## 1.5.1 Basic Operations

Mathematica's ability to deal with symbolic expressions, as well as numbers, allows you to use it for many kinds of mathematics.

Calculus is one example. With Mathematica, you can differentiate an expression symbolically, and get a formula for the result.

This finds the derivative of .
 In[1]:=  D[ x^n, x ]
 Out[1]=
Here is a slightly more complicated example.
 In[2]:=  D[x^2 Log[x + a], x]
 Out[2]=

 D[f, x] the (partial) derivative Integrate[f, x] the indefinite integral Sum[f, {i, , }] the sum Solve[lhsrhs, x] solution to an equation for Series[f, {x, , order}] a power series expansion of about the point Limit[f, x->] the limit Minimize[f, x] minimization of with respect to

Some symbolic mathematical operations.

Getting formulas as the results of computations is usually desirable when it is possible. There are however many circumstances where it is mathematically impossible to get an explicit formula as the result of a computation. This happens, for example, when you try to solve an equation for which there is no "closed form" solution. In such cases, you must resort to numerical methods and approximations. These are discussed in Section 1.6.

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