Topics:
Calculus

Essay,
Pages 1 (218 words)

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To make this more concrete, consider the case in which you want to switch between

rectangular and polar coordinates. In rectangular coordinates, you use x and y to

locate a point in the plane: in polar coordinates. vow use r. the distance from the

origin, and theta, the angle from the x-axis.

[Graph]

Thus, the change of variables for this equation is x equals r cosine theta and y

equals r sine theta.

x = r cos θ

y = r sin θ

So, in fact, if a function f depends on x and y, then you can plug x and y into r and

theta to get

the function of f: f = f(x, y)

Then you can ask yourself, what is the partial derivative of a function with respect to

a particular variable? You want to take the partial derivative of fwith respect to x

times cosine theta plus the partial derivative of f with respect to y times y sine theta.

δf/δr=df/dx δx/δr+δf/δy δy/δr =f_x cosθ f_y sinθ

In the same way, you can

express derivatives either in terms of x and y or in terms of

r and theta with simple relations between them.

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