Chapter 22 - Equations

Abstract

Equations can be classified as linear, polynomial, radical, or transcendental. Polynomial equations consist of sums of integer powers of variables, whereas radical equations may contain rational powers. Transcendental equations contain transcendental functions such as sin ( x ) or log ( x + y) . The main command for linear, polynomial, and radical equations is solve, and that for transcendental equations is Find root. If one has linear equations in the form of a coefficient matrix and right-hand-side vector, then LinearSolve is easy to use. For polynomial equations, Solve gives an answer for generic values of the possible parameters of the equations. If an exhaustive analysis of the solutions is wanted for all possible values of the parameters in polynomial equations, then Reduce can be used. If Solve cannot obtain exact solutions for polynomial equations, then NSolve can be used to calculate the solutions numerically. Either writing down the equations explicitly with variables or giving the left-hand-side coefficient matrix and the right-hand-side vector can represent linear systems.