DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

When you set up mathematical formulas, you often have to introduce various kinds of local objects or "dummy variables". You can treat such dummy variables using modules and ...

Primitives which can take multiple elements. Some primitives have multi-element forms that can be processed and rendered more quickly by the Mathematica front end than the ...

Elementary transcendental functions. Mathematica gives exact results for logarithms whenever it can. Here is log_21024. You can find the numerical values of mathematical ...

When you write down a set of simultaneous equations in Mathematica, you are specifying a collection of constraints between variables. When you use Solve, you are finding ...

Ways to enter Greek letters in a notebook. Here is a palette for entering common Greek letters. You can use Greek letters just like the ordinary letters that you type on your ...

Mathematica's notebook interface is a very powerful typesetting system that allows you to enter formulas as they are written in mathematical literature, using two-dimensional ...

"Defining Variables" discussed assignments such as x=y which set x equal to y. Here we discuss equations, which test equality. The equation x==y tests whether x is equal to ...

The built-in Mathematica iteration functions such as Table and Sum evaluate their arguments in a slightly special way. When evaluating an expression like Table[f,{i,i_max}], ...