Calculus One and Several Variables

ISBN-10: 0471231207

ISBN-13: 9780471231202

Edition: 9th 2003 (Revised)

List price: $224.95
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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

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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