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And what is the justification to consider or not to consider dy=dx?

-An Engineer, Weak in Calculus

-An Engineer, Weak in Calculus

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- Thread starter gikiian
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- #1

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And what is the justification to consider or not to consider dy=dx?

-An Engineer, Weak in Calculus

-An Engineer, Weak in Calculus

- #2

mfb

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It is like "y=x". It can be true, in some specific problem, but it is meaningless as general equation.

- #3

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So dy and dx are going to change their relationship depending on the curve (or plane, etc.) that we're considering, and also on where we are on the curve.

- #4

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It's not assumed because (in general) there is no justification in assuming it. Pretty much as mfb said.And what is the justification to consider or not to consider dy=dx?

I don't think that addresses the OP's question, since they were asking about a differential area element rather than the slope of a curve.mfb is correct. Let's consider the equation y = sin(x). Then dy/dx = cos(x). If we use the chain rule (or pretend that dy/dx is a fraction for a moment), we find that dy = cos(x)*dx.

- #5

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So dy and dx are going to change their relationship depending on the curve (or plane, etc.) that we're considering, and also on where we are on the curve.

Moderator's note: thread moved from Classical Physics to Calculus

It's not assumed because (in general) there is no justification in assuming it. Pretty much as mfb said.

I don't think that addresses the OP's question, since they were asking about a differential area element rather than the slope of a curve.

If we take a differential area inside an ellipse with major axis along y, then will dy be greater than dx?

- #6

Office_Shredder

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For numerical techniques however it is often advantageous to not have squares. For example if I wanted to integrate [itex] f(x,y) = \cos(x+100y) [/itex]

The function is changing a lot more along the y direction than the x direction, so if I wanted to split up my region into rectangles, and take the value of f at the middle of the rectangle, multiply by the area and add them all up, I would be better off having my rectangles be a lot longer in the x direction than the y direction from an accuracy/time to calculate trade off.

- #7

HallsofIvy

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dy can be greater than dx, dx can be greater than dy, or they could be equal. The areIf we take a differential area inside an ellipse with major axis along y, then will dy be greater than dx?

- #8

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dy can be greater than dx, dx can be greater than dy, or they could be equal. The areindependent..

Thanks.

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