

Double and Iterated Integrals.

Centroids and Moments of Inertia of Plane Areas.

Double Integration Applied to Volume Under a Surface and the Area of A Curved Surface.

Triple Integrals.

Masses of Variable Density.

Differential Equations of First and Second Order.

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Summary

Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­more than104,000 copies were bought of the prior edition!­­includes problems and examples using graphing calculators.

Table of Contents

Linear Coordinate Systems.

Absolute Value.

Inequalities.

Rectangular Coordinate Systems.

Lines.

Circles.

Equations and Their Graphs.

Functions.

Limits.

Continuity.

The Derivative.

Rules for Differentiating Functions.

Implicit Differentiation.

Tangent and Normal Lines.

Law of the Mean.

Increasing and Decreasing Functions.

Maximum and Minimum Values.

Curve Sketching.

Concavity.

Symmetry.

Review of Trigonometry.

Differentiation of Trigonometric Functions.

Inverse Trigonometric Functions.

Rectilinear and Circular Motion.

Related Rates.

Differentials.

Newton's Method.

Antiderivatives.

The Definite Integral.

Area Under a Curve.

The Fundamental Theorem of Calculus.

The Natural Logarithm.

Exponential and Logarithmic Functions.

L'Hopital's Rule.

Exponential Growth and Decay.

Applications of Integration I: Area and Arc Length.

Applications of Integration II: Volume.

Techniques of Integration I: Integration by Parts.

Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions.

Techniques of Integration III: Integration by Partial Fractions.

Miscellaneous Substitutions.

Improper Integrals.

Applications of Integration II: Area of A Surface of Revolution.

Parametric Representation of Curves.

Curvature. Plane Vectors.

Curvilinear Motion.

Polar Coordinates.

Infinite Sequences.

Infinite Series.

Series with Positive Terms.

The Integral Test.

Comparison Tests.

Alternating Series.

Absolute and Conditional Convergence.

The Ratio Test. Power Series.

Taylor and Maclaurin Series.

Taylor's Formual with Remainder.

Partial Derivatives.

Total Differential.

Differentiability. Chain Rules.

Space Vectors.

Surface and Curves in Space.

Directional Derivatives.

Maximum and Minimum Values.

Vector Differentiation and Integration.

Double and Iterated Integrals.

Centroids and Moments of Inertia of Plane Areas.

Double Integration Applied to Volume Under a Surface and the Area of A Curved Surface.

Triple Integrals.

Masses of Variable Density.

Differential Equations of First and Second Order.

Publisher Info

Publisher: McGraw-Hill Publishing Company

Published: 1999

International: No

Published: 1999

International: No

Absolute Value.

Inequalities.

Rectangular Coordinate Systems.

Lines.

Circles.

Equations and Their Graphs.

Functions.

Limits.

Continuity.

The Derivative.

Rules for Differentiating Functions.

Implicit Differentiation.

Tangent and Normal Lines.

Law of the Mean.

Increasing and Decreasing Functions.

Maximum and Minimum Values.

Curve Sketching.

Concavity.

Symmetry.

Review of Trigonometry.

Differentiation of Trigonometric Functions.

Inverse Trigonometric Functions.

Rectilinear and Circular Motion.

Related Rates.

Differentials.

Newton's Method.

Antiderivatives.

The Definite Integral.

Area Under a Curve.

The Fundamental Theorem of Calculus.

The Natural Logarithm.

Exponential and Logarithmic Functions.

L'Hopital's Rule.

Exponential Growth and Decay.

Applications of Integration I: Area and Arc Length.

Applications of Integration II: Volume.

Techniques of Integration I: Integration by Parts.

Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions.

Techniques of Integration III: Integration by Partial Fractions.

Miscellaneous Substitutions.

Improper Integrals.

Applications of Integration II: Area of A Surface of Revolution.

Parametric Representation of Curves.

Curvature. Plane Vectors.

Curvilinear Motion.

Polar Coordinates.

Infinite Sequences.

Infinite Series.

Series with Positive Terms.

The Integral Test.

Comparison Tests.

Alternating Series.

Absolute and Conditional Convergence.

The Ratio Test. Power Series.

Taylor and Maclaurin Series.

Taylor's Formual with Remainder.

Partial Derivatives.

Total Differential.

Differentiability. Chain Rules.

Space Vectors.

Surface and Curves in Space.

Directional Derivatives.

Maximum and Minimum Values.

Vector Differentiation and Integration.

Double and Iterated Integrals.

Centroids and Moments of Inertia of Plane Areas.

Double Integration Applied to Volume Under a Surface and the Area of A Curved Surface.

Triple Integrals.

Masses of Variable Density.

Differential Equations of First and Second Order.