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Sax S2 FIGURE 0.1. The triangle with vertices (0,0), (1,0), (1/2, 1/2) and positive orientation. Consider the triangle T depicted in Fig. 0.1. It has vertices (0,0), (1,0), (1/2, 1/2), and sides S1, S2, S3 labeled as in the picture. a) Give a parametrization of S1, S2, S3 with orientation as in the picture Cousider the outgoing normal vectors to S1, S2 and S3 given by A, (0, –1), -,1), =-1,1). (1, 1), i3 = %3D V2 oreover consider the vector ficld F(r, y) = (x, y). %3D b) Compute the flux = , F- īds using the definition of line integral. c) Compute the flux using the divergence theorem.

Sax S2 FIGURE 0.1. The triangle with vertices (0,0), (1,0), (1/2, 1/2) and positive orientation. Consider the triangle T depicted in Fig. 0.1. It has vertices (0,0), (1,0), (1/2, 1/2), and sides S1, S2, S3 labeled as in the picture. a) Give a parametrization of S1, S2, S3 with orientation as in the picture Cousider the outgoing normal vectors to S1, S2 and S3 given by A, (0, –1), -,1), =-1,1). (1, 1), i3 = %3D V2 oreover consider the vector ficld F(r, y) = (x, y). %3D b) Compute the flux = , F- īds using the definition of line integral. c) Compute the flux using the divergence theorem.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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of 1 80% Sax S2 FIGURE 0.1. The triangle with vertices (0,0), (1,0), (1/2, 1/2) and positive orientation Consider the triangle T depicted in Fig. 0.1. It has vertices (0, 0), (1,0), (1/2, 1/2), and sides S1, S2, S3 labeled as in the picture. a) Give a parametrization of S1, S2, S3 with orientation as in the picture. Cousider the outgoing normal vectors to S1, S2 and S3 given by = (0, –1), ñ2 = (1, 1), ig = -1,1). V2 V2 Moreover consider the vector field F(x, y) = (x, y). b) Compute the flux = , F- īds using the definition of line integral. c) Compute the flux using the divergence theorem. 1.
Transcribed Image Text:of 1 80% Sax S2 FIGURE 0.1. The triangle with vertices (0,0), (1,0), (1/2, 1/2) and positive orientation Consider the triangle T depicted in Fig. 0.1. It has vertices (0, 0), (1,0), (1/2, 1/2), and sides S1, S2, S3 labeled as in the picture. a) Give a parametrization of S1, S2, S3 with orientation as in the picture. Cousider the outgoing normal vectors to S1, S2 and S3 given by = (0, –1), ñ2 = (1, 1), ig = -1,1). V2 V2 Moreover consider the vector field F(x, y) = (x, y). b) Compute the flux = , F- īds using the definition of line integral. c) Compute the flux using the divergence theorem. 1.
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