Simulation is now an integral part of
modern fundamental and applied science, and in terms of importance it
approaches traditional experimental and theoretical methods
scientific knowledge.
The purpose of the course is to expand students' understanding of modeling as a method
scientific knowledge, about the use of a computer as a tool for research activities.
The modeling process requires mathematical calculations,
which in the vast majority of cases are very complex. For
development of programs that allow modeling a particular process, from
learners will need not only knowledge of specific languages
programming, but also possession of methods of computational mathematics. At
studying this course it seems appropriate to use packages
applied programs for mathematical and scientific calculations,
targeted at a wide range of users.
mathematical modeling with the development of information computer
technology has become an independent and important area of application
computers. At present, computer modeling in scientific and
practical research is one of the main methods of knowledge.
Without computer simulation, it is now impossible to solve large
scientific and economic tasks. A technology for studying complex
problems based on the construction and analysis using computational
techniques of the mathematical model of the object under study.
This research method is called computational.
experiment. The computational experiment is applied practically in
all branches of science - in physics, chemistry, astronomy, biology, ecology, even in
such purely humanities as psychology, linguistics and philology,
except scientific fields computational experiments are widely used in
economics, sociology, industry, management. Webinar plan:
1. Computer simulation as a method of scientific
knowledge
2. Classification of models
3. Basic concepts of QM
4. Stages of computer simulation 1. Computer modeling as a method of scientific knowledge
The Computer Simulation course is a new and rather challenging course in
cycle information disciplines. Insofar as the KM course is
interdisciplinary course for its successful development requires the presence of the most
diverse knowledge: firstly, knowledge in the chosen subject area - if
we model physical processes, we must have a certain level of
knowledge of the laws of physics, modeling ecological processes - biological
laws, modeling economic processes - knowledge of the laws of economics, except
moreover, because computer simulation uses almost the entire apparatus
modern mathematics, knowledge of the basic mathematical
disciplines - algebra, mathematical analysis, theory of differential equations,
mathematical statistics, probability theory.
To solve mathematical problems on a computer, you need to be proficient in
full scope of numerical methods for solving nonlinear equations, systems
linear equations, differential equations, be able to approximate and
interpolate functions. And, of course, fluency is assumed
modern information technology, knowledge of programming languages
and proficiency in application development. Conducting a computational experiment has a number of advantages over
so-called natural experiment:
- SE does not require complex laboratory equipment;
- a significant reduction in the time spent on the experiment;
- the possibility of free control of parameters, their arbitrary
changes, up to giving them unreal, implausible
values;
- the possibility of carrying out a computational experiment where
full-scale experiment is impossible due to the remoteness of the investigated
phenomena in space (astronomy) or because of its significant
prolongation in time (biology), or because of the possibility of making
irreversible changes in the process being studied. CM is also widely used for educational and training purposes.
KM - the most adequate approach in the study of subjects
natural science cycle, the study of QM opens up wide opportunities
to understand the connection of computer science with mathematics and other natural and social sciences.
The teacher can use ready-made computer
models to demonstrate the phenomenon under study, whether it be movement
astronomical objects or the movement of atoms or a model of a molecule or
microbial growth, etc., the teacher can also challenge students to develop
specific models, modeling a specific phenomenon, the student will not only master
specific learning material, but will also acquire the ability to pose problems and
tasks, predict research results, make reasonable estimates,
highlight the main and secondary factors for building models,
choose analogies and mathematical formulations, use a computer
to solve problems, to analyze computational experiments.
Thus, the use of CM in education makes it possible to bring
methodology of educational activity with the methodology of research
work that should be of interest to you as future teachers. 2. Classification of models
Depending on the construction tools, the following classes of models are distinguished:
- verbal or descriptive models they are also called in some literature
verbal or textual models (for example, a police report from a place
incidents, Lermontov's poem "Quiet Ukrainian Night");
- full-scale models (model of the solar system, toy boat);
- abstract or iconic models. We are interested in mathematical models
phenomena and computer models belong to this class.
