The Ultimate Math 192 Cheat Sheet

The Ultimate Math 192 Cheat Sheet - Area of a Smooth...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Area of a Smooth Surface: = d c b a v u dv du A r r Parametric Surface Integral: = d c b a v u S dv du v u h v u g v u f G d z y x G r r )) , ( ), , ( ), , ( ( ) , , ( Partial Derivatives: ) , ( ) , ( ) , ( ) , ( lim 2 2 2 ) , ( b a f b a f dx f dy dydx f f dx f f h y x f y h x f h x f yx xy xy xx y x = = = =- + = Implicit Differentiation: y x F F dx dy- = Gradient Field: k j i z f y f x f f + + = Directional Derivative: u u u = = f f D ds df P P ) ( , , , ) , , ( z y x P c x y x f = = Tangent Plane: ) )( ( ) )( ( ) )( ( =- +- +- z z P f y y P f x x P f z y x Normal Line: t P f z z t P f y y t P f x x z y x ) ( , ) ( , ) ( + = + = + = )) , ( , , ( ) , ( y x f y x P y x f z = = Tangent Plane: ) ( ) )( ( ) )( ( =--- +- z z y y P f x x P f y x Differential: dy y x f dx y x f df y x ) , ( ) , ( + = Estimating Change: ( 29 ds f df P = u Coordinate Conversion Formulas Cylindrical to Spherical to Spherical to Rectangular Rectangular Cylindrical z z r y r x = = = sin cos cos sin sin cos sin = = = z y x = = = cos sin z r d d d d dr r dz dz dy dx dV sin 2 = =...
View Full Document

This note was uploaded on 02/13/2008 for the course CHEM 3890 taught by Professor Hines, m during the Fall '08 term at Cornell University (Engineering School).

Page1 / 2

The Ultimate Math 192 Cheat Sheet - Area of a Smooth...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online