ANeTour.nb

Calculus with Mathematica

Mathematica will help you learn the subject with prepared NoteBooks and extend your computational power with simple commands that you can use to do complicated computations.

Suppose we solve the Ideal Gas Law for pressure, . If we only vary one quantity on the right side, you can differentiate the expression. The following commands show how Mathematica finds these "partial derivatives."

Notice that the derivative

asks for the derivative of

with respect to

, where the constant

when

, and

are constant. You know the rule

from beginning calculus. (It is just a different letter from the rule .) This part shouldn't seem strange except for the D[.,.]-notation.

We will put all the derivatives together in a total differential as follows:

Extend your computational power

Mathematica can help you differentiate and integrate more complicated functions like the "covariance" function next (that arises in probability and quantum mechanics.)

Converted by Mathematica May 7, 2001