You can classify models by subject area:
- physical models,
- biological,
- sociological,
- economic, etc.
Classification of the model according to the applied mathematical apparatus:
- models based on the use of ordinary differential equations;
- models based on the application of partial differential equations;
- probabilistic models, etc. Depending on the purpose of modeling, there are:
- Descriptive models (descriptive) describe the objects being modeled and
phenomena and, as it were, fix a person's information about them. An example would be
model of the solar system, or a model of the movement of a comet, in which we
we model the trajectory of its flight, the distance at which it will pass from the Earth
We have no way to influence the comet's motion or the motion
planets of the solar system;
- Optimization models serve to search best solutions at
subject to certain conditions and restrictions. In this case, the model
includes one or more parameters available to our influence, for example,
well-known traveling salesman problem, optimizing his route, we reduce
transportation cost. Often it is necessary to optimize the process for several
parameters at once, and the goals can be very contradictory, for example,
headache of any housewife - how to feed tastier, more high-calorie and cheaper
family;
- Game models (computer games);
- Training models (all kinds of simulators);
- Simulation models (models that attempt to more or less
full and reliable reproduction of some real process,
for example, modeling the movement of molecules in a gas, the behavior of a colony
microbes, etc.). There is also a classification of models in
depending on their change over time. Distinguish:
-Static models - unchanged in time;
- Dynamic models - the state of which changes
with time. 3. Basic concepts of QM
Model - an artificially created object that reproduces in a certain
the form of a real object - the original.
Computer model - representation of information about the system being modeled
computer means.
System - a set of interrelated elements that have properties,
different from the properties of individual elements.
An element is an object that has properties that are important for modeling purposes.
In the computer model, the properties of an element are represented by the values of the characteristics of the element.
The relationship between elements is described using quantities and algorithms, in particular
computational formulas. The state of the system is represented in the computer model by the set
characteristics of elements and links between elements.
The structure of the data describing the state is independent of the specific
state and does not change when changing states, only the value changes
characteristics.
If the states of the system are functionally dependent on some
parameter, then the process is called a set of states corresponding to
ordered parameter change.
The parameters in the system can change both continuously and discretely.
In a computer model, the change in a parameter is always discrete. Continuous
processes can be simulated on a computer by choosing a discrete series
parameter values so that successive states are little more than
different from each other, or, in other words, minimizing the time step. Statistical models are models in which
information about one state of the system is provided.
Dynamic models - models in which
information about system states and shift processes
states. Optimization, simulation and
probabilistic models are dynamic models.
In optimization and simulation models
state change sequence corresponds to
change of the modeled system in time. IN
probabilistic models, the change of states is determined
random variables. 4. Stages of computer simulation
Modeling begins with the object of study. At the 1st stage, laws are formed,
managing research, there is a separation of information from the real
object, essential information is formed, insignificant information is discarded,
the first step of abstraction takes place. Information transformation is defined
problem to be solved. Information relevant to one task may be
irrelevant to the other. The loss of essential information leads to
wrong solution or does not allow to get a solution at all. Accounting
irrelevant information causes unnecessary complexity, and sometimes creates
insurmountable obstacles to a solution. Transition from real object to
information about it is comprehended only when the task is set. In the same time
the problem statement is refined as the object is studied. That. at stage 1 in parallel
there are processes of purposeful study of the object and clarification of the problem. Also on
At this stage, information about the object is prepared for processing on a computer. The so-called formal model of the phenomenon is built, which contains:
- A set of constants, constants that characterize the simulated
the object as a whole and its constituent parts; called statistical or
constant parameters of the model;
- A set of variables, changing the value of which can be controlled
behavior of the model, called dynamic or control
parameters;
- Formulas and algorithms linking values in each of the states
the object being modeled;
- Formulas and algorithms that describe the process of changing the states of the simulated
object. At stage 2, the formal model is implemented on a computer,
suitable software for this, a solution algorithm is built
problems, a program is written that implements this algorithm, then written
The program is debugged and tested on specially prepared test
models.
