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# MULTIVARI CALCULUS (QI)(H) MATH 2210

Utah State University

GPA 3.66

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This 2 page Class Notes was uploaded by Benton Yundt on Wednesday October 28, 2015. The Class Notes belongs to MATH 2210 at Utah State University taught by Bryan Bornholdt in Fall. Since its upload, it has received 8 views. For similar materials see /class/230414/math-2210-utah-state-university in Mathematics (M) at Utah State University.

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Date Created: 10/28/15

MATH 2210 Chapter 12 Review Know the following concepts and skills thoroughly Time will not allow you to perform all of the integration but you will likely be asked to set up nearly every possibility Method of Lagrange Multipliers 118 Riemann Sum de nition of double integral 121 mam1 22 fxy AA D 11 1 Average value of x on a region D 121 1 fav 7 fxydA g 141quot Fubini s Theorem for rectangular regions 122 and 127 Volume ofa solid using double integrals 122 and 123 Area ofa region using double integrals 123 AD D 0 Polar Coordinates and Double Integrals 124 0 Total charge density mass and centroids 125 and 127 0 Surface area 126 Know how to compute the cross product of 2 vectors 0 Triple integrals 127 and 128 0 Volume of a solid using triple integrals VE j dV E Key Skills Sketching the region D of integration of a double integral Changing the order of integration in a double integral by moving through the region D first parallel to the xaXis and then in y OR moving through the region D first parallel to the anis and then in x Converting to polar coordinates in a double integral over a region bounded by circles or polar curves Example the rose r cos 639 Calculating the cross product of 2 vectors Determining the order of integration in a triple integral Step 1 First visualize moving through the region with respect to a particular variable Then project the region onto the coordinate plane of the remaining two variables Step 2 Determine the limits of integration of the inner integral in terms of the outer two variables Step 3 Determine the limits of the middle integral by moving through the projected region in one of the remaining variables These may be in terms of the outer variable or constants Step 4 Determine the limits of the remaining variable These will be constants Review your homework problems well as this is your best preparation MATH 2210 Review of Topics Limits and Continuity Partial Derivatives Linear Differentials df dx fydy fzdz Linear Approximation off Lx fx05y0520x x0fxo yo zoy y0fzx05y0520Z ZO Gradient of a scalar function f Direction of steepest increase Level curves level sets of a function surface Directional Derivatives projection of gradient onto a unit vector u The Chain Rule tree diagram Implicit differentiation Optimization critical points second derivative tests saddle point Lagrange Multipliers Riemann Sum and de nite integrals Double and triple integrals and the region of integration Reversing the order of integration Balance first Moments and Center of Mass Surface Area Vector function r xi yj zk Vector Fields F Pi Qj Rk Gradient Field conservative elds potential function Curl and divergence of velocity uid field Flux across a boundary circulation along a curve Green s Theorem Stokes Theorem Divergence Theorem

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