Stocks question(multivariable calculus)

In summary, to calculate the surface integral \iint_{M}^{}rot(\vec{F})\vec{dS}, we can use the formula \iint_{D}\frac{rot\vec{F}\cdot \vec{N}}{|\vec{N}\cdot\vec{K}|}dxdy and convert to polar coordinates for integration.
  • #1
slonopotam
6
0
calculate
[tex]
\iint_{M}^{}rot(\vec{F})\vec{dS}
[/tex]
where
[tex]
\vec{F}=(y^2z,zx,x^2z^2)
[/tex]
M is a part of \(\displaystyle z=x^2+y^2\) which is located in \(\displaystyle 1=x^2+y^2\)
and its normal vector points outside

i am used to solve it like this
[tex]
\iint_{M}^{}rot\vec{F}\vec{dS}=\iint_{D}\frac{rot\vec{F}\cdot \vec{N}}{|\vec{N}\cdot\vec{K}|}dxdy
[/tex]
[tex]
\vec{N}=(2x,2y,-1)
[/tex]
[tex]
\iint_{M}^{}\vec{F}\vec{dS}=\iint_{D}\frac{(-x,2xz^2-y^2,z-yz) \cdot (2x,2y,-1)}{1}dxdy
[/tex]
now i convert into polar coordinates

x^2+y^2=r
is this method ok?
 
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  • #2


Yes, this method is correct. To solve this integral, you can follow the steps outlined in your post. First, calculate the curl of \vec{F} using the formula for three-dimensional curl. Then, use the normal vector \vec{N} to determine the direction of the surface and calculate the dot product with the curl of \vec{F}. Finally, convert the integral into polar coordinates to solve for the surface integral. This method is commonly used for calculating surface integrals and is a valid approach to solving this problem.
 

What are stocks?

Stocks, also known as shares or equities, are a type of investment that represent ownership in a company. When you buy stocks, you are essentially buying a small piece of the company and become a shareholder.

How are stock prices determined?

The price of a stock is determined by the supply and demand in the stock market. If there is a high demand for a particular stock, the price will go up. On the other hand, if there is a low demand, the price will decrease.

What is the difference between stocks and bonds?

Stocks and bonds are both types of investments, but they have significant differences. Stocks represent ownership in a company, while bonds represent debt. Stocks also have higher potential for returns, but also carry more risk compared to bonds.

How do you calculate the return on a stock?

The return on a stock can be calculated by taking the change in stock price, adding any dividends received, and dividing by the initial investment. This gives you the percentage return on your investment.

What is the role of multivariable calculus in stocks?

Multivariable calculus is used in financial analysis and modeling to understand the relationships between different variables, such as stock prices and market trends. It helps in predicting future stock prices and making informed investment decisions.

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