2.05.4.Literacy - Accumulation Authors: Bill Davis, Horacio...

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Accumulation Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 2.05 2D Integrals and the Gauss-Green Formula LITERACY What you should be able to handle away from the machine. · L.1) Here's a plot of a certain surface z = f @ x, y D over the rectangle R in the xy-plane consisting of all points 8 x, y, 0 < with - 2 § x § 2 and - 1 § y § 3: Here's an embellishment of the same plot: Each of the vertical plotted poles has its base at a point 8 x, y, 0 < in the rectangle R. What does the length of each plotted pole measure? · L.2) Given a specific function f @ x, y D , how do you expect the output from the Mathematica instructions Plot3D[f[x,y], {x,0,4}, {y, -3, 5}] and ParametricPlot3D[{x, y, f[x,y]}, {x, 0, 4}, {y, -3, 5}] to be related? · L.3) Here's a plot of a certain surface z = f @ x, y D over (or under) the rectangle R in the xy-plane consisting of all points 8 x, y, 0 < with - 1 § x § 2 amd - 1 § y § 3 shown with a plot of R: Why does the plot signal that Ÿ Ÿ R f @ x, y D x y > 0? · L.4) Here's a plot of a certain surface z = f @ x, y D over (or under) the rectangle R in the xy-plane consisting of all points 8 x, y, 0 < with - 1 § x § 1 and - 1 § y § 2 shown with a plot of R: Why does the plot signal that Ÿ Ÿ R f @ x, y D x y < 0? · L.5) Here's a plot of a certain surface z = f @ x, y D over (and under) the rectangle R in the xy- plane consisting of all points 8 x, y, 0 < with - 1 § x § 2 and - 1 § y § 3 shown with a plot of R: Why does the plot strongly suggest that Ÿ Ÿ R f @ x, y D x y > 0? How does the sign of f
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This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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2.05.4.Literacy - Accumulation Authors: Bill Davis, Horacio...

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