## Mathematics for the Maxwell-Boltzmann Distribution
Mathematics Section: Integrals
In our study of the MBS distribution
we will encounter many integrals of the following form:
All of these integrals have
an exponential term exp(-cu This one integral we just
take as a definition. We call this integral I The Differentiation Method
We begin with the above equation and take the derivative of both sides with respect to c: performing the derivatives yields We have now derived an expression
for I We can repeat the same procedure
as many times as we want. For example, differentiating the expression for
I We could continue on and
find expressions for I Now, we can perform the same
differentiation method to convert I Once again, we can continue
on to find I © Andrew M. Rappe |