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Mathematical Modeling Jn Kapur Pdf Download
is a description of the system using mathematical concepts and language. One of the possible approaches is to write a description in terms of the objective function.
To describe any system in terms of the objective function, in addition to the code, in addition to describing the types of elements, a class of properties describing the behavior of the system can also be indicated.
Here we see the following description plan:
Characteristics – Attributes
Structure description – A way to describe a structure
Description and use of the parametric mechanism – Way of describing the implementation
Relationship description – Relationship between parameters
Description of operations – Description of operations
Description of classes – Class
Description of processes – Processes
Description of variables – Variables
Description of properties – Properties
Features – Features
Here is an example of a system description in the form of a book:
In this case (book), we will talk about three physical models of the system: “world” and “life” (physical bodies) and “time” (the material world), taking into account the “time calculation” system
Model “world”:
In the “world” model, as already mentioned, the following classes of properties are distinguished:
Description – The environment that is the subject of this process;
Description – type – “Mir 5” and other
Description of the object – Subject
Description of interaction with other items – Interaction
Description of models – systems – methods – functions
And, finally, we will leave without attention for the time being the third category – the description of subsystems.
We will briefly present the definition of concepts and conceptual schemes in terms of the system. It is also important that the representation of the model is carried out in the form of a diagram:
And here the question arises: why is a group of complex objects called models?
Indeed, a complex object includes many elements. Each of these elements, as a rule, has its own concept and some distinctive characteristic, which in essence characterizes the system differently.
Thus, a group of separate objects (or one object) is an object described in the model language.
Next, let’s try to describe the system using simple mathematical objects that are currently widely used to describe processes.
Imagine that we have an object “man” and a system where each object has only one common property – “moral values”.
As a result of such a system in a more general form, we represent it in the form of the following model:
And now let’s make a representation of this system in accordance with existing mathematical models.Namely, imagine that we use the following model to describe human behavior:
It becomes clear that the “man 5” model is a “man” model
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