- #1
nysnacc
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Homework Statement
Homework Equations
Green's theorem
The Attempt at a Solution
DO I first parametrize? For 1st part, I have 3 parametrizations, which I can then find the normal vector, and use in the integrals?
Applying Green's Theorem: Solving Parametrized Homework Problems
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- Green's theorem Theorem
In summary, Green's Theorem is a mathematical theorem that relates the line integral around a simple closed curve in the plane to a double integral over the region inside the curve. It is significant because it allows for the calculation of enclosed area without direct calculation. It is used in various real-world applications in physics and engineering. To fully understand it, one should have a strong understanding of calculus and vector calculus. Green's Theorem has limitations, including only being applicable to simple closed curves in two-dimensional spaces.
Green's theorem
DO I first parametrize? For 1st part, I have 3 parametrizations, which I can then find the normal vector, and use in the integrals?
- #2
vela
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I'm sure there are examples of similar problems worked out in your textbook. Try using them as a model for solving these problems.
1. What is Green's Theorem?
Green's Theorem is a mathematical theorem that relates the line integral around a simple closed curve in the plane to a double integral over the region inside the curve. It is named after the mathematician George Green.
2. What is the significance of Green's Theorem?
Green's Theorem is significant because it allows us to calculate the area enclosed by a closed curve without having to directly calculate the area. It also has many applications in physics and engineering, such as calculating work and flux in vector fields.
3. How is Green's Theorem used in real-world applications?
Green's Theorem is commonly used in physics and engineering, such as in the calculation of work and flux in vector fields. It is also used in fluid dynamics, electromagnetism, and many other areas of science and engineering.
4. What are the prerequisites for understanding Green's Theorem?
In order to fully understand Green's Theorem, one should have a strong understanding of calculus, particularly of line integrals and double integrals. Knowledge of vector calculus is also helpful.
5. Are there any limitations to Green's Theorem?
Green's Theorem is limited to calculating the area of simple closed curves in the plane. It cannot be applied to curves that intersect or are self-intersecting. It also only applies to two-dimensional spaces and cannot be extended to three-dimensional spaces.
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