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# CSU Pomona - MATH 2140 - Study Guide - Final

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CSU Pomona - MATH 2140 - Study Guide - Final

##### Description: This study guide overs the main points that can possibly be on the final exam.
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Join more than 18,000+ college students at California State Polytechnic University who use StudySoup to get ahead
##### Description: This study guide overs the main points that can possibly be on the final exam.
2 Pages 55 Views 44 Unlocks
• Notes, Study Guides, Flashcards + More!

Unformatted text preview: che Parliava Ch 2:03 problems) Preparkes of del products 7. N. V 1. V.. 2. V.w.w.y 4.10) - (.w)w) Properties or cross product : x 18) - 19 Tangert plones 2-2. = fal XY-Y+f;(o) y-yo) max/min Problem - Find Critico Point fx=0& y=0 Studysou Soup 2.X2: det () edut la 1) = 19:|- ae-be 3x3: (1 3) -182.-442+ clie A = (fm-qui-em-gnij + (el-fWK Equestions of lines planes: Parametric equations X = X Y yo +b+ Scalo equat of plane al X-X) + b( yo) + C(2-2) = 0 plane passes through (X, Yo, 2.) repel vector a,b,c) calar form of the equation of a line! F(t) = To ty =<xo, Yo, Zo>+ t <a,b,c> Ch 13: vector valued fxns Position, Velocity, auclation Position (4) velocity: r'(+) . accelerationir"(+) Are length: Le sip'Ald+ Normal Tangential Normal Vectors: Tangental componets (ar): - Then look for D determine if it is a saddle point, or local max/min - local min if D>0% f xx>0 - local max if D>0.\$ f xx<0 - Saddle point if A Study Soup Study Soup Ch 15. Multiple integrals - Double Integral (speegel) SS f(x)dA R = {1xx)| asxsb, csysd} Polor Coordinates r = 1x2 + y2 "() V: . r' lir'(+) Normal Componets (an): The point in polar coordinates lir' (t) r"(+) 11 Kur .X:rcoso y=rsino '(U)Application to Area SS FOYDA - STF (72016, smordo R={(re)) asr biases 5) tiple Integral : Consider a Exn fix ) 3 Variables defined a A Study Soup box Study Soup Study Soup B = {cxM.2)| asxsb, leyed, razsss ISS FOX,Y, 2)dx dydz Apolication of Volume let Ebe a solid in 3-D If we write E as = {x,y,2)) asx5b, 3104729-00); U, WXN) 2 SUR UN} Ch 16 Integrals vector field - line integrals' f4 (7(4) 1F%C4 lat) be able to compute Solid tetrahedron JSS xZ dv StudySoup A Study Soup Study Soup Study Soup Parametrize the curve fim FIX YU. z.)As-SFCX,Y,Z)ds - S F(ruli'culdt were play at = firu-dipleDeterming if vector field is conservetive o F(X,Y)= P(x, y) { 4 QUX) a vector field on region D P(x,y), Q.(x,y), have continues 1st partial derivatives on D If Dis simply connected Then, the vector field is conservative if and only if Study Soup a 20 A Study Soup ay 2x Study Soup Study Soup Study Soup Greens Theorma Sport@dy = Js (29-24) de D A Study Soup cinos pas dinos Stud

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