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2. List of finite element software packages - Wikipedia

   en.wikipedia.org/wiki/List_of_finite_element...

   Full API for Java and, through add-on product, Matlab Runtime parsed mathematical expression in input files Fully scriptable in as m-file Matlab scripts and the GUI supports exporting models in script format automatic differentiation: Yes Yes Yes Forward-mode for Jacobian computation, symbolic differentiation capabilities multiphysics:

3. List of open-source software for mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_open-source...

   SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.

4. Automatic differentiation - Wikipedia

   en.wikipedia.org/wiki/Automatic_differentiation

   Symbolic differentiation faces the difficulty of converting a computer program into a single mathematical expression and can lead to inefficient code. Numerical differentiation (the method of finite differences) can introduce round-off errors in the discretization process and cancellation. Both of these classical methods have problems with ...

5. PDFtk - Wikipedia

   en.wikipedia.org/wiki/Pdftk

   PDFtk (short for PDF Toolkit) is a toolkit for manipulating Portable Document Format (PDF) documents. [3] [4] It runs on Linux, Windows and macOS. [5] It comes in three versions: PDFtk Server (open-source command-line tool), PDFtk Free and PDFtk Pro (proprietary paid). [2] It is able to concatenate, shuffle, split and rotate PDF files.

6. Numerical differentiation - Wikipedia

   en.wikipedia.org/wiki/Numerical_differentiation

   The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.

7. Finite difference method - Wikipedia

   en.wikipedia.org/wiki/Finite_difference_method

   The method is based on finite differences where the differentiation operators exhibit summation-by-parts properties. Typically, these operators consist of differentiation matrices with central difference stencils in the interior with carefully chosen one-sided boundary stencils designed to mimic integration-by-parts in the discrete setting.

8. GNU TeXmacs - Wikipedia

   en.wikipedia.org/wiki/GNU_TeXmacs

   GNU TeXmacs is a scientific word processor and typesetting component of the GNU Project.It originated as a variant of GNU Emacs with TeX functionalities, though it shares no code with those programs, while using TeX fonts. [4]

9. Functional derivative - Wikipedia

   en.wikipedia.org/wiki/Functional_derivative

   A formula to determine functional derivatives for a common class of functionals can be written as the integral of a function and its derivatives. This is a generalization of the Euler–Lagrange equation : indeed, the functional derivative was introduced in physics within the derivation of the Lagrange equation of the second kind from the ...