Xnor[e_1, e_2, ...] is the logical XNOR (not XOR) function. It gives True if an even number of the e_i are True, and the rest are False. It gives False if an odd number of ...

Finding singular values and norms of matrices. The singular values of a matrix m are the square roots of the eigenvalues of m.m^*, where * denotes Hermitian transpose. The ...

A typical Mathematica notebook containing text, graphics, and Mathematica expressions. The brackets on the right indicate the extent of each cell. Mathematica notebooks are ...

There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. Of these four areas, the study of exact solutions ...

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

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 ...

Converting notebooks to HTML. Export has many options applying to HTML export that allow you to specify how notebooks should be converted for web browsers with different ...

In doing many kinds of calculations, you need to evaluate expressions when variables take on particular values. In many cases, you can do this simply by applying ...

When you make a function definition using :=, the value of the function is recomputed every time you ask for it. In some kinds of calculations, you may end up asking for the ...

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...