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Figure 2. Xcas can solve equations, calculate derivatives, antiderivatives and more. Figure 3. Xcas can solve differential equations. Xcas is a user interface to Giac, which is an open source [2] computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Xcas is written in C++. [3]
However, this formal similarity notwithstanding, possessing a complex-antiderivative is a much more restrictive condition than its real counterpart. While it is possible for a discontinuous real function to have an anti-derivative, anti-derivatives can fail to exist even for holomorphic functions of a complex variable.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
In particular, Nyström methods work directly with second-order equations. geometric integration methods [18] [19] are especially designed for special classes of ODEs (for example, symplectic integrators for the solution of Hamiltonian equations). They take care that the numerical solution respects the underlying structure or geometry of these ...
This visualization also explains why integration by parts may help find the integral of an inverse function f −1 (x) when the integral of the function f(x) is known. Indeed, the functions x ( y ) and y ( x ) are inverses, and the integral ∫ x dy may be calculated as above from knowing the integral ∫ y dx .
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
For example, to obtain the antiderivative of that has the value 400 at x = π, then only one value of will work (in this case =). The constant of integration also implicitly or explicitly appears in the language of differential equations. Almost all differential equations will have many solutions, and each constant represents the unique ...