The first argument given to DSolve is the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. Here ...

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

Just as the equation x^2+3x==2 asserts that x^2+3x is equal to 2, so also the inequality x^2+3x>2 asserts that x^2+3x is greater than 2. In Mathematica, Reduce works not only ...

The method "DoubleStep" performs a single application of Richardson's extrapolation for any one-step integration method. Although it is not always optimal, it is a general ...

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...

NDSolve returns solutions as InterpolatingFunction objects. Most of the time, simply using these as functions does what is needed, but occasionally it is useful to access the ...

When Mathematica plots a graph for you, it has to make many choices. It has to work out what the scales should be, where the function should be sampled, how the axes should ...

The leading term of a polynomial can be chosen in many different ways. For multivariate polynomials, sorting by the total degree of the monomials is often useful. Different ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

Newton's method for nonlinear equations is based on a linear approximation so the Newton step is found simply by setting M_k(p)=0, Near a root of the equations, Newton's ...