Theme 3. Mathematical modeling. Computer Mathematics Systems

4. Computer Mathematics Systems

With the advent of the PC, a number of software systems were created that implemented a wide range of methods for solving various problems in mathematics.

Systems of computer mathematics replace the work of mathematicians - theorists and analysts of a high level. There are already discoveries made using such systems.

The term " computer mathematics " includes a set of both theoretical and methodological tools, as well as modern software and hardware, allowing to perform all mathematical calculations with high accuracy and productivity, to build complex chains of computational algorithms with wide possibilities of visualization of processes and data when processing them. .

Initially, systems of computer mathematics were divided into two different groups: for numerical and symbolic (analytical) calculations.

The first group was Eureka, MathCAD, MatLAB, Excel.

The second group included Derive, MuPAD, Mathematica and Maple. Today, this classification is conditional.

Each of these systems of computer mathematics has the characteristic features of the internal construction and implementation of the interface.

MathCAD arithmetic computing system

MathCAD is a popular computer mathematics system designed to automate solving common mathematical problems in various fields of science, technology, and learning.

The name MathCAD comes from the words MATHematic (mathematics) and CAD (Computer Aided Design). Developer - MathSoft Inc. ( http://www.mathsoft.com ). To date, MathCAD 15 is used. The price is about $ 800.

System Structure:

• document editor - system for typing text, formulas, charts, etc .;
• MathConex - Integrator with other systems;
• Help system - thematic and indexed directory of help;
• quick cheat sheet - short examples with minimal comment, built-in operators and functions, etc.

The calculations in MathCAD can be done in one of three ways:

• selecting operation in the menu;
• using toolbars;
• addressing the relevant functions.

A document in MathCAD, called WorkSheets (worksheets), combines a code written in a visually-oriented language, which is almost the same as the usual language of mathematics.

The description of the algorithm is carried out in the usual mathematical form with the use of commonly accepted symbols, for example, root square, integral, matrix, etc.

The MathCAD interface is a collection of tools that provide MathCAD management through the keyboard and mouse.

Main menu and standard toolbar.

The panels of analytical calculations provide a quick set of arithmetic operators, plotting, matrix operations, and the like.

The following concepts and objects of the MathCAD system are identified - identifiers, constants, variables, arrays, operators, functions, control structures, etc.

Constants are named objects that store constant values, for example, a number. Some constants are systemic.

Operators are the elements of the language in which mathematical expressions are created. These include symbols of arithmetic operations, derivatives, integrals, etc.

Built-in functions implement the implementation of generally accepted mathematical calculations, in particular, trigonometric sin ( x ) .

MatLAB engineering calculation system

The MatLAB system (abbreviated as MATrix LABoratory - matrix laboratory) is an interactive system for utilizing engineering and scientific calculations with a focus on working with data arrays.

Created by MatLAB by MathWork Inc. (http://www.mathwork.com USA). Widely began to be used in the late 80's after the appearance of the MatLAB 4.0 market. The price is about $ 2940.

Among the main areas of MatLAB application are mathematical calculations, data analysis and visualization, application development, including graphical user interface. Built-in universal interfaces make it easy to work with external information sources, integrate with procedures written in C, Java, etc.

MatLAB has digital processing of signals and images, designing control systems, science, etc. Multiplatform MatLAB has made it one of the most widely used products - it has actually become the world-wide standard of technical computing.

The system is different from other similar thanks to:

• designation for engineering calculations;
• a programming language that is close to BASIC is used ;
• easy integration with other systems.

Calculations in the MatLAB environment can be performed in the following modes:

• calculator;
• programming.
• work with vectors and matrices.

System of scientific researches Mathematica

Mathematica System - Wolfram Research , Inc. ( http://www.wolfram.com/ ) has an extremely wide range of tools that translate complex mathematical algorithms into applications. The price is about $ 1460.

Mathematica 1, which appeared in 1988, became the first serious system of computer algebra, which aroused interest from lecturers of universities, postgraduates, engineers and scientists all over the world.

All the algorithms contained in the course of higher mathematics of higher educational institutions are laid in the memory of the system Mathematica .

Mathematica began to feel the sharp competition of other systems of computer mathematics, such as Maple.

Often, users abandoned Mathematica simply because they did not understand the language of the functional programming of the system, the unusual typing of the input by the keys Shift + Enter (usually the input is fixed with the Enter key ), unusual function names, such as Sin [x], with parameters in square brackets and others "trivia".

The advantages of Mathematica include elements of dynamic variables, interactive interface, performs computing faster than its competitors through the support of the capabilities of modern multi-core processors.