Contents
Definition of Mathematical Model Types of Variables The Mathematical Modeling Cycle Classification of Models

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Definitions of Mathematical Model
Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a process that attempts to match observation with symbolic statement. A mathematical model uses mathematical language to describe a system. Building a model involves a trade-off between simplicity and accuracy. The success of a model depends on how easily it can be used and how accurate are its predictions.

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Types of Variables
A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The variables represent some properties of the system. There are four basic groups of variables: – – – – Input variables Parameters Random variables Decision variables (output variables)

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The Mathematical Modeling Cycle

Simplify Real World Problem
Interpret

Mathematical Model

Program

Conclusions Simulate

Computer Software

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The Mathematical Modeling Cycle
1. Identify and understand the problem, draw diagrams 2. Define the terms in your problem 3. Identify important variables and constants and determine how they relate to each other. 4. State the assumptions as you focus on particular aspects of the phenomenon. 5. Develop the equation(s) that express the relationships between the variables and constants.

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The Mathematical Modeling Cycle
The Real World
A non-mathematical setting

The Mathematical World
An abstract representation

Representation Pose a question Create a model
Identify relevant variables, determine the form of the answer and the objects that best capture the relationships between the variables

...definition for a model
According to Wilson’s definition a model is the explicit interpretation of one’s understanding of a situation, or simply of one’s idea about that situation. It can be expressed in mathematics, symbols or words. But it is essentially a description of entities, process or attributes and the relationships between them. It may be prescriptive or illustrative, but about all, it must be useful.
Describe the purpose and uses of...

...Types of Models in Economics
From the definition of a model, it has been said that models in economics have the wide range of forms including graphs, diagrams, and mathematicalmodels. Economists use these models in different purposes; it depends on many factors such as what type of raw data they have, how they can represent the data, and what they want from the model they use. In this section...

...Mathematicalmodel
A mathematicalmodel is a description of a system using mathematical language. The process of developing a mathematicalmodel is termed mathematical modelling (also writtenmodeling). Mathematicalmodels are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g....

...Mathematical modelling of a hyperboloid container
Mathematicalmodel is a method of simulating real-life situations with mathematical equations to forecast their future behaviour. Eykhoff (1974) defined a mathematicalmodel as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'. Mathematical...

...analysis of models and data sets
James F. Pricea)
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
Received 22 May 2002; accepted 4 November 2002 Dimensional analysis is a widely applicable and sometimes very powerful technique that is demonstrated here in a study of the simple, viscous pendulum. The ﬁrst and crucial step of dimensional analysis is to deﬁne a suitably idealized representation of a phenomenon by listing the relevant variables, called the...

...problems, represent different problems and transfer knowledge and skill about the different problems. Mathematicalmodels have often being developed to solve and represent these problems especially in natural sciences and engineering disciplines (Arnold 2000). Mathematicalmodels can be defined as a mathematical language that would describe the behavior of a system or rather a problem. Mathematical modeling...

...Mathematical modeling is commonly used to predict the
behavior of phenomena in the environment. Basically,
it involves analyzing a set of points from given data
by plotting them, finding a line of "best fit" through
these points, and then using the resulting graph to
evaluate any given point. Models are useful in
hypothesizing the future behavior of populations,
investments, businesses, and many other things that
are characterized by fluctuations. A...

...Research Project
Mathematical Programming Based Modeling
For Supply Chain Management Control
Muhammad Faisal
Department of Engineering Management, Abasyn University, Islamabad, Pakistan.
Abstract
Economic globalization has forced and is still forcing enterprises to develop new global manufacturing and distribution concepts. A growing number of products are produced in multiple plants dispersed around the globe. This paper designs and discusses a...