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ADV MULTIVAR CALC 1 MATH 324

UW
GPA 3.76

Travis Kopp

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COURSE
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Travis Kopp
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Class Notes
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Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 324 at University of Washington taught by Travis Kopp in Fall. Since its upload, it has received 56 views. For similar materials see /class/192063/math-324-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15
Math 324 Midterm Review Sheet Fall 20081 This is a list of topics you need to be familiar with as covered in class and on the home work for the midterm on Friday along with the sections in the book where they are discussed Preliminaries 0 partial differentiation 143 o polar coordinates 103 1 convert functions fy to polar coordinates 2 polar curves 7 90 0 vectors 1 basic properties 122 2 dot product7 cross product 1237 124 3 equation for a plane 125 o parameterized curves 131 Double Integrals o iterated integrals7 Fubini7s theorem7 partial integration 152 0 type I type II regions7 changing order of integration 153 0 double integration in polar coordinates 154 o calculating mass7 center of mass7 moments of inertia 155 0 change of variables in two variables 159 Line Integrals 0 line integral of a function with respect to arclength 162 0 line integral of a function with respect to X and y 162 Surface Integrals o parameterized surfaces 166 1 surfaces of graphs7 eg z fy 2 planes 3 the sphere of radius R 0 surface integrals of functions 167 Good Luck on the exam Math 324 Final Review Sheet Fall 2008 1 This is a list of topics you need to be familiar with as covered in class and on the homework for the nal on Thursday along with the sections in the book where they are discussed Preliminaries 0 partial differentiation 143 o polar coordinates 103 1 convert functions fy to polar coordinates 2 polar curves 7 90 0 vectors 1 basic properties 122 2 dot product7 cross product 1237 124 3 equation for a plane 125 o parameterized curves 131 Chain Rule and Gradient o generalized chain rule 145 0 gradient 146 1 de nition and interpretation of gradient 2 chain rule in terms of gradient 3 directional derivatives 4 using the gradient to nd a normal to surface de ned by Fy7 z k Double Integrals o iterated integrals7 Fubini7s theorem7 partial integration 152 0 type I type ll regions7 changing order of integration 153 0 double integration in polar coordinates 154 o calculating mass7 center of mass7 moments of inertia 155 0 change of variables in two variables 159 Triple Integrals 0 type l7 ll and Ill regions7 changing order of integration 157 o calculating mass7 center of mass7 moments of inertia 156 0 change of variables in three variables 159 o spherical and cylindrical coordinates and integration 158 Math 324 Final Review Sheet Line Integrals 0 line integral of a function with respect to arclength 162 o calculating mass7 center of mass7 moments of inertia 162 0 line integral of a function with respect to X and y 162 0 line integral of a vector eld 162 Surface Integrals o parameterized surfaces 166 1 surfaces of graphs7 eg z fy 2 planes 3 the sphere of radius R 0 surface integrals of functions 167 o calculating mass7 center of mass7 moments of inertia 167 o orientation on surfaces 167 1 de nition of an orientation 2 induced orientation on boundary curves 0 surface integrals ux of a vector eld 167 Derivatives o the gradient Vf 146 o in two dimensions7 the vector eld derivative dF Q1 7 Pg 164 o in three dimensions7 the curl V gtlt F 165 o divergence V F 165 o Laplace operator sz V Vf 165 0 basic properties of these 1 dVf07 VgtltVf0 2 divcurlF0 Fall 2008 2 Math 324 Final Review Sheet Fall 2008 3 Theorems 0 Fundamental Theorem of Line lntegrals 163 1 statement of theorem 2 conservative vector elds have path independent line integrals 3 vector elds with path independent line integrals are conservative o Green7s Theorem 164 statement of Green7s Theorem using Green7s Theorem to calculate area 1 2 3 simple connectedness in the plane 4 if F is de ned on a simply connected region and dF E 07 then F is conservative 5 Green7s theorem on regions 77with holes 7 ie not simply connected 0 Stoke7s Theorem 168 H statement of Stoke7s Theorem 3 simple connectedness in space 9 if F is de ned on a simply connected region in space and V gtlt F E 07 then F is conservative r ux of curl F across a closed surface is always 0 o Divergence Theorem 169 Good Luck on the exam

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