Abstract
This chapter provides an overview of the numbers and equations available to users in Mathematica. The equation kinds can be linear, polynomial, algebraic, and transcendental equations in one or more variables as well as ordinary and partial differential equations involving one or several unknown functions of one or more variables. There are two important measures attached to numbers in Mathematica: precision, which is the total number of significant digits in x; and accuracy, which is the number of significant decimal digits to the right of the decimal point in x. It is possible to specify the form in which Mathematica displays floating point numbers. Mathematica can deal with numbers in different bases and convert values between different bases. Six numerical functions exist in Mathematica, namely, NDSolve, NIntegrate, NProduct, NRoots, NSolve, and NSum. There are seven minimum ways to approach ordinary differential equations in Mathematica: DSolve, N[ DSolve[-] ], NDSolve, the package DSolve.m, the package RungeKutta.m, series solutions, and Laplace transform methods in the package LaplaceTransform.m.
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