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The function Ai(x) and the related function Bi(x), are linearly independent solutions to the differential equation =, known as the Airy equation or the Stokes equation. Because the solution of the linear differential equation d 2 y d x 2 − k y = 0 {\displaystyle {\frac {d^{2}y}{dx^{2}}}-ky=0} is oscillatory for k <0 and exponential for k >0 ...
In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations. [9]
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft , it is primarily targeted at students as a learning tool.
A simple arithmetic calculator was first included with Windows 1.0. [6]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
A graphing-calculator plug-in is available for simple calculations and manipulations MathML MiraiMath: Yes Yes No Yes No Yes Yes No Java WYSIWYG Editor, Open Source. Can be used as alternative front end to GNU Octave: Yes MyTexPoint: No Yes No Yes Yes No No No a small free program for inserting LaTeX equations into PowerPoint with a screen-shot ...
Most root-finding algorithms can find some real roots, but cannot certify having found all the roots. Methods for finding all complex roots, such as Aberth method can provide the real roots. However, because of the numerical instability of polynomials (see Wilkinson's polynomial ), they may need arbitrary-precision arithmetic for deciding which ...
The asymptotic behaviour is very good: generally, the iterates x n converge fast to the root once they get close. However, performance is often quite poor if the initial values are not close to the actual root. For instance, if by any chance two of the function values f n−2, f n−1 and f n coincide, the algorithm fails completely. Thus ...
If x is a simple root of the polynomial , then Laguerre's method converges cubically whenever the initial guess, , is close enough to the root . On the other hand, when x 1 {\displaystyle \ x_{1}\ } is a multiple root convergence is merely linear, with the penalty of calculating values for the polynomial and its first and second derivatives at ...