Презентация «Construction principles»

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Презентация «Construction principles»

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construction principles and classification of mathematical models Zhanar Omarova Associate Professor
construction principles and classification of mathematical models Zhanar Omarova Associate Professor of IITU Department of Information Systems and Mathematical Modeling
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Main goal of all external world discovery of investigations should be the rational order and harmony
Main goal of all external world discovery of investigations should be the rational order and harmony which God gave to the world and revealed it to us in the language of mathematics. Johannes Kepler …
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Mathematical modeling is a specific form of the world cognition, which is able to translate the laws
Mathematical modeling is a specific form of the world cognition, which is able to translate the laws of nature studied by individual sciences into mathematical language, to see real-life events …
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Researcher studies objects of interest, watches the course of events, and interferes in them by aski
Researcher studies objects of interest, watches the course of events, and interferes in them by asking certain questions and getting appropriate answers. After examining some information about the …
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Simplified diagram of the cognition process Simplified diagram of the cognition process
Simplified diagram of the cognition process Simplified diagram of the cognition process
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main stages of mathematical modeling
main stages of mathematical modeling
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principles of the mathematical model construction It is possible to identify some common laws in the
principles of the mathematical model construction It is possible to identify some common laws in the construction of mathematical models. First of all, we should understand what exactly is the object …
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After determination of the system functions and independent variables, we have to specify the coordi
After determination of the system functions and independent variables, we have to specify the coordinate system within which a mathematical model will be constructed. After determination of the …
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Having written mathematical relations which express cause-and-effect relation for the phenomenon, we
Having written mathematical relations which express cause-and-effect relation for the phenomenon, we will find out that besides the system functions and independent variables mathematical model …
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Thus, the mathematical model usually includes three classes of characteristics. Parameters of the pr
Thus, the mathematical model usually includes three classes of characteristics. Parameters of the process in each case are fixed quantities which compose the input data. Independent variables are not …
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Process of construction mathematical model includes the following elements: Object of study Function
Process of construction mathematical model includes the following elements: Object of study Functions of the system condition / System functions Independent variables Coordinate system Reasons for …
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Now we have specific mathematical relations. They should be studied on the basis of various quantita
Now we have specific mathematical relations. They should be studied on the basis of various quantitative and qualitative methods. Conducting appropriate analysis using only mathematical tools …
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classification of mathematical models Depending on the specifics of variables constituting mathemati
classification of mathematical models Depending on the specifics of variables constituting mathematical models, we can specify some of the principles of classification. Lumped parameter system, in …
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Stochastic models, which may have impact on the process random factors. Stochastic models, which may
Stochastic models, which may have impact on the process random factors. Stochastic models, which may have impact on the process random factors. Deterministic models, in which such impact is ignored, …
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Equation of the falling body The first mathematical model, which meets all academic requirements is
Equation of the falling body The first mathematical model, which meets all academic requirements is associated with the name of Galileo and describes the process of falling bodies under their own …
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If the velocity v of the body is known, we obtain the relation If the velocity v of the body is know
If the velocity v of the body is known, we obtain the relation If the velocity v of the body is known, we obtain the relation = v (l. l) Equation (1. 1), we suppose, should describe the process under …
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In the third stage of the study we will try to interpret the results. First of all, we have to find
In the third stage of the study we will try to interpret the results. First of all, we have to find out whether constructed model describes the phenomenon in question. To do this, we compare the …
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Obviously, the position of the body will essentially depend on the exact position of the body at som
Obviously, the position of the body will essentially depend on the exact position of the body at some initial time. Suppose that body has initial height: Obviously, the position of the body will …
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We again interpret the results and find out mismatch of calculated height of falling body to its exp
We again interpret the results and find out mismatch of calculated height of falling body to its experimental value. Indeed, a simple experiment shows that in the period of falling the body velocity …
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The variation law of the body velocity is not known. Velocity of change of the function v, that is i
The variation law of the body velocity is not known. Velocity of change of the function v, that is its derivative (or second derivative of the coordinate ÿ) in mechanics is called acceleration and is …
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Definition of the body height is reduced to finding its derivative (velocity). For calculation of ve
Definition of the body height is reduced to finding its derivative (velocity). For calculation of velocity is required to find its derivative (acceleration). Reliable experiment shows that the …
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Positive value g = -а is called free fall acceleration, and it is an absolute constant which is inde
Positive value g = -а is called free fall acceleration, and it is an absolute constant which is independent from process conditions. Thus, the relation (1. 6) can be written as: Positive value g = -а …
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Solving equation (1. 8) with the initial condition (1. 7), we find that the velocity of a falling bo
Solving equation (1. 8) with the initial condition (1. 7), we find that the velocity of a falling body will be changed by the following law: Solving equation (1. 8) with the initial condition (1. 7), …
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The additional information Then, based on the properties of the mathematical model we can get some a
The additional information Then, based on the properties of the mathematical model we can get some additional information on the behavior of the system under study. In particular, it is important for …
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Another characteristic of the process, which has practical importance, is the body velocity at the f
Another characteristic of the process, which has practical importance, is the body velocity at the falling time. For a given initial height of the body, it is equal to: Another characteristic of the …
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A final remark concerns the conditions of applicability of the mathematical model. The model describ
A final remark concerns the conditions of applicability of the mathematical model. The model describes the studied process only in the time interval from zero to T, as long as the body does not reach …
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Thus, the complete mathematical model of the process includes the state equations (1. 1), (1. 8) on
Thus, the complete mathematical model of the process includes the state equations (1. 1), (1. 8) on the time interval 0 <t <T , the initial conditions (1. 3), (1. 7), relation (1. 9) to find …
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main elements of the mathematical model of the falling body process
main elements of the mathematical model of the falling body process
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It should be noted that the results correspond to some particular level of study of the process, and
It should be noted that the results correspond to some particular level of study of the process, and if necessary can be refined. Thus, we have completely ignored the effect of air resistance, the …
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Thank you for your attention!
Thank you for your attention!


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