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 |