Understanding Coordinate Transforms: Partial Derivatives

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In summary, the conversation revolved around transforming coordinates using partial derivatives. The speaker was having trouble understanding the thought process behind it and asked for help. They also mentioned reading about covariant and contravariant vectors and offered to provide an example if needed. The other person clarified that partial derivatives are only used for local transformations and provided a link for more information.
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Storm Butler
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Hey, I am having trouble understanding how you can transform one set of coordinates into another using partial derivatives i just don't get the whole thought process behind it. I came across this while reading about covariant and contrivariant vectors. If anyone can help clear up how this works i would really appreciate it. Also if i need to be more specific about what i mean or if you would like to see an example of what I am talking about just ask and i would be happy to post it up.
 
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Hi Storm Butler! :wink:
Storm Butler said:
Hey, I am having trouble understanding how you can transform one set of coordinates into another using partial derivatives …

We don't use partial derivatives for the transformation itself, we can only use them for a very local transformation, or for transforming the d part in an integral: ∫∫∫dx dy dz = ∫∫∫ (jacobian) da db dc.

see http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant" for some details. :smile:
 
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What is a coordinate transform?

A coordinate transform is a mathematical operation that converts a set of coordinates from one reference frame to another. It allows for the representation of a point in one coordinate system to be expressed in another coordinate system.

What are partial derivatives?

Partial derivatives are a type of derivative that measures the rate of change of a multivariable function with respect to one of its variables, while holding the other variables constant. They can be thought of as slopes in a specific direction on a graph.

How are partial derivatives used in coordinate transforms?

Partial derivatives are used in coordinate transforms to calculate how a coordinate changes in one reference frame when the coordinate system is transformed to another reference frame. They allow for the mapping of coordinates between different reference frames.

What is the chain rule and how is it related to coordinate transforms?

The chain rule is a mathematical rule that allows for the calculation of the derivative of a composition of two or more functions. It is related to coordinate transforms because it is used to calculate the partial derivatives needed to transform coordinates between reference frames.

Why is understanding coordinate transforms important in science?

Understanding coordinate transforms is important in science because it allows for the accurate representation and analysis of data in different reference frames. This is crucial in many fields of science, including physics, engineering, and geography.

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