Index P...

parabola	Antiderivative of a Parabola
	Example 1: The Square Function
	Examples of Parabolas
	Example 2: Finding focus and directrix
	Problems
	Second Degree Curves (Cases)
	Problems
	Simpson's Rule
parabola.	Parabolas
parabolic cylinder	Quadric Cylinders
	Example 2: Parabolic Cylinder
paraboloid	Stokes' Theorem
	Example 2
parallelogram	Theorem 1: The Line
	Example 7: Diagonals of a Parallelogram Bisect Each Other (Proof)
parametric curve	Parametric Curves
parametric equation	Theorem 1: The Line
	Problems
	Example 1
	Parametic Equations
partial derivatives	Partial Derivatives
	Definition
	"Round d" Notation
	Example 1
	Example 2
	Partial Derivatives of Functions of Three or More Variables
	Example 3
	Problems
	Area Of A Smooth Surface
	Example 1
	Example 2
	Oriented Surface
	Surface Integral
	Example 3
	Problems
partial sum	Sums of Infinite Series
	Example 2: Partial Sum Sequence
	Example 1: Alternating Harmornic Series Converging
	Alternating Series Test
	Theorem 1: Converging Geometric Series
partial sums	Alternating Series Test
particular	Example 5
particular solution	First Order Differential Equation
	Example 1
	Example 3
	Problems
	Example 2 - Population Growth
	Example 5 - Mass-Spring System
	Problems
	Principle of Second Order Superposition
	Example 3
	Example 4
	Example 6
	Problems (Particular and General Solution of Differential Equations)
partition points	Partition Points
Path Independence Theorem	Gauss' Theorem
path of a ball	Example 2: The Length of the Path of a Ball
perimeter, triangle, vector, zero vector	Example 5
period	Graphs of Solutions of Second Order Homogeneous Linear Equations
perpendicular	Perpendiculars and Parallels - Theorem 3
perpendicular coordinate axes	Vectors and Lines in Space
phase shift	Graphs of Solutions of Second Order Homogeneous Linear Equations
	Problems
pi	Definition of Radians
piecewise smooth boundary	Corollary to Green's Theorem
piecewise smooth curve	Line Integral
	Definitions
	Piecewise Smooth Curve
	Example 3: Piecwise Smooth Curve
plane	Stokes' Theorem
	Example 2
plane in space	Planes in Space
plane region	Green's Theorem
point	Example 4: Determining Whether Tree Points Are on the Same Line
point in space	Points, Lines and Vectors
point-slope equation	Definition
point-slope formula	Theorem 1: Slope Of a Line
polar coordinates	Polar 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
	Problems
	Theorem 1: Direction of a Curve at the Origin
polar form	Example 4
	Problems
polar region	Double Integrals in Polar Coordinates
polynomial	Example 6: Polynomial
	Example 4
polynomial of degree two,	Example 2
population as a function	Example 2 - Population Growth
position	Vectors
position vector	Vectors 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 infinite	Hyperreal Numbers
	Example 3
	Example 4
	Example 5
positive infinitesimal	I. The Extension Principle
positive integers	Some Important Sets of Real Numbers
positive series	Summary of Series Convergence Tests
positive square root	Example 4: Functions Described by Explicitly Giving Its Domain
	Example 5: Functions Within a Closed Interval
positive term series	Positive 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
	Problems
potential function	Potential 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 function	Power Function
power of a complex number	Example 5
power rule	Integration Rules
	Power Rule for Rational Exponents
	Example 4: Power Rule for Rational Exponents
	Theorem 2 (Power Rule)
power series	Theorem 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
	Problems
	Theorem 1: Derivatives And Integrals Of Power Series
	Example 1: Derivative and Integral
	Theorem 2: Radius of Convergence
	Problems
	Example 4
	Taylor Series - Definition
	Theorem 1
	Review of Power Series (MacLaurin Series)
	Problems
	Definition of Power Series
	Corollary: Interval of Convergence
price	Vectors
principle of induction	Principle of Induction
Principle of Superposition	Example 5
	Principle of Superposition
	Second Order Linear Differential Equation with Constant Coefficients
problems	Problems
	Problems
	Problems
	Problems
	Problems
	Problems
	Problems
	Extra Problems for Chapter 2
	Extra Problems
product	Integral of Products
Product Rule	Example 3
purely imaginary number	Example 6
Pythagoras	Distance Between Two Points