A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences such as physics, biology, earth science, meteorology and engineering disciplines like computer science, artificial intelligence, but also in the social sciences Physi
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A crucial part of the modeling process is the evaluation of whether or not a given mathematical model describes a system accurately. This question can be difficult to answer as it involves several different types of evaluation. In this regard we have discussed the limitations of modeling in following sections.

Differential equations occur quite frequently in our daily life. The motion of an object can always be associated with a differential equation. The change in prices of commodities, the flow of fluids, the concentration of chemicals etc., often lead to differential equations. Such equations may depend on one or more independent variables. Further, it may include the derivatives of the first or high
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Mathematical Modeling in terms of differential equations arises when the situation modeled involves some continuous variables varying with respect to other continuous variables and we have reasonable hypothesis about the rate of change of dependent variables with respect to independent variables. Mathematical models in terms of ordinary differential equations will be studied in this unit and the u
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Differential equations occur quite frequently in our daily life. The motion of an object can always be associated with a differential equation. The change in price of commodities, the flow of fluids, the concentration of chemicals, etc., often lead to differential equation. Such equations may depend on one or more independent variables.

In mathematics, an ordinary differential equation (ODE) is an equation in which there is only one independent variable and one or more derivatives of a dependent variable with respect to the independent variable, so that all the derivatives occurring in the equation are ordinary derivatives.

The combat model provides a ,mathematical representation of missile battles between modern warships. It was developed by Wayne Hughes at the U.S. Naval Postgraduate School in Monterey. The model describes the basic elements of modern missile combat in a very simple way. This is similar to how the Lanchester square law provides a simple model of modern gun combat.

In mathematical modeling of planetary motions, we have considered need for the study of motion under central forces, Components of velocity and acceleration vectors along radial and transverse directions, motion under inverse square law and Kepler's laws of planetary motions. The circular motion and motion of satellites consists of circular and elliptical motions of satellites.

A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown or difficult to measure without this technique.

A variational principle is a scientific principle used within the calculus of
variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions.

This unit reports the successful simulation of nonlinear distributed model of flood waves in open channels using a much simpler nonlinear lumped conceptual model.

After studying this unit, students will be able to analyse about convection diffusion processes-Burger's equation which will cover Burger's equation and the plane wave solution, Cole-Hopf transformation and the exact solution of Burger's equation. They will also be able to explain asymptotic behavior of the exact solution of Burger's equation and Burger's initial and boundary value problem and exp
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Air pollution is the introduction of chemicals, particulate matter or biological materials that cause harm or discomfort to humans or other living organisms or cause damage to the natural environment or built environment, into the atmosphere. The atmosphere is a complex dynamic natural gaseous system that is essential to support life on planet Earth.

An inventory of air contaminants is a necessary first step towards control of air pollution. Air pollutants can be either natural or may be the result of various activities of man like industrial operations. The industrial contaminants can be either by products of external combustion like smoke, dust and sulphur oxides or by products of internal combustion like the reactions in petrol and diesel e
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After studying this unit, students will be able to construct and analyse mathematical principle of air pollution using gradient diffusion model. They will also be able to explain conservation of mass, conservation of momentum and conservation of species/turbulent flow in the atmosphere.

Suspended Particulate Matter (SPM) is solid and liquid particle suspended in
ambient air of which particle size is not more than 10 micro-m. In this unit, we have considered the effects of SPM on human body and climate etc.

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