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

Last Update: 2006-11-25