Testing is the process of executing a program in order to identify
errors. Selection test model is a kind of art, although for this
developed and successfully implemented some basic principles
testing.
Testing is a destructive process, therefore it is considered that the test is successful,
if an error is found. Check the computer model for compliance
original, check how well or poorly the model reflects the main
properties of an object is often possible with the help of simple model examples, when
the simulation result is known in advance. At the 3rd stage, working with a computer model, we carry out directly
computational experiment. We investigate how our model will behave in that
or otherwise, with certain sets dynamic parameters, trying
predict or optimize something depending on the set
tasks.
The result of a computer experiment will be an information
a model of the phenomenon, in the form of graphs, the dependences of some parameters on others,
diagrams, tables, demonstration of the phenomenon in real or virtual time
and so on. Information modeling at the present stage of development
informatics is impossible without the involvement of technical means, primarily
computers and telecommunications, without the use of programs and
algorithms, as well as ensuring the conditions for the use of these funds on
specific workplace, i.e. achievements of science called ergonomics.
Ergonomics is the science that studies the interaction between man and machine.
in the specific conditions of production activities in order to
rationalization of production.
Ergonomic requirements are:
in the optimal distribution of functions in the "man-machine" system;
rational organization of the workplace;
compliance of technical means with psychophysiological, biomechanical and
anthropological requirements;
creating optimal for life and human performance
indicators of the working environment;
obligatory observance of sanitary and hygienic requirements
to working conditions. V.V. Vasiliev, L.A. Simak, A.M. Rybnikov. Mathematics and
computer simulation of processes and systems in the environment
MATLAB/SIMULINK. Textbook for students and graduate students. 2008
91 pages
Computer simulation of physical problems in
Microsoft Visual Basic. Textbook Author: Alekseev D.V.
SOLON-PRESS, 2009
Author: Orlova I.V., Polovnikov V.A.
Publisher: Vuzovskiy textbook
Year: 2008 Anfilatov, V. S. System analysis in management [Text]: study guide / V. S.
Anfilatov, A. A. Emelyanov, A. A. Kukushkin; ed. A. A. Emelyanova. – M.:
Finance and statistics, 2002. - 368 p.
Venikov, V.A. Theory of similarity and modeling [Text] / V.A. Venikov, G.V.
Venikov.- M.: Vyssh.shk., 1984. - 439 p.
Evsyukov, V. N. Analysis of automatic systems [Text]: educational and methodological
manual for the implementation of practical tasks / V. N. Evsyukov, A. M.
Chernousov. - 2nd ed., Spanish. - Orenburg: IPK GOU OGU, 2007. - 179 p.
Zarubin, V. S. Mathematical modeling in technology [Text]: textbook. for universities /
Ed. V. S. Zarubina, A. P. Krishchenko. - M.: Publishing House of MSTU named after N.E. Bauman, 2001. -
496 p.
Kolesov, Yu. B. Modeling systems. Dynamic and hybrid systems [Text]:
uch. allowance / Yu.B. Kolesov, Yu.B. Senichenkov. - St. Petersburg. : BHV-Petersburg, 2006. - 224 p.
Kolesov, Yu.B. Systems Modeling. Object-oriented approach [Text] :
Uch. allowance / Yu.B. Kolesov, Yu.B. Senichenkov. - St. Petersburg. : BHV-Petersburg, 2006. - 192 p.
Norenkov, I. P. Fundamentals of computer-aided design [Text]: textbook for
universities / I. P. Norenkov. - M .: Publishing house of MSTU im. N.E. Bauman, 2000. - 360 p.
Skurikhin, V.I. Mathematical modeling [Text] / V. I. Skurikhin, V. V.
Shifrin, V. V. Dubrovsky. - K .: Technique, 1983. - 270 p.
Chernousova, A. M. Software automated systems
design and management: tutorial[Text] / A. M. Chernousova, V.
N. Sherstobitova. - Orenburg: OGU, 2006. - 301 p.
Stage I Problem statement. Stage I Problem statement. According to the nature of the formulation, all tasks can be divided into three groups: The first group includes tasks in which it is required to investigate how the characteristics of the object will change with some impact on it: "what will happen if? ..". For example, would it be sweet if you put two teaspoons of sugar in your tea? The second group of tasks has the following formulation: what impact should be made on the object so that its parameters satisfy some given condition? This problem statement is often referred to as "how to do it in order to? ..". For example, how large should a balloon filled with helium be in order for it to rise up with a load of 100 kg? The third group is complex tasks. An example of such an integrated approach is the solution of the problem of obtaining a chemical solution of a given concentration. This stage characterized by two main points: description of the task; definition of modeling goals; 3.
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The presentation on the topic "Computer Models" has been prepared for mastering the types of models: subject and information. The presentation helps in the assimilation of figurative and iconic models, the process of formalization and visualization of models, the need and ways to build models.
- Model representation forms
- Subject Models
- figurative models
- iconic models
- Visualization of formal models
- Formalization
- Examples and need for models
- Ways of building models
For the teacher to teach
Format
pptx (powerpoint)
Number of slides
Galdin V. A.
Audience
Words
Abstract
Present
purpose
slide 1
MBOU LSOSH No. 3 Lokot, Brasovsky district.
Teacher: Galdin Vasily Alekseevich.
slide 2
Model:
slide 3
Model representation forms
- subject (material)
- informational
slide 4
Subject Models
- reproduce the geometric, physical and other properties of objects in the material world (for example, a globe, dummies, models of crystal lattices, buildings).
information models.
- represent objects and processes in figurative or symbolic form.
slide 5
slide 6
Figurative models:
- drawings, photographs, etc. represent visual images and fixed on some medium.
Slide 7
iconic models
- are built using different languages (sign systems), for example, Newton's law, periodic table, maps, graphs, diagrams.
Slide 8
Visualization of formal models:
- the use of various forms for clarity (block diagrams, graphs, spatial drawings, models electrical circuits or logical devices, graphs, diagrams…)
- animation: dynamics, change, relationship between quantities.
Slide 9
Formalization:
- the process of building information models using formal languages.
- physical information models (Ohm's law, electric circuit),
- mathematical models (algebra, geometry, trigonometry),
- astronomical models (model of Ptolemy and Copernicus),
- formal logical models (half-adder, trigger), etc.
Slide 10
Examples and the need for models:
- visual form of the image (globe),
- an important role in the design and creation of various technical devices, machines, mechanisms, buildings or electrical circuits (aircraft, car),
- application of models in theoretical science - theories, laws, hypotheses (model of the atom, Earth, solar system),
- application in artistic creativity (painting, sculpture, theatrical performances).
slide 11
Ways to build models:
- text editors,
- graphic editor,
- presentations,
- Macromedia Flash,
- building a model using one of the applications: spreadsheets, DBMS.
- building an algorithm for solving the problem and coding it in one of the programming languages (Visual Basic, Pascal, Basic, etc.)
slide 12
Geoinformation models
- Planet Earth 4.2
slide 13
Task number 1:
Using the Graphics program to plot function graphs:
a) y=cos(x),
b) y=2cos(x),
c) y=cos(x-2),
d) y=cos(x) - 3
- Save as picture in bmp format
- Insert a picture in Word and sign the names of the functions
Slide 14
slide 15
- y=cos(x)
- y=2cos(x)
- y=cos(x-2)
- y=cos(x)-3
slide 16
Task number 2:
Using the Table program, find the molar mass of substances (write data in a notebook): a) H2O
b) HNO3
c) HSO4
d) HCl
- Find and save information about the chemical element: hydrogen and oxygen
- Put data into Word
Slide 17
Slide 18
Slide 19
Task number 3:
Slide 20
slide 21
Model:
- an object that reflects the essential features of the studied object, process or phenomenon.
