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Calculus Demystified A Self Teaching Guide

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ISBN-10: 0071393080

ISBN-13: 9780071393089

Edition: 2003

Authors: Steven G. Krantz

List price: $19.95
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This is a self-teaching guide for anyone who wants to learn or to refresh their knowledge of calculus without taking a formal course. Frequent review, assessment, and application of the ideas should help students to retain and to internalize all of the important concepts.
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Book details

List price: $19.95
Copyright year: 2003
Publisher: McGraw-Hill Professional Publishing
Publication date: 8/1/2002
Binding: Paperback
Pages: 368
Size: 7.25" wide x 8.75" long x 1.00" tall
Weight: 1.342

Preface
Basics
Introductory Remarks
Number Systems
Coordinates in One Dimension
Coordinates in Two Dimensions
The Slope of a Line in the Plane
The Equation of a Line
Loci in the Plane
Trigonometry
Sets and Functions
Examples of Functions of a Real Variable
Graphs of Functions
Plotting the Graph of a Function
Composition of Functions
The Inverse of a Function
A Few Words About Logarithms and Exponentials
Foundations of Calculus
Limits
One-Sided Limits
Properties of Limits
Continuity
The Derivative
Rules for Calculating Derivatives
The Derivative of an Inverse
The Derivative as a Rate of Change
Applications of the Derivative
Graphing of Functions
Maximum/Minimum Problems
Related Rates
Falling Bodies
The Integral
Introduction
Antiderivatives and Indefinite Integrals
The Concept of Antiderivative
The Indefinite Integral
Area
Signed Area
The Area Between Two Curves
Rules of Integration
Linear Properties
Additivity
Indeterminate Forms
l'Hopital's Rule
Introduction
l'Hopital's Rule
Other Indeterminate Forms
Introduction
Writing a Product as a Quotient
The Use of the Logarithm
Putting Terms Over a Common Denominator
Other Algebraic Manipulations
Improper Integrals: A First Look
Introduction
Integrals with Infinite Integrands
An Application to Area
More on Improper Integrals
Introduction
The Integral on an Infinite Interval
Some Applications
Transcendental Functions
Introductory Remarks
Logarithm Basics
A New Approach to Logarithms
The Logarithm Function and the Derivative
Exponential Basics
Facts About the Exponential Function
Calculus Properties of the Exponential
The Number e
Exponentials with Arbitrary Bases
Arbitrary Powers
Logarithms with Arbitrary Bases
Calculus with Logs and Exponentials to Arbitrary Bases
Differentiation and Integration of log[subscript a] x and a[superscript x]
Graphing of Logarithmic and Exponential Functions
Logarithmic Differentiation
Exponential Growth and Decay
A Differential Equation
Bacterial Growth
Radioactive Decay
Compound Interest
Inverse Trigonometric Functions
Introductory Remarks
Inverse Sine and Cosine
The Inverse Tangent Function
Integrals in Which Inverse Trigonometric Functions Arise
Other Inverse Trigonometric Functions
An Example Involving Inverse Trigonometric Functions
Methods of Integration
Integration by Parts
Partial Fractions
Introductory Remarks
Products of Linear Factors
Quadratic Factors
Substitution
Integrals of Trigonometric Expressions
Applications of the Integral
Volumes by Slicing
Introduction
The Basic Strategy
Examples
Volumes of Solids of Revolution
Introduction
The Method of Washers
The Method of Cylindrical Shells
Different Axes
Work
Averages
Arc Length and Surface Area
Arc Length
Surface Area
Hydrostatic Pressure
Numerical Methods of Integration
The Trapezoid Rule
Simpson's Rule
Bibliography
Solutions to Exercises
Final Exam
Index