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1.5.11 Packages for Symbolic Mathematics

There are many Mathematica packages which implement symbolic mathematical operations. This section describes a few examples drawn from the standard set of packages distributed with Mathematica. As discussed in Section 1.3.10, some copies of Mathematica may be set up so that the functions described here are automatically loaded into Mathematica if they are ever needed.

Laplace Transforms

Laplace transforms.

  • This loads the Laplace transform package. In some versions of Mathematica, you may not need to load this package explicitly.
  • In[1]:= <<Calculus`LaplaceTransform`

  • This evaluates a Laplace transform.
  • In[2]:= LaplaceTransform[ t^3 Exp[a t], t, s ]


  • Here is the inverse transform.
  • In[3]:= InverseLaplaceTransform[%, s, t]


    Fourier Transforms

    Fourier transforms.

  • This loads the symbolic Fourier transform package.
  • In[1]:= <<Calculus`FourierTransform`

  • This evaluates a Fourier transform.
  • In[2]:= FourierTransform[ t^2 Sin[t], t, w ]


    Vector Analysis

    Vector analysis.

  • This loads the vector analysis package. In some versions of Mathematica, you may not need to load the package explicitly.
  • In[1]:= <<Calculus`VectorAnalysis`

  • This specifies that a spherical coordinate system with coordinate names r, theta and phi should be used.
  • In[2]:= SetCoordinates[Spherical[r, theta, phi]]


  • This evaluates the gradient of

    in the spherical coordinate system.
  • In[3]:= Grad[r^2 Sin[theta]]