The replacement operator /. allows you to apply transformation rules to a specific expression. Often, however, you want to have transformation rules automatically applied ...

When you have numerical data, it is often convenient to find a simple formula that approximates it. For example, you can try to "fit" a line or curve through the points in ...

If you use a text-based interface to Mathematica, then the input you give must consist only of characters that you can type directly on your computer keyboard. But if you use ...

MathLM Mathematica

Introduction ODE Integration Methods Partial Differential Equations

The basic idea behind the "StiffnessSwitching" method is to provide an automatic means of switching between a nonstiff and a stiff solver. The "StiffnessTest" and ...

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...

The Padé approximation is a rational function that can be thought of as a generalization of a Taylor polynomial. A rational function is the ratio of polynomials. Because ...

The mathematical operations we have discussed so far are exact. Given precise input, their results are exact formulas. In many situations, however, you do not need an exact ...

There are many situations where you want to write a particular algebraic expression in the simplest possible form. Although it is difficult to know exactly what one means in ...