Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Calculate the circulation, SF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 4y - 4x and C is the boundary of S, the part of the surface z = 9x² - y²2 above the xy-plane, oriented upward. Note that C is a circle in the xy-plane. Find a F(t) that parameterizes this curve. r(t) with

Calculate the circulation, SF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 4y - 4x and C is the boundary of S, the part of the surface z = 9x² - y²2 above the xy-plane, oriented upward. Note that C is a circle in the xy-plane. Find a F(t) that parameterizes this curve. r(t) with

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
See similar textbooks
icon
Related questions
Question

please help with this!

Calculate the circulation, SF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 4yi — 4x and C is the boundary of S, the part of the surface z = 9 — x² - y² above the xy-plane, oriented upward. Note that C is a circle in the xy-plane. Find a r(t) that parameterizes this curve. r(t) = with <t< (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterization.) With this parameterization, the circulation integral is ScF¹ · dr = Sº | dt, where a and b are the endpoints you gave above. Evaluate your integral to find the circulation: SF. dr = Using Stokes' Theorem, we equate SF · dỡ = ſçcurl ♬ · dÃ. Find curl F Noting that the surface is given by z = 9 - x² - y²2, find d.à = dy dx. With R giving the region in the xy-plane enclosed by the surface, this gives Ss ₁ curl F. d.à = SR dy dr. Evaluate this integral to find the circulation: ScF·dr = f curl F · dà : = -0
Transcribed Image Text:Calculate the circulation, SF. dr, in two ways, directly and using Stokes' Theorem. The vector field F = 4yi — 4x and C is the boundary of S, the part of the surface z = 9 — x² - y² above the xy-plane, oriented upward. Note that C is a circle in the xy-plane. Find a r(t) that parameterizes this curve. r(t) = with <t< (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterization.) With this parameterization, the circulation integral is ScF¹ · dr = Sº | dt, where a and b are the endpoints you gave above. Evaluate your integral to find the circulation: SF. dr = Using Stokes' Theorem, we equate SF · dỡ = ſçcurl ♬ · dÃ. Find curl F Noting that the surface is given by z = 9 - x² - y²2, find d.à = dy dx. With R giving the region in the xy-plane enclosed by the surface, this gives Ss ₁ curl F. d.à = SR dy dr. Evaluate this integral to find the circulation: ScF·dr = f curl F · dà : = -0
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS