1. What is mathematical modeling?

Mathematical modeling is a process of describing actual phenomena with mathematical language. The actual phenomena here include both concrete natural phenomena such as free fall and abstract phenomena.

For example, the customer's value orientation to a certain commodity. The description here includes not only the description of external form and internal mechanism, but also the prediction, experiment and explanation of actual phenomena.

We can also intuitively understand this concept: mathematical modeling is a way to turn pure mathematicians (mathematicians who only know mathematics but don't know its application in practice) into things.

The process of philosophers, biologists, economists and even psychologists.

2. What is a mathematical model?

Mathematical model refers to the actual things or phenomena described in mathematical language. Generally, it is a mathematical simplification of practical things. It is often close to the actual thing in a sense.

The abstract form exists, but it is essentially different from the real thing. There are many ways to describe an actual phenomenon, such as recording, video recording, metaphor, rumors and so on.

Wait a minute. In order to make the description more scientific, logical, objective and repeatable, people use a language that is generally considered rigorous to describe various phenomena. This language is

What is described in mathematical language is called a mathematical model. Sometimes we need to do some experiments, but these experiments are often based on abstract mathematical models.

The experiment itself is also a theoretical substitute for the actual operation.

3. Why do you want to build a mathematical model?

In the field of science, mathematics has become the most widely used communication language for researchers because of its well-known accuracy-because they generally believe that nature is strictly evolved.

Yes, although the laws governing evolution may be complex and even chaotic. Therefore, people often establish various mathematical models for practical things in order to describe them through the investigation of the models.

Explain, predict or analyze the laws related to practical things.

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Introduction of Mathematical Modeling Software

Generally speaking, there are four commonly used softwares for learning mathematical modeling, namely: matlab, lingo, Mathematica and SAS. Let's briefly introduce these four kinds.

1 overview. matlab

MATLAB stands for matrix laboratory. Besides excellent numerical calculation ability, it also provides professional symbolic calculation and text processing.

Management, visual modeling, simulation and real-time control.

The basic data unit of MATLAB is matrix, and its instruction expression is very similar to that commonly used in mathematics and engineering, so it is better to solve problems with MATLAB than with C and FORTRAN.

Language is much easier to do the same thing.

At present, the popular MATLAB 5.3/Simulink 3.0 includes a main package with hundreds of internal functions and more than 30 toolboxes, which can be divided into functional tools.

Packaging and theme kits. The function toolkit is used to expand the functions of MATLAB, such as symbolic calculation, visual modeling and simulation, word processing and real-time control. Theme toolkits are professional.

Toolkit, control toolkit, signal processing toolkit, communication toolkit, etc. All fall into this category.

Openness makes MATLAB popular with users. Except for internal functions, all MATLAB main package files and various toolkits are readable and modifiable files. Users can modify the source program.

Or add your own program to build a new special toolbox.

2. Overview 2. mathematics

Wolfram Research is a pioneer of high-tech computer computing, founded by stephen wolfram, the inventor of complex theory.

1987, 1988 introduced Mathematica, a high-tech computer operation software, which is a genius product comparable to the Nobel Prize. Mathematica is a set of comprehensive numbers used to

And symbolic operation, providing top-level software that is easy to use for more than one million researchers, engineers, physicists, analysts and other technical professionals around the world.

Scientific computing environment. At present, it has been widely used in academia, electrical engineering, chemistry, civil engineering, information engineering, finance, medicine, physics, statistics, education and publishing, OEM and other fields.

Widely used.

Characteristics of Mathematica

Mathematica 5, with its high-order calculation method, rich mathematical function library and huge mathematical knowledge base, can perform numerical operations in linear algebra such as eigenvectors and inverse matrices faster and better than Matlab R 13, providing the most accurate numerical operation results in the industry.

Mathematica can not only perform numerical calculation, but also provide the best designable symbolic operation.

Rich mathematical function library can quickly solve calculus, linear algebra, differential equations, complex variable functions, numerical analysis, probability statistics and so on.

Mathematica can draw graphs of professional functions in various professional fields, provide rich graphical representation methods and visualize the results.

Mathematica can organize professional scientific papers and periodicals, make calculation and typesetting complete in the same environment, provide high-quality editable typesetting formulas and tables, automatically optimize the typesetting of screen and print, organize the plan from initial concept to final report, and provide the best compatibility for the output of txt, html, pdf and other formats.

It can be combined with C, C++, Fortran, Perl, Visual Basic and Java to provide powerful high-level language interface functions and make program development more convenient.

Mathematica itself is a simple and easy-to-learn programming language. Mathematica provides interactive and rich help functions, so that users can learn and sell now. Powerful, easy to operate and easy to learn, it can shorten the research and development time most effectively.

3.3.lingo overview

LINGO is used to solve nonlinear programming (NLP- nonlinear programming) and quadratic programming (QP- quadratic programming).

LINGO 6.0 student edition can publish at most 300 variables, 150 constraint rule problems, and its standard edition has a solving ability exceeding 10 4. Although Lin Duohe

LINGO can't directly solve the goal planning problem, but it can be decomposed into the planning problem that LINDO and LINGO can solve by sequence algorithm.

Integration of Modeling Language and Solving Engine

LINGO is a comprehensive tool to build and solve linear, nonlinear and integer optimization models faster, simpler and more effectively. LINGO provides a powerful language and a fast solving engine to explain and solve the optimization model.

■ Simple model representation

LINGO can quickly formulate linear, nonlinear and integer problems, which is easy to read, understand and modify.

■ Convenient data input and output selection

The model established by LINGO can get data directly from the database or worksheet. Similarly, LINGO can directly output the solution results to a database or worksheet.

■ Powerful solution engine

LINGO's built-in solving engine includes linear, nonlinear (convex and non-convex), quadratic, quadratic constraint and integer optimization.

■ Interactive modeling or creating turnkey applications

LINGO provides a completely interactive environment for you to build, solve and analyze models. LINGO also provides dll and OLE interfaces for users to call from written programs.

■ Extensive documentation and help functions

All the tools and documents provided by LINGO can help you get started quickly. LINGO user manual has detailed functional definitions.

4. Overview 4. SAS software

The full name of SAS system is Statistics Analysis System, which was first written by two graduate students of biostatistics at the University of North Carolina. 1976, SAS software institute was established and SAS software was officially launched. SAS is a large-scale integrated information system for decision support, but the earliest function of the software system is limited to statistical analysis, which is still an important part and core function. The current version of SAS is version 9.0, and its size is about1g. After years of development, SAS has been adopted by nearly 30,000 organizations in more than 20 countries and regions around the world, with more than 3 million direct users, covering financial, medical and health, production, transportation, communication, government, education, scientific research and other fields. In Britain, America and other countries, skilled use of SAS for statistical analysis is one of the conditions for many companies and scientific research institutions to choose materials. In the field of data processing and statistical analysis, SAS system is known as the international standard software system, and was selected as the first choice product for establishing database in 1996 ~ 1997. Is a giant in the field of statistical software. Here is just one example: in the FDA's new drug approval procedure, it is stipulated that the statistical analysis of new drug test results can only be carried out by SAS, and the calculation results of other software are invalid! Even the simple mean and standard deviation are not good! This shows the authoritative position of SAS.

SAS system is a composite software system, which consists of several functional modules, and its basic part is BAS.