Abstract
To introduce the subject, we consider a few examples of nonlinear equations:
is an algebraic equation; there is only one unknown, but it occurs in the third power. There are three solutions, of which two are conjugate complex.
is a transcendental equation. Again, only one unknown is present, but now in a transcendental function. There are denumerably many solutions.
is a transcendental equation only in an unessential way, since it can be transformed at once into a quadratic equation for eix. While there are infinitely many solutions, they can all be derived from two solutions through addition of multiples of 2π.
is a system of two nonlinear algebraic equations in two unknowns x and y. It can be reduced to one algebraic equation of degree 9 in only one unknown. This latter equation has nine solutions which generate nine pairs of numbers (x i ,y i ), i = 1,…, 9, satisfying the given system. (There are fewer if only real x,y are admitted.)
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Rutishauser, H. (1990). Nonlinear Equations. In: Gutknecht, M. (eds) Lectures on Numerical Mathematics. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3468-5_4
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