# Symbolic Calculations with Units

The Wolfram System's ability to deal with symbolic expressions, as well as numbers, allows you to use it for many kinds of mathematics. The Wolfram System's unit system utilizes this symbolic code base, facilitating calculus using Quantity expressions.

Solve[equation,vars] | solution to an equation for x |

Integrate[f,x] | the indefinite integral |

D[f,x] | the (partial) derivative |

Some symbolic mathematical operations that operate on Quantity expressions.

## General

Many symbolic commands are capable of understanding units. Still, there are times when you might wish to add or remove units. These can be handled by the Wolfram System's general substitution mechanism.

## Solve

Solve is aware of Quantity and will automatically determine the units of unknown variables within the equation. Units for variables can be specified by inserting the variable inside a Quantity expression with the desired units.

## Integrate

Integrate is aware of Quantity and will correctly combine the units of the integrand and integration variables. If the variable of integration is a Quantity object, then its QuantityMagnitude is used as the integration variable for performing the integration, and its QuantityUnit will be combined with the units of the integrand in the result. In general, it is best to enter the input in one of two forms:

1. The integrand and all the integration variables are Quantity objects.

2. Quantity objects only appear in the limits of definite integration.

Input can be entered in other ways, but Integrate will fail if it cannot determine a consistent assignment of units for all expressions. The assumed dimensions of the integration variable in definite integration will vary depending on how the variable and limits are expressed. For a specification like {x,Quantity[a,"unit1"],Quantity[b,"unit2"]}, x is assumed to have the same dimensions as "unit1" and "unit2". For a specification like {Quantity[x,"unit"],a,b}, x itself is generally assumed to be dimensionless. In this latter case, a and b must be quantities of the same dimensions as unit.

## D

D is aware of Quantity and will correctly combine the units of Quantity objects in the expression being differentiated with the units of the differentiation variables.