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This project work also aims at determining the correct value of density by clearing the objects touching the borders of the image. In this project three applications are taken into account and using Matlab with image processing toolbox the count and density values are calculated for each.
An autonomous system is a system of ordinary differential equations of the form = (()) where x takes values in n-dimensional Euclidean space; t is often interpreted as time. ...
In practice, it is usually possible to simplify the problem by replacing the full set of equations of state with a simple approximation. Some common approximations are: Vacuum: = Perfect fluid: = (+) + where =
MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. [1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
For an arbitrary system of ODEs, a set of solutions (), …, are said to be linearly-independent if: + … + = is satisfied only for = … = =.A second-order differential equation ¨ = (,, ˙) may be converted into a system of first order linear differential equations by defining = ˙, which gives us the first-order system:
MATLAB was created in the 1970s by Cleve Moler, who was chairman of the computer science department at the University of New Mexico at the time. It was a free tool for academics. It was a free tool for academics.
GNU Octave is a scientific programming language for scientific computing and numerical computation.Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.