(8) Address the surface integral 1 = F (2nd type or normal (perpendicular)) of the (3x3) vector function (3- dimensional vector field) F(x, y, z) in 3 variables x, y, z over the domain of integration D, with D= Sp, where C₁ is the section Sp of the surface S, as described below, within the 3-dimensional xy space (plane) E³, in particular: P P (i) Provide the transformation formula for the surface integral I over D transforming it into an 2- dimensional (double (scalar)) integral over P (ii) Complete the calculation of the above (surface) integral| Given: F=F(x, y, z) = (x + y + z, x - y + z, x²) S: as in (6) P Sp= g(xry) = 2x + y² with xy-projection P= [0,1] * [0,2] = rectangle in xy space

(8) Address the surface integral 1 = F (2nd type or normal (perpendicular)) of the (3x3) vector function (3- dimensional vector field) F(x, y, z) in 3 variables x, y, z over the domain of integration D, with D= Sp, where C₁ is the section Sp of the surface S, as described below, within the 3-dimensional xy space (plane) E³, in particular: P P (i) Provide the transformation formula for the surface integral I over D transforming it into an 2- dimensional (double (scalar)) integral over P (ii) Complete the calculation of the above (surface) integral| Given: F=F(x, y, z) = (x + y + z, x - y + z, x²) S: as in (6) P Sp= g(xry) = 2x + y² with xy-projection P= [0,1] * [0,2] = rectangle in xy space

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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