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Calculus III (Assignment Problems) / Surface Integrals / Stokes' Theorem   [Notes] [Practice Problems] [Assignment Problems]

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On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.


Paul
August 7, 2018


Calculus III - Assignment Problems
Line Integrals Previous Chapter  
Surface Integrals of Vector Fields Previous Section   Next Section Divergence Theorem

 Stokes’ Theorem

 

1. Use Stokes’ Theorem to evaluate  where  and S is the portion of  below  with orientation in the negative z-axis direction. 

 

2. Use Stokes’ Theorem to evaluate  where  and S is the portion of   in front of  with orientation in the positive y-axis direction.  

 

3. Use Stokes’ Theorem to evaluate  where  and C is the triangle with vertices ,  and C has a clockwise rotation if you are above the triangle and looking down towards the xy-plane.  See the figure below for a sketch of the curve.

 

4. Use Stokes’ Theorem to evaluate  where  and C is is the circle of radius 1 at  and perpendicular to the x-axis.  C has a counter clockwise rotation if you are looking down the x-axis from the positive x-axis to the negative x-axis.  See the figure below for a sketch of the curve.

 

Surface Integrals of Vector Fields Previous Section   Next Section Divergence Theorem
Line Integrals Previous Chapter  

Calculus III (Assignment Problems) / Surface Integrals / Stokes' Theorem    [Notes] [Practice Problems] [Assignment Problems]

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