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Real life Application of Differential Equation

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on 2 March 2014

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Transcript of Real life Application of Differential Equation

Differential Equation
A differential equation is an equation involving derivatives of an unknown function and possibly the function itself as well as the independent variable.

Radioactive Half-Life
A stochastic (random) process
The RATE of decay is dependent upon the number of molecules/atoms that are there
Negative because the number is decreasing
K is the constant of proportionality

Rate Laws
An integrated rate law is an expression involving the rate of reaction and the species involved in the reaction
Consider the reaction:

A

The rate of change of A is dependent upon the concentration of A

First Order
First Order since it only depends upon the concentration linearly

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Real life Application of Differential Equation
They are used to model real life situations
Uses?
Physics – Schrodinger, atomic physics
Chemistry – Rate Laws, Statistical Thermo
…Synthetic Biology
dn
dt
=
-Kn
B
Second order
A Second Order rate law would depend upon
the square of the concentration:

Relationship between spices and total size of population
A useful parameter implicit in every pair of schedules of births and deaths is the intrinsic rate of natural increase, sometimes called the Malthusian parameter. Rates of reproduction and death rates evolve in concert -- when either is high the other is usually low.
A population whose size increases linearly in time would have a constant population growth rate given by
Growth rate of population = (Nt -N0) / (t -t0) = dN/dt = constant
Exponential population growth is described by the simple differential equation

Logistic Growth Model

Real-life populations do not increase forever. There is some limiting factor such as food or living space.

There is a maximum population, or carrying capacity, M.

A more realistic model is the logistic growth model where growth rate is proportional to both the size of the population (y) and the amount by which y falls short of the maximal size (M-y). Then we have the equation:

Some Application of