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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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Let o be the surface 7x + 2y + 6z = 7 in the first octant, oriented upwards. Let C be the oriented boundary of o. Compute the work done in moving a unit mass particle around the boundary of o through the vector field F = (x − 4y)i + (4y – 10z)j + (10z − x)k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of a positively using the standard form, tv+P with 0 ≤ t ≤ 1, starting with the segment in the xy plane. C₁ (the edge in the xy plane) is parameterized by C₂ (the edge following C₁) is parameterized by C3 (the last edge) is parameterized by Ja F.dr = Sai F.dr = F.dr = C3 [F Ər Əx F.dr = STOKES' THEOREM o may be parameterized by r(x, y) : (x, y, f(x, y)) : curl F = [f (curl F). ndS= = S S dy dx
Transcribed Image Text:Let o be the surface 7x + 2y + 6z = 7 in the first octant, oriented upwards. Let C be the oriented boundary of o. Compute the work done in moving a unit mass particle around the boundary of o through the vector field F = (x − 4y)i + (4y – 10z)j + (10z − x)k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of a positively using the standard form, tv+P with 0 ≤ t ≤ 1, starting with the segment in the xy plane. C₁ (the edge in the xy plane) is parameterized by C₂ (the edge following C₁) is parameterized by C3 (the last edge) is parameterized by Ja F.dr = Sai F.dr = F.dr = C3 [F Ər Əx F.dr = STOKES' THEOREM o may be parameterized by r(x, y) : (x, y, f(x, y)) : curl F = [f (curl F). ndS= = S S dy dx
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