Line Integrals Complex Numbers

In summary, the individual is seeking assistance with understanding how to parametrize a curve for line integrals over a simple closed curve. They are looking for tips and resources on this topic and have a test coming up soon. It is suggested that if the curve is a simple curve, the parametrization will be (t, f(t)), and if it is a circle, the parametrization will be (cos(t), sin(t)). More information is needed for further assistance.
  • #1
chota
22
0
Hi,

I am currently studying complex numbers and I am at the part we have to find line integrals over a simple closed curve gamma(t)..

I know the definition, but when i read a problem I am n ot sure how to parameratize the curve. I was wondering if there are some tricks to this. Would anyone be able to direct me to some useful site about this topic, any help would be appreciated (test in a couple of days)

THank You

ChoTa
 
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  • #2
what does the curve look like? you're going to have to volunteer more information if you're expecting help.
 
  • #3
If the curve is a simple curve, y=f(x), then your parametrization will be (t, f(t)). If your curve is a circle, the parametrization will be (cos(t), sin(t)). Otherwise, as ice109 said, you'll have to volunteer more information.
 

1. What is a line integral in complex numbers?

A line integral in complex numbers is a type of integral that is performed over a curve in the complex plane. It involves integrating a complex-valued function along a given path or curve in the complex plane.

2. How is a line integral in complex numbers different from a regular line integral?

A line integral in complex numbers is different from a regular line integral because it involves integrating a function with complex-valued inputs and outputs. This means that the path of integration can be any curve in the complex plane, rather than just a straight line as in regular line integrals.

3. What is the purpose of performing a line integral in complex numbers?

The purpose of performing a line integral in complex numbers is to calculate the total change of a complex-valued function along a given curve in the complex plane. This can be useful in many areas of mathematics, physics, and engineering, such as in calculating electric and magnetic fields.

4. How is a line integral in complex numbers calculated?

A line integral in complex numbers is calculated by breaking down the path of integration into small segments, and then approximating the integral using Riemann sums. This process involves taking the limit as the size of the segments approaches zero, resulting in an exact value for the integral.

5. What are some real-world applications of line integrals in complex numbers?

Line integrals in complex numbers have many real-world applications, such as in calculating electric and magnetic fields, fluid flow, and work done by a force field. They are also used in complex analysis and the study of conformal mappings in mathematics.

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