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Old Sep 20th 2008, 10:03 PM   #1
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Partial differentiation

I found a book in library about partial differentiation. Quantum mechanics uses it a lot?

Its application seems to be useful to physics. However, I found it very difficult since the first page of the book! Do I need to know that or to say when should I know about partial differentiation?
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Old Sep 21st 2008, 02:25 PM   #2
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Originally Posted by werehk View Post
I found a book in library about partial differentiation. Quantum mechanics uses it a lot?

Its application seems to be useful to physics. However, I found it very difficult since the first page of the book! Do I need to know that or to say when should I know about partial differentiation?
as far as what applications you will need partial differentiations for, i cannot say. but partial differentiation itself is a math topic. have you done calc 3? you should have learned it there. basically the idea is, you have a multi-variable function and you want to take its derivative with respect to one variable. this is partial differentiation, since you are essentially differentiating the "part" with the variable you want. under this form of differentiation, you treat all other variables as constants.

example, let's say we have a function $\displaystyle f(x,y) = 3x^2 + 4y^2 + 2xy$. then, $\displaystyle f_x(x,y) = \frac {\partial f}{\partial x}$ refers to the derivative of the function $\displaystyle f$ with respect to $\displaystyle x$. a similar notation goes for the partial derivative of $\displaystyle f$ with respect to $\displaystyle y$.

here, $\displaystyle f_x = 6x + 2y$ ..................i treated all $\displaystyle y$'s as constants. so, for example, the derivative with respect to $\displaystyle x$ of $\displaystyle 4y^2$ is zero. since this is a constant as far as $\displaystyle x$ is concerned.

similarly, $\displaystyle f_y = 8y + 2x$

and of course, the usual properties of differentiation apply: chain rule, product rule, quotient rule.....

does this help?
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