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Overview
Published in Brian Vick, Applied Engineering Mathematics, 2020
Some tremendous software packages are currently available. Two of the best and most popular choices are Mathematica and MATLAB®. Mathematica is a powerful software package and programming language, which combines numerical computations, symbolic manipulation, graphics, and text. Its symbolic manipulation capabilities are the most powerful ever developed. Mathematica is built on the powerful unifying idea that everything can be represented as a symbolic expression.MATLAB® is also a programming language that combines numerical computations with graphics. It also has symbolic manipulation capability. The basic data structure in MATLAB® (Matrix Laboratory) is the matrix.Programming sophisticated software packages can be powerful tools only if one has the necessary skill to program them. This requires logical and structured programming skills. These can only be achieved through tremendous study, practice, and patience.
Overview on the numerical engineering simulation software
Published in Nicolae Vasiliu, Daniela Vasiliu, Constantin Călinoiu, Radu Puhalschi, Simulation of Fluid Power Systems with Simcenter Amesim, 2018
Nicolae Vasiliu, Daniela Vasiliu, Constantin Călinoiu, Radu Puhalschi
Mathematica32 is a symbolic mathematical computation program, sometimes called a computer algebra program, used in many scientific, engineering, mathematical, and computing fields. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois. The Wolfram language is the programming language used in Mathematica. This software has nearly 5000 built-in functions covering all areas of technical computing—all carefully integrated, so they work perfectly together, and all included in a fully integrated system. Mathematica builds in unprecedentedly powerful algorithms across all areas—many of them created at Wolfram using unique development methodologies and the unique capabilities of the Wolfram language. Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across all areas, capable of handling large-scale problems, with parallelism, GPU computing, and more. Mathematica uses the Wolfram Notebook Interface, which allows you to organize everything you do in rich documents that include text. Wolfram System Modeler is an easy-to-use, next-generation modeling, and simulation environment for cyber-physical systems. Using drag-and-drop from the large selection of built-in and expandable modeling libraries, you can build industrial strength, multidomain models of your complete system. Adding the power of Mathematica the designer obtains a fully integrated environment for analyzing, understanding, and quickly iterating system designs.
Chapter 20: Symbolic and Numerical Solutions of ODES with Mathematica
Published in Andrei D. Polyanin, Valentin F. Zaitsev, Handbook of Ordinary Differential Equations, 2017
Andrei D. Polyanin, Valentin F. Zaitsev
The most important features of Mathematica are fast symbolic, numerical, acoustic, and parallel computation; static and dynamic computation, and interactive visualization; it can incorporate new user-defined capabilities; it is available for almost all operating systems; it has a powerful and logical programming language; there is an extensive library of mathematical functions and specialized packages; an interactive mathematical typesetting sys-tem is available; and there are numerous free resources (e.g., see the Mathematica Learning Center, www.wolfram.com/support/learn; Wolfram Demonstrations Project, demonstrations.wolfram.com; Wolfram Library Archive, library. wolfram.com; Wolfram Information Center, library.wolfram.com/infocenter; Wolfram Community, community.wolfram.com, etc.).
Imaging phase plane models
Published in International Journal of Mathematical Education in Science and Technology, 2023
Richard F. Melka, Hashim A. Yousif
Our SageMath program calculates phase plane portraits and is provided subsequently. We point out that Wolfram Alpha can also easily calculate the phase plane portrait. Once this program is activated, the user is prompted to enter the expressions of and given by Equation (1) and the ranges of the variables of . The user does not need to write software, thereby it serves as a convenient ancillary tool. However, the user has no control over the graph details such as the size graph’s letters and the numbers as well as the density of the curves. If these details are needed, Mathematica could be used instead. Mathematica offers many predefined functions and integrated packages; furthermore, it has powerful symbolic computation capability along with graphing, modelling and visualization.