- figurative models
- iconic models
slide 22
Homework:
- p. 2.1 - 2.4, pp. 80 -86
- notes in a notebook.
View all slides
Abstract
MBOU LSOSH No. 3 p. Lokot
Brasovsky district
Goals and objectives:
General education
Educational
educators
expanding horizons,
Equipment:
During the classes
Organizing time
Knowledge update
What are our goals and objectives?
Theoretical material of the lesson
� � �
� � �
� � �
� � �
� � �
Formalization:
� � �
theatrical performances).
Ways to build models:
text editors,
graphic editor,
presentations,
Macromedia Flash,
Message: 1 student
1) Geoinformation models
(Message - see attachment)
Message: 2 student
(Message - see attachment)
Message: 3 student
natural science models
(Message - see attachment)
Task number 1:
a) y=cos(x),
b) y=2cos(x),
c) y=cos(x-2),
Task number 2:
Place the data in Word.
Task number 3:
Mathematical model:
Astronomical model:
Physical model:
Summing up the lesson
Survey: 1) Model definition,
2) Types of models,
6) The need for models,
Grading:…
p. 2.1 - 2.4, pp. 80 -86
notes in a notebook.
�PAGE � �PAGE �2�
MBOU LSOSH No. 3 p. Lokot
Brasovsky district
Teacher: Galdin Vasily Alekseevich
Lesson topic: "Computer models"
Goals and objectives:
General education
students should master the basic basic concepts of computer science: model, model definition,
learn the types of models: subject and information,
assimilate figurative and symbolic models, the process of formalization and visualization of models,
the need and ways to build models using a computer,
Educational
form a holistic perception of the world around,
to develop an information vision of the phenomena and processes of the surrounding world when creating and using models,
show the application of models in related sciences and fields: mathematics, physics, chemistry, geography, etc.
educators
formation of cognitive interest of students,
expanding horizons,
the formation of creative thinking in the description of the surrounding world by various subjects of the information and communication environment.
Equipment:
computer class, screen, projector, presentation, handout, global computer network Internet.
During the classes
Organizing time
Knowledge update
The topic of our lesson is computer models, let's remember in which lessons you met with the concept of "model".
Give examples and explain the given "models".
What should we consider today?
What are our goals and objectives?
Theoretical material of the lesson
Model - an object that reflects the essential features of the studied object, process or phenomenon.
Forms of representation of models: subject and informational.
Object models: reproduce the geometric, physical and other properties of objects in the material world (for example, a globe, dummies, models of crystal lattices, buildings).
� � �
Information models: represent objects and processes in figurative or symbolic form.
� � �
Figurative models: drawings, photographs, etc. represent visual images and are fixed on some kind of carrier.
� � �
Sign models are built using various languages (sign systems), for example, Newton's law, periodic table, maps, graphs, diagrams.
Visualization of formal models:
the use of various forms for clarity (block diagrams, graphs, spatial drawings, models of electrical circuits or logical devices, graphs, diagrams ...)
� � �
animation: dynamics, change, relationship between quantities.
� � �
Formalization:
the process of building information models using formal languages.
physical information models (Ohm's law, electric circuit),
mathematical models (algebra, geometry, trigonometry),
astronomical models (model of Ptolemy and Copernicus),
formal logical models (half-adder, trigger), etc.
� � �
Examples and the need for models:
visual form of the image (globe),
an important role in the design and creation of various technical devices, machines, mechanisms, buildings or electrical circuits (airplane, car),
application of models in theoretical science - theories, laws, hypotheses (model of the atom, Earth, solar system),
application in artistic creativity (painting, sculpture,
theatrical performances).
Ways to build models:
text editors,
graphic editor,
presentations,
Macromedia Flash,
building a model using one of the applications: spreadsheets, DBMS.
building an algorithm for solving the problem and coding it in one of the programming languages (Visual Basic, Pascal, Basic, etc.)
