2-form oriented triangle, Differential Forms

In summary, the task is to find the value of the 2-form dxdy+3dxdz on an oriented triangle with coordinates (0,0,0), (1,2,3), and (1,4,0) in that order. The book does not provide any examples on how to calculate with 2-forms, but only gives a brief description and four problems. The answer is a negative rational number and it is unclear how to derive a rational number from this. It is recommended to read the first chapter of the book for more information.
  • #1
unintuit
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Homework Statement


Find the value of the 2-form dxdy+3dxdz on the oriented triangle with (0,0,0) (1,2,3) (1,4,0) in that order.

Homework Equations

The Attempt at a Solution


I have tried various subtraction of these coordinates and applying them to the formula but the answer is in the back of the book and I fail to see how one could get that answer.
The book does not give one example of how to calculate with 2-forms there is but a brief description and then 4 problems.

This is a problem from Edward's, 'Advanced Calculus: A Differential Forms Approach'

The answer is a negative rational number. I also fail to see how I derive a rational number from this.
 
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  • #2
This is an unusual formulation, but have you read the first chapter of that book ?
 

FAQ: 2-form oriented triangle, Differential Forms

What is a 2-form oriented triangle?

A 2-form oriented triangle is a mathematical concept used in differential geometry and multivariable calculus. It is a triangle in three-dimensional space that is oriented in a specific direction, and it is associated with a 2-form, which is a multilinear function that assigns a value to each pair of tangent vectors at each point on the triangle.

What are differential forms?

Differential forms are mathematical objects used to study the behavior of functions in multiple dimensions. They are used to describe quantities such as area, volume, and flow, and they are often used in conjunction with other mathematical tools, such as vectors and matrices, to solve complex problems in fields such as physics and engineering.

How are 2-form oriented triangles used in differential forms?

2-form oriented triangles are used in differential forms to represent changes in quantities, such as area and volume, over a given surface or region. By associating a 2-form with a triangle, we can calculate the integral of the 2-form over the triangle, which gives us a measure of the change in the quantity over that region.

What are the applications of 2-form oriented triangles and differential forms?

2-form oriented triangles and differential forms have a wide range of applications in mathematics, physics, and engineering. They are used to study the behavior of quantities such as electric and magnetic fields, fluid flow, and curvature of surfaces. They are also used in the development of mathematical models for physical phenomena and in the solution of differential equations.

What is the relationship between 2-form oriented triangles and differential forms?

2-form oriented triangles and differential forms are closely related, as the 2-form is associated with the triangle and used to calculate integrals over the triangle. The use of 2-form oriented triangles allows for a more efficient and elegant representation of quantities in multiple dimensions, making it a powerful tool in many areas of mathematics and science.

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