Search results
Results from the WOW.Com Content Network
In this manner log function is a multi-valued function (often referred to as a "multifunction" in the context of complex analysis). A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between −π and π. These are the chosen principal values. This is the principal branch of the log function.
Complex valued elementary functions can be multiple-valued over some domains. The principal value of some of these functions can be obtained by decomposing the function into simpler ones whereby the principal value of the simple functions are straightforward to obtain.
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...
The principal value of this function is single-valued, typically chosen to be the unique value of the argument that lies within the interval (−π, π]. [1] [2] In this article the multi-valued function will be denoted arg(z) and its principal value will be denoted Arg(z), but in some sources the capitalization of these symbols is exchanged.
Title page for the third edition of the book. A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions (colloquially known as Whittaker and Watson) is a landmark textbook on mathematical analysis written by Edmund T. Whittaker and George N. Watson, first published by Cambridge ...
In many Australian and New Zealand schools, a principal is the head administrator of a school who has been appointed to her/his position by the school board, superintendent, or other body. The principal, often in conjunction with the school board, makes the executive decisions that govern the school, as well as having the authority over the ...
Hamilton's principal function = (,;,) is obtained from the action functional by fixing the initial time and the initial endpoint , while allowing the upper time limit and the second endpoint to vary. The Hamilton's principal function satisfies the Hamilton–Jacobi equation, a formulation of classical mechanics .
Unlike the principal, the vice-principal does not have quite the decision-making authority that the principal carries. Although they still carry nearly the same authority among students, vice-principals do not have the same power on the board. Experience as an assistant principal is often a prerequisite for advancement to a principalship.