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

Index P...

parabolaAntiderivative of a Parabola
 Example 1: The Square Function
 Examples of Parabolas
 Example 2: Finding focus and directrix
 Second Degree Curves (Cases)
 Simpson's Rule
parabolic cylinderQuadric Cylinders
 Example 2: Parabolic Cylinder
paraboloidStokes' Theorem
 Example 2
parallelogramTheorem 1: The Line
 Example 7: Diagonals of a Parallelogram Bisect Each Other (Proof)
parametric curveParametric Curves
parametric equationTheorem 1: The Line
 Example 1
 Parametic Equations
partial derivativesPartial Derivatives
 "Round d" Notation
 Example 1
 Example 2
 Partial Derivatives of Functions of Three or More Variables
 Example 3
 Area Of A Smooth Surface
 Example 1
 Example 2
 Oriented Surface
 Surface Integral
 Example 3
partial sumSums of Infinite Series
 Example 2: Partial Sum Sequence
 Example 1: Alternating Harmornic Series Converging
 Alternating Series Test
 Theorem 1: Converging Geometric Series
partial sumsAlternating Series Test
particularExample 5
particular solutionFirst Order Differential Equation
 Example 1
 Example 3
 Example 2 - Population Growth
 Example 5 - Mass-Spring System
 Principle of Second Order Superposition
 Example 3
 Example 4
 Example 6
 Problems (Particular and General Solution of Differential Equations)
partition pointsPartition Points
Path Independence TheoremGauss' Theorem
path of a ballExample 2: The Length of the Path of a Ball
perimeter, triangle, vector, zero vectorExample 5
periodGraphs of Solutions of Second Order Homogeneous Linear Equations
perpendicularPerpendiculars and Parallels - Theorem 3
perpendicular coordinate axesVectors and Lines in Space
phase shiftGraphs of Solutions of Second Order Homogeneous Linear Equations
piDefinition of Radians
piecewise smooth boundaryCorollary to Green's Theorem
piecewise smooth curveLine Integral
 Piecewise Smooth Curve
 Example 3: Piecwise Smooth Curve
planeStokes' Theorem
 Example 2
plane in spacePlanes in Space
plane regionGreen's Theorem
pointExample 4: Determining Whether Tree Points Are on the Same Line
point in spacePoints, Lines and Vectors
point-slope equationDefinition
point-slope formulaTheorem 1: Slope Of a Line
polar coordinatesPolar Coordinates
 Example 1: Ploting Points
 Example 2: Circle and Straight Line
 Example 3: Spiral of Archimedes
 Example 4: Parabola
 Example 5: Hyperbola
 Example 6: Sine
 Example 7: Spiral and Circle
 Theorem 1: Direction of a Curve at the Origin
polar formExample 4
polar regionDouble Integrals in Polar Coordinates
polynomialExample 6: Polynomial
 Example 4
polynomial of degree two,Example 2
population as a functionExample 2 - Population Growth
position vectorVectors and Plane Geometry
 Example 5: Midpoint of a Linesegment (Proof)
 Example 6: Finding the Midpoint of a Line Segment
 Example 7: Diagonals of a Parallelogram Bisect Each Other (Proof)
 Lines in Space
 Position, Direction, and Normal Vectors
positive infiniteHyperreal Numbers
 Example 3
 Example 4
 Example 5
positive infinitesimalI. The Extension Principle
positive integersSome Important Sets of Real Numbers
positive seriesSummary of Series Convergence Tests
positive square rootExample 4: Functions Described by Explicitly Giving Its Domain
 Example 5: Functions Within a Closed Interval
positive term seriesPositive Term Series - Theorem 1
 Example 1: Harmonic Series Diverges to ∞
 Example 2: Geometric Series
 Comparison Test
 Example 3: Test for Convergence
 Example 4: Test for Convergence
 Limit Comparison Test
 Example 5: Limit Comparison Test
 Theorem 2: Integral Test.
 Corollary: p Series
 Example 6: p Series
 Example 7: Text for Convergence
 Example 8: Integral Test
potential functionPotential Function of the Vector Field
 Example 1
 Theorem 1
 Example 2
 Example 3
 Theorem 2 (Path Independence Theorem)
 Example 3 (Continued)
 Example 4
 Example 5
 Lemma About Derivatives Of Partial Integrals
 Proof of Theorem 1
 Theorem 1 (Three Variables)
power functionPower Function
power of a complex numberExample 5
power ruleIntegration Rules
 Power Rule for Rational Exponents
 Example 4: Power Rule for Rational Exponents
 Theorem 2 (Power Rule)
power seriesTheorem 1: Convergence and Divergence
 Example 1: Interval Of Convergence
 Example 2: Interval of Convergence (Half-open)
 Example 3: Interval of Convergence (-∞, ∞)
 Example 4: Radius of Convergence
 Example 5: Interval of Convergence
 Theorem 1: Derivatives And Integrals Of Power Series
 Example 1: Derivative and Integral
 Theorem 2: Radius of Convergence
 Example 4
 Taylor Series - Definition
 Theorem 1
 Review of Power Series (MacLaurin Series)
 Definition of Power Series
 Corollary: Interval of Convergence
principle of inductionPrinciple of Induction
Principle of SuperpositionExample 5
 Principle of Superposition
 Second Order Linear Differential Equation with Constant Coefficients
 Extra Problems for Chapter 2
 Extra Problems
productIntegral of Products
Product RuleExample 3
purely imaginary numberExample 6
PythagorasDistance Between Two Points

Last Update: 2006-11-25