Suppose S is a region in the xy-plane with a boundary oriented counterclockwise. What is the normal to S? Explain why Stokes’ Theorem becomes the circulation form of Green’s Theorem.

Braxton Pugh 2021-01-04 Answered
Suppose S is a region in the xy-plane with a boundary oriented counterclockwise. What is the normal to S? Explain why Stokes’ Theorem becomes the circulation form of Green’s Theorem.
You can still ask an expert for help

Want to know more about Green's, Stokes', and the divergence theorem?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

SchepperJ
Answered 2021-01-05 Author has 96 answers
Step 1
Consider the surface in xy-plane as z = g(x,y).
Step 2
Obtain the value of zxandzyaszx=gxandzy=gy respectively
Thus, the parametric form becomes zx,zy,1=gx,gy,1
If the vector product of two vectors is obtained, the direction of the vector product is perpendicular to both the vectors.
The components zx,andzy lie on the xy- plane, hence the vector product zx×zy, lie perpendicular to the xy- plane.
Therefore, the normal to the surface is the same as that of xy- plane.
Here, surface is just a plane.
Hence, there is only one normal vector at every point of the plane.
Thus, the normal vector in Stokes’ theorem becomes the unit vector that results in circulation form of Green’s theorem.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-01-25
I have a multivariable function that is composed of six variables; four of these are constants C1,C2,C3,C4 and the other two variables are x and y. The function is defined as follows
Xi(x,y,C1,C2,C3,C4) I would like to find the maximum value of Xi over x{,} and y{,}. What is the rigorous mathematical notation I should use to describe this. Is this fine:
max{Xi(x,y,C1,C2,C3,C4)}
asked 2021-12-08
On the final examination in Engineering Data Analysis, the mean was 72 and the standard deviation was 15.
a. Determine the standard scores (z-values) of students receiving the grade of 65.
b. Determine the standard scores (z-values) of students receiving the grade of 85
c. Determine the probability that a student will score greater than 75.
d. Determine the probability that a student will score lower than 65.
e. Find the grade corresponding to a standard score of 1.
asked 2022-05-02
Solve for w in the equation y-1=4wy-6.
asked 2021-09-16
Requires Uploaded Supporting Analysis Find dydx by implicit differentiation. y22x=4y
asked 2021-09-04

(a)Show that for all complex numbers z and w
|zw|2+|z+w|2=2|z|2+2|w|2
(b) Let u,v be complex numbers such that |u|=|v|=1and|uv|=2 Use part (a) to express u in terms of v.

asked 2022-01-16
Brad and Lena are recording their classmates' eye color for a statistics assignment. In Brad's class, 3 out of the 25 students have green eyes. In Lena's class, 2 out of the 20 students have green eyes. Which class has the greater ratio of green-eyed students to total students?
asked 2021-11-17
Loring Brace and colleagues at the University of Michigan Museum of Anthropology indicate that the size of human teeth continues to grow. Decrease, and that the evolutionary process is not yet stop. In northern Europeans, for example, tooth size the reduction is now 1% in 1000 years. What size will the teeth of our descendants be in 20,000 years? Now (as a percentage of our current tooth size)?
The analysis of tooth shrinkage by

New questions