You can define the derivative in Mathematica of a function f of one argument simply by an assignment like f'[x_]=fp[x]. This defines the derivative of f(x) to be fp(x). In ...

Differentiating a known function gives an explicit result. Differentiating an unknown function f gives a result in terms of f'. Mathematica applies the chain rule for ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Here is a homogeneous equation in which the total degree of both the numerator and the denominator of the right-hand side is 2. The two parts of the solution list give ...

DSolve can be used for finding the general solution to a differential equation or system of differential equations. The general solution gives information about the structure ...

This gives a result for the integral of x^n that is valid for almost all values of n. For the special case of x^-1, however, the correct result is different. The overall goal ...

Numerical sums, products and integrals. Here is a numerical approximation to ∑_(i=1)^∞((1)/(i^3)). NIntegrate can handle singularities in the integration region.

Mathematical constants. Euler's constant EulerGamma is given by the limit γUnderscriptBox[lim, RowBox[{m, , ∞}], LimitsPositioning -> True](UnderoverscriptBox[∑, RowBox[{k, ...

Naming Conventions Generic and Nongeneric Cases Numerical Functions

Testing for numeric quantities. Pi is a symbol, so Pi+3 is not explicitly a number. It does however have a numerical value.