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Partial differentiation is the same thing as regular differentiation,
except it applies to functions of two and more variables.  The
differentiation with respect to a particular variable is performed in the
usual manner, and all other variables are treated as constants.  It is
used, obviously, when the rate of change of the function with respect to
a particular variable is needed.

Laplace transform of f(x) is an improper integral integral(e^(-st)f(x))
on [0,infinity)
It takes a function f of x and transforms it into a function F of s.  It
is used to transform a linear constant coefficient differential equation
into an algebraic equation with a hope that the algebraic equation would
be easier to solve than the original ODE.  It is most useful when the ODE
has a specific form, particularly if it involves the Heaviside function.

The best way to learn these things, though is to take a class in
multivariable calculus or elementary differential equations

Electfreak(�q�l���~) wrote:

> hihi,all mathematicans,I'm a mathematic idiot!I hope you can solve my
> question!
>
> What's a Partial Differentiation?And how/ when can I apply that??
> I'm so confuse between Partial Differentiation and Differentiation!
>
> and what's Laplace Transform?also,how/when  can I apply that??
>
> I 'm very desperately,I can improve my mathematics!
> I hope you can help me to answer my questions!
> Thanks in advance!
>
> mailto:electfreak@mailcity.com

Electfreak(�q�l���~) wrote in message <35210037.E4E24D8C@mailcity.com>...

>What's a Partial Differentiation?And how/ when can I apply that??

"Normal" differentiation handles

y=f(x).

"partial" differentiation handles

z = f(x,y) and more.

This sort of function can't be drawn on two axes. It needs three, so there
are many different ways down the slope from a maximum, for example.

>and what's Laplace Transform?
Useful.

A partial derivative is a derivative of a function of more than one
variable with respect to only one of those variables.  E.g., z = x^2 +
y^3.  The partial derivative of z w.r.t. x is 2x.  The partial of z
w.r.t. y is 3y^2.  In other words, to take the partial w.r.t one
variable, you treat all other variables as constants.  If z=xy, the the
partial of z w.r.t. y is x, and the partial of z w.r.t. x is y.

Electfreak(�q�l���~) wrote:

> hihi,all mathematicans,I'm a mathematic idiot!I hope you can solve my
> question!
>
> What's a Partial Differentiation?And how/ when can I apply that??
> I'm so confuse between Partial Differentiation and Differentiation!
>
> and what's Laplace Transform?also,how/when  can I apply that??
>
> I 'm very desperately,I can improve my mathematics!
> I hope you can help me to answer my questions!
> Thanks in advance!
>
> mailto:electfreak@mailcity.com