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 ...
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 ...
"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 ...
Mathematica usually pays no attention to whether variables like x stand for real or complex numbers. Sometimes, however, you may want to make transformations which are ...
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 ...
Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.
A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...
In many practical situations it is convenient to consider limits in which a fixed amount of something is concentrated into an infinitesimal region. Ordinary mathematical ...
Ways to get pieces of matrices. Matrices in Mathematica are represented as lists of lists. You can use all the standard Mathematica list-manipulation operations on matrices. ...