Problem 9.1 Green's theorem in the plane Using Green's theorems, compute the circulation and flux of the following vector fields: a) F(x, y) = (x+y)i — (x² + y²)j around and across the triangle bounded by y = 0, z = 1 and y = x. b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2. c) F(x, y) = arctan(y/z)i + ln(z² + y²)j around and across the boundary of the region defined by 1
Problem 9.1 Green's theorem in the plane Using Green's theorems, compute the circulation and flux of the following vector fields: a) F(x, y) = (x+y)i — (x² + y²)j around and across the triangle bounded by y = 0, z = 1 and y = x. b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2. c) F(x, y) = arctan(y/z)i + ln(z² + y²)j around and across the boundary of the region defined by 1
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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![Problem 9.1 Green's theorem in the plane
Using Green's theorems, compute the circulation and flux of the following vector fields:
a) F(x, y) = (x+y)i - (x² + y²)j around and across the triangle bounded by y = 0, z = 1
and y = x.
b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2.
c) F(x, y) = arctan(y/z)i + ln(x² + y2)j around and across the boundary of the region
defined by 1 <r < 2 and 0 << in polar coordinates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77ccc228-61ae-45bc-bff3-36e89ce5abe9%2F41d71a2b-167e-47bc-a607-f8ab8e11f0ee%2Fi98mzmr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 9.1 Green's theorem in the plane
Using Green's theorems, compute the circulation and flux of the following vector fields:
a) F(x, y) = (x+y)i - (x² + y²)j around and across the triangle bounded by y = 0, z = 1
and y = x.
b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2.
c) F(x, y) = arctan(y/z)i + ln(x² + y2)j around and across the boundary of the region
defined by 1 <r < 2 and 0 << in polar coordinates.
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