Consolidation of the studied material
Message: 1 student
1) Geoinformation models (e.g. Planet Earth 4.2)
(Message - see attachment)
Message: 2 student
2) Graphics program (consider examples of graphing functions)
(Message - see attachment)
Message: 3 student
natural science models
Periodic system of elements of D.I. Mendeleev
(Message - see attachment)
3) Completion of independent tasks:
Task number 1:
Using the Graphics program to plot function graphs:
a) y=cos(x),
b) y=2cos(x),
c) y=cos(x-2),
Insert a picture in Word and sign the names of the functions.
Task number 2:
Using the Table program, find the molar mass of substances (write data in a notebook): a) H2O, b) HNO3, c) HSO4, d) HCl.
Place the data in Word.
Task number 3:
Consider interactive models on the Internet:
Mathematical model:
Astronomical model:
Physical model:
Summing up the lesson
Survey: 1) Model definition,
2) Kinds of models,
3) Examples of material and information models,
4) Figurative and iconic models, examples,
5) Visualization and formalization of models,
6) The need for models,
7) Methods for building models,
8) Examples of models discussed in the lesson,
9) Models in related fields and sciences.
Grading:…
Homework
p. 2.1 - 2.4, pp. 80 -86
notes in a notebook.
�PAGE � �PAGE �2�
Download abstractslide 1
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The presentation on the topic "Computer modeling" (Grade 10) can be downloaded absolutely free of charge on our website. Project subject: Informatics. Colorful slides and illustrations will help you keep your classmates or audience interested. To view the content, use the player, or if you want to download the report, click on the appropriate text under the player. The presentation contains 7 slide(s).
Presentation slides
slide 1
COMPUTER MODELLING
GOU secondary school of the Frunzensky district of St. Petersburg No. 212 Informatics teacher Selezneva R.S.
slide 2
Object and process models
A model is a simplified representation of a real object, process or phenomenon. Modeling - building models for the study and study of objects, processes, phenomena. Models of objects can be reduced copies of architectural structures or works of art, as well as visual aids in a school office, etc. A model can reflect something that really exists, say, a hydrogen atom. Solar system, lightning discharge. Classification of models Models are classified according to the following criteria: Area of use Consideration of the time factor (dynamics) in the model Branch of knowledge Method of representation of models
slide 3
Classification by area of use
Models Training Experienced
Scientific and technical
Game Simulation
Training models - visual aids, various simulators, training programs. Experimental models are reduced or enlarged copies of the designed object. For example, a model ship is tested in a pool to determine the ship's roll stability. Scientific and technical models - for the study of processes and phenomena. An example is a device that simulates a lightning discharge. Game models are military, economic, sports, business games. They seem to rehearse the behavior of the object in various situations. Simulation models are an experiment that mimics reality. For example, suppose a school wants to introduce a new subject. A number of schools are selected for the experiment, and then the results are checked.
slide 4
CLASSIFICATION ACCORDING TO THE FACTOR OF TIME AND AREA OF USE
MODELS Static Dynamic
A static model is a one-time slice of information on an object. For example, an examination of schoolchildren in a dental clinic gives a picture of the state of their oral cavity on this moment time. Dynamic model - allows you to see changes in an object over time. Example. A student card from a dental clinic for many years.
slide 5
Classification by way of presentation
Material Information Sign Verbal Computer Non-computer
slide 6
Material models - reproduce the geometric and physical properties of the original and always have a real embodiment. Example. Children's toys, stuffed birds, maps on history, geography, rocket model, etc. Information models - they cannot be seen with your own eyes and touched, they do not have a material embodiment. They are based on information. An information model is a set of information that characterizes the properties and states of an object, process, or phenomenon. verbal model - information model in a mental or spoken form. Example, human behavior when crossing the street. The person analyzes the situation and then takes action. A sign model is an information model expressed special signs, i.e. by means of any formal language. Example, drawings, texts, graphs and diagrams. A computer model is a model implemented by means of a software environment. Example, computer program(music editor), which allows you to type musical text, print it, make an arrangement.
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