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Description:

This edition offers students a clearer understanding of calculus and insight into mathematics. It includes a wealth of rich problem sets which give relevance to calculus for students.

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Book details

List price: $224.95 Edition: 9th Copyright year: 2003 Publisher: John Wiley & Sons, Incorporated Publication date: 12/24/2002 Binding: Hardcover Pages: 1280 Size: 8.75" wide x 10.50" long x 1.75" tall Weight: 5.830 Language: English

AuthorTable of Contents

Precalculus Review

What is Calculus?

Review of Elementary Mathematics

Review of Inequalities

Coordinate Plane

Analytic Geometry

Functions

The Elementary Functions

Combinations of Functions

A Note on Mathematical Proof; Mathematical Induction

Limits and Continuity

The Limit Process (An Intuitive Introduction)

Definition of Limit

Some Limit Theorems

Continuity

The Pinching Theorem; Trigonometric Limits

Two Basic Theorems

The Derivative; The Process of Differentiation

The Derivative

Some Differentiation Formulas

Thed/dx Notation Derivatives of Higher Order

The Derivative as a Rate of Change

The Chain Rule

Differentiating the Trigonometric Functions

Implicit Differentiation Rational Powers

The Mean-Value Theorem; Applications of the First and Second Derivatives

The Mean-Value Theorem

Increasing and Decreasing Functions

Local Extreme Values

Endpoint Extreme Values; Absolute Extreme Values

Some Max-Min Problems

Concavity and Points of Inflection

Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps

Some Curve Sketching

Velocity and Acceleration; Speed

Related Rates of Change Per Unit Time

Differentials

Newton-Raphson Approximations

Integration

An Area Problem; A Speed-Distance Problem

The Definite Integral of a Continuous Function

The Function f(x) = Integral from a to x of f(t) dt

The Fundamental Theorem of Integral Calculus

Some Area Problems

Indefinite Integrals

Working Back from the Chain Rule; theu-Substitution

Additional Properties of the Definite Integral

Mean-Value Theorems for Integrals; Average Value of a Function

Some Applications of the Integral

More on Area

Volume by Parallel Cross-Sections; Discs and Washers

Volume by the Shell Method

The Centroid of a Region; PappusA?s Theorem on Volumes

The Notion of Work

Fluid Force

The Transcendental Functions

One-to-One Functions; Inverse Functions

The Logarithm Function, Part I

The Logarithm Function, Part II

The Exponential Function

Arbitrary Powers; Other Bases

Exponential Growth and Decay

The Inverse Trigonometric Functions

The Hyperbolic Sine and Cosine

The Other Hyperbolic Functions

Techniques of Integration

Integral Tables and Review

Integration by Parts

Powers and Products of Trigonometric Functions

Integrals Featuring Square Root of (a^2 - x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 - a^2)

Rational Functions; Partial Functions

Some Rationalizing Substitutions

Numerical Integration

Differential Equations

First-Order Linear Equations

Integral Curves; Separable Equations

The Equationya??a?? +aya??+by = 0

The Conic Sections; Polar Coordinates; Parametric Equations

Geometry of Parabola, Ellipse, Hyperbola

Polar Coordinates

Graphing in Polar Coordinates

Area in Polar Coordinates

Curves G

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