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The resulting object is called an object copy or simply copy of the original object. Copying is basic but has subtleties and can have significant overhead. There are several ways to copy an object, most commonly by a copy constructor or cloning. Copying is done mostly so the copy can be modified or moved, or the current value preserved.
In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, [1] [2] and extended by Ralph Kochenburger [3] is an approximate procedure for analyzing certain nonlinear control problems.
In the definition, the functional derivative describes how the functional [()] changes as a result of a small change in the entire function (). The particular form of the change in ρ ( x ) {\displaystyle \rho (x)} is not specified, but it should stretch over the whole interval on which x {\displaystyle x} is defined.
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
The precise meaning of the variables and depends on the context of the application and the required level of mathematical rigor. The domain of these variables may take on a particular geometrical significance if the differential is regarded as a particular differential form , or analytical significance if the differential is regarded as a ...
In mathematics, the total derivative of a function f at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one.
The original notation employed by Gottfried Leibniz is used throughout mathematics. It is particularly common when the equation y = f(x) is regarded as a functional relationship between dependent and independent variables y and x.
In this case, if we make a very large matrix with complex exponentials in the rows (i.e., cosine real parts and sine imaginary parts), and increase the resolution without bound, we approach the kernel of the Fredholm integral equation of the 2nd kind, namely the Fourier operator that defines the continuous Fourier transform. A rectangular ...