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Contents
Contents
Index
Contents
Preface
Computers
Definite and Indefinite Integrals
The Definite Integral
The definition of area under curve
Relation between velocity and area
Definition of Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and Change
Indefinite Integrals
Examples
Physical Intuition
Substitution and Symmetry
The Substitution Rule
The Substitution Rule for Definite Integrals
Symmetry
Applications to Areas, Volume, and Averages
Using Integration to Determine Areas Between Curves
Examples
Computing Volumes of Surfaces of Revolution
Average Values
Polar Coordinates and Complex Numbers
Polar Coordinates
Areas in Polar Coordinates
Examples
Complex Numbers
Polar Form
Complex Exponentials and Trig Identities
Trigonometry and Complex Exponentials
Integration Techniques
Integration By Parts
Trigonometric Integrals
Some Remarks on Using Complex-Valued Functions
Trigonometric Substitutions
Factoring Polynomials
Integration of Rational Functions Using Partial Fractions
Approximating Integrals
Improper Integrals
Convergence, Divergence, and Comparison
Sequences and Series
Sequences
Series
The Integral and Comparison Tests
Estimating the Sum of a Series
Tests for Convergence
The Comparison Test
Absolute and Conditional Convergence
The Ratio Test
The Root Test
Power Series
Shift the Origin
Convergence of Power Series
Taylor Series
Applications of Taylor Series
Estimation of Taylor Series
Some Differential Equations
Separable Equations
Logistic Equation
Index
About this document ...
William Stein 2006-03-15
