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Our last month will be combining the multivariate calculus with vector calculus and this culminates in several important theorems which tie all of Calculus III topics together into several beautiful and useful packages!
Calculus 3 Concepts Cartesian coords in 3D given two points: (x1,y1,z1)and(2 2,z2), Distance between them:p ( x 1 2)2+(y z Midpoint: (x1 +2 2, y1 2 2, z1+z2 2) Sphere with center (h,k,l) and radius r: (x h ) 2+(y k z l =r Vectors Vector: ~u Unit Vector: ˆu Magnitude: ||~u = q 2 1 +u2 2 +u2 3 Unit Vector: ˆu= ~u ||~u Dot Product ~u·~v ...
Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 12/9/2022 7:11:52 AM
Created Date: 3/16/2008 2:13:01 PM
I can write the formula using algebra, which allows any constant speed sand any time of travel t: The distance f at constant speed s in travel time t is f Ds times t.
P1 =(X1,Y1,Z1), P2= (X2,Y2,Z2) √[(X2 -X1 ) 2 + (Y2-Y1) 2 + (Z2-Z1) 2 ] Vectors. Force points in the direction in which vectors the force acts and its length is a measure of the force's strength. Velocity points in the direction of vector motion and its length is the speed of the moving object.
We will be looking at the equations of graphs in 3-D space as well as vector valued functions and how we do calculus with them. We will also be taking a look at a couple of new coordinate
