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# Disadvantages of Mathematical Model

The basic idea behind developing a mathematical model is to make things easier to explain certain application of science, economics, and political science or even sociology related theories.
The most intriguing part of such models is that these help understand the fundamental concepts in real world situation. These can come in any form varying from statistical models to gaming console.
The underlying point in such models is to make one understand the concepts in more in depth manner. The models throw up lot of interesting facts about the concepts and help in getting the basics of such theories.

Mathematical models also significantly reduces the time to come to an conclusion, true but these models also throws up some other valid points as well. Are these models good enough for all such situations that we come across every day? A mathematical model will not take into account the physical system, biotic or abiotic conditions that prevail in any particular region or country.
Secondly the formulas or rules that are applied to find a conclusion out of an impending situation may not give the actual scenario and only provide factual data. This leads to a situation where many points are either missed or are overlooked and ultimately leads to wrong conclusion.

To drive these points lets discuss some real life situation. The Asian tsunami and before that the Eastern India super cyclone that occurred in the recent past gave us a brief idea that around 200 thousand people died. The Governments came to conclusion about these numbers by taking into account the database that was available in their system. No one took into account the floating population that stayed in that area during that time. This lead to an conclusion that post catastrophe compensation provided was good enough and even during the rescue operation the Government departments were clueless about how many people needs to evacuated and how much of stationaries need to be distributed.

In both the above mentioned situation the data available in system were taken into consideration but not the real time head count.
Even for planning commission the entire five year planning is based on data and a number collected from citizens are again bereft of real facts and instead carries lots of inferences. The entire public distribution system depends upon these vital statistics but mathematical model won’t take into account the religious belief or stigmas into account and provide a different version of the entire thing.
Mathematical models are well accepted till these above mentioned fields are taken into consideration.

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From Wikipedia

Mathematical model

Note: The term model has a different meaning inmodel theory, a branch of mathematical logic. An artifact which is used to illustrate a mathematical idea may also be called a mathematical model, and this usage is the reverse of the sense explained below.

A mathematical model is a description of a system using mathematical language. The process of developing a mathematical model is termed mathematical modelling (also written modeling). Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively.

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.

## Examples of mathematical models

• Population Growth. A simple (though approximate) model of population growth is theMalthusian growth model. A slightly more realistic and largely used population growth model is the logistic function, and its extensions.
• Model of a particle in a potential-field. In this model we consider a particle as being a point of mass which describes a trajectory in space which is modeled by a function giving its coordinates in space as a function of time. The potential field is given by a function V : R3â†’ R and the trajectory is a solution of the differential equation
m \frac{d^2}{dt^2} x(t) = - \operatorname{grad} \left( V \right) (x(t)).
Note this model assumes the particle is a point mass, which is certainly known to be false in many cases in which we use this model; for example, as a model of planetary motion.
• Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labeled 1,2,...,n each with a market price p1, p2,..., pn. The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of commodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which is used to purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of rational behavior in this model then becomes an optimization problem, that is:
\max U(x_1,x_2,\ldots, x_n)
subject to:
\sum_{i=1}^n p_i x_i \leq M.
x_{i} \geq 0 \; \; \; \forall i \in \{1, 2, \ldots, n \}
This model has been used in general equilibrium theory, particularly to show existence and Pareto efficiency of economic equilibria. However, the fact that this particular formulation assigns numerical values to levels of satisfaction is the source of criticism (and even ridicule). However, it is not an essential ingredient of the theory and again this is an idealization.

Modelling requires selecting and identifying relevant aspects of a situation in the real world.

## Background

Often when engineers analyze a system to be controlled or optimized, they use a mathematical model. In analysis, engineers can build a descriptive model of the system as a hypothesis of how the system could work, or try to estimate how an unforeseeable event could affect the system. Similarly, in control of a system, engineers can try out different control approaches in simulations.

A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The values of the variables can be practically anything; real or integer numbers, boolean values or strings, for example. The variables represent some properties of the system, for example, measured system outputs often in the form of signals, timing data, counters, and event occurrence (yes/no). The actual model is the set of functions that describe the relations between the different variables.

## Building blocks

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Mathematics

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Question:The importance of mathematical modeling/simulations in the experimenting process? Do you see any advantages/disadvantages using this type of "experimenting" over the experimental work? Even if you could give me some good web sites to look at that will help me better understand mathematical modeling and simulations.

Answers:Disadvantage: First of all, any model is not the real system. There is never a perfect model. Results could be influenced by model innacuracies. Advantages: A lot cheaper than running experiments on the real thing, where experiments may not even be possible, or they may just be impractical. For instance, suppose the experiment invlved economic impact of using a certain production process over a 3 year period. It wouldn't be practical to run 3 year experiments, but simulation experiments on a model of the system could be done with nearly instantaneous results.

Question:I am doing this assignment,and i have to get the advantages and disadvantages of mathematics...but i already have the advantages,,all i need is the disadvantages of mathematics.I really need help

Question:A direct answer OR where can i get it on the internet(website)? An alternative answer can be a list of the advantages of mathematical modelling.

Answers:All approaches in the sciences use mathematical modeling. Newton's calculus is mathematical model for gravitation effects. Einstein's model is better and could make predictions which Newton's couldn't (as well). Other part - modelling is much cheaper than carrying out physical experiments in many cases, and in many cases only modeling is possible -- black holes for example

Question:A plague of locusts attacked an area of fruit trees covering 200 hectares. The insects move devouring it at a constant rate of 3.28 hectares per day. Find a mathematical model that determines the number of hectares that are invade in x days. Describes another model of the number of hectares not attacked yet after x days. How many hectares of locusts have eaten after 7 days? How quickly wipe out the entire area?

Answers:number of hectares that are invaded in x days: 3.28x Describes another model of the number of hectares not attacked yet after x days: 200 - 3.28x How many hectares of locusts have eaten after 7 days? 3.28 * 7 How quickly wipe out the entire area? 200/3.28