The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Index I...

identity functionConstant Function
Identity LawVector Sums - Theorem 1
imaginary partComplex Numbers
imfinite limitsProblems For Section 5.1
implicit differentiationRelated Rates
 Sollution Two: Implicit Differentiation
improper integralCorollary: p Series
improper integral, convergenceExample 8: Integral Test
incrementIndependent and Dependent Variables
 Increment and Total Differentiatial
 Example 1: Increment and Total Differential (Product Function)
 Example 2: Increment and Total Differential (Biquadratic Function)
Increment TheoremNewton's Method
 Increment Theorem for Two Variables
indefinite integralIntroduction
 Indefinite Integral
independent variableDrawing Graphs of Functions
 Example 3: Finding Values of Terms by Substitution
 Example 3: Distace between Two Parting Ships (Three Variables depending on Time)
 Solids of Revolution
 Disc Method
 Example 1: Right Circular Cone
 Region Between Two Curves - Solid of Revolution
 Example 4
 Example 5
 Second Order Homogeneous Linear Equations
independent variablesIndependent and Dependent Variables
indeterminate formRules For Infinitesimal, Finite and Infinite Numbers
inductionPrinciple of Induction
Inequality RuleTheorem 1: Convergent Sum Rules
infiniteApplication of the Principles
 Rules For Infinitesimal, Finite and Infinite Numbers
 Definition: Limit of a Sequence
 Theorem 1: Sequences approaching ∞
 Example 8: Sequences Approaching ∞
infinite double Riemann sumInfinite Double Riemann Sum
infinite hyperreal numbersSummary
infinite limitTheorem 2: Integral Test.
infinite limitsInfinite Limits
 Examples 1 & 2: Three Types of Limits
 Example 3
 Example 4
 Example 5
 Example 6: Polynomial
 Example 7
 Example 8: Sine
 Example 9: Limit for Cos x Does Not Exist
infinite partial sumComparison Test
infinite Riemann sumInfinite Riemann sum
 Theorem: Infinite Riemann Sum
 Numerical Integration
infinite sequenceSeries
infinite seriesTheorem 2: Diverging Geometric Series
 Partial Sum Σ
Infinite Sum TheoremArea Between Two Curves
 Volume of a Solid
 Area of Surface of Revolution
 Parametic Equations
infinitely closeAlgebraic Manipulation of Hyperreal Numbers
 Limits and Curve Sketching
 Example 2
 Problems For Section 5.3
infinitely largeProblems For Section 5.3
infinitely smallInfinitesimal Number
 The Hyperreal Line
infinitesimalTheorem 1: Arbitrary Infinitesimals
 Infinitesimal Number
 The Hyperreal Line
 I. The Extension Principle
 Application of the Principles
 Rules For Infinitesimal, Finite and Infinite Numbers
 Theorem 3:
 Example 1
 Infinite Sum Theorem - Definition
 Theorem 1: Sequences approaching ∞
infinitesimal lengthInfinite Sum Theorem - Proof
infinitesimal microscopeExistence of Limits
 Infinite Sum Theorem - Definition
infinitesimal microscopesThe Hyperreal Line
infitesimalExample 4
initial valueExample 3
initial value problemFirst Order Initial Value Problem
 Solve the Initial Value Problem
 Example 5
 Existence Theorem
 Example 2
 Example 3
inscribed cylinderCylinder Property
integerExample 9: Limit for Cos x Does Not Exist
integer numbersSome Important Sets of Real Numbers
integralAntiderivative of a Line
 Antiderivative of a Parabola
 Antiderivative of Velocity
 Power Function
 Definite Integral
 Theorem 4: Integrals of Trigonometric Functions
 Power Series Formulas
 Area of a Semicircle
integral of a logarithmic functionExample 3
integral of productsIntegral of Products
integral testSummary of Series Convergence Tests
integrals of logarithmic functionsProblems
integrationSimple Examples of Integration
 Example 8
 Example 5: Area Under a Line
 Extra Problems
integration by change of variablesProblems
integration by partsExample 2
 Example 8
integration constantElimination of the Integration Constant
 Integration Constant
integration rulesIntegration Rules
integration theoremsIntroduction
interior critical pointSecond Derivative Test
 Example 7
interior pointInterior Points of Intervals
 Direct Test
Intermediate Value TheoremInverse Trigonometric Function - Definitions
intervalInterior Points of Intervals
 Second Derivative Test
 Example 7
 Corollary: Interval of Convergence
interval of convergenceExample 5: Interval of Convergence
inverse functionInverse Functions
 Not Every Function Has a Inverse Function
inverse function ruleInverse Function Rule
inverse functionsCommon Inverse Functions
 Power Rule for Rational Exponents
irrotationalExample 3
 Example 5
Iterated Integral TheoremMass and Density

Last Update: 2006-11-25