Search results
Results from the WOW.Com Content Network
The expression (,) (read: "the map taking x to f of x comma t nought") represents this new function with just one argument, whereas the expression f(x 0, t 0) refers to the value of the function f at the point (x 0, t 0).
Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...
During the mid-20th century, some mathematicians adopted postfix notation, writing xf for f(x) and (xf)g for g(f(x)). [18] This can be more natural than prefix notation in many cases, such as in linear algebra when x is a row vector and f and g denote matrices and the composition is by matrix multiplication. The order is important because ...
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1.
The solutions –1 and 2 of the polynomial equation x 2 – x + 2 = 0 are the points where the graph of the quadratic function y = x 2 – x + 2 cuts the x-axis. In general, an algebraic equation or polynomial equation is an equation of the form =, or = [a]
The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).
Formally, let p(x, y) be a complex polynomial in the complex variables x and y. Suppose that x 0 ∈ C is such that the polynomial p(x 0, y) of y has n distinct zeros. We shall show that the algebraic function is analytic in a neighborhood of x 0. Choose a system of n non-overlapping discs Δ i containing each of these zeros. Then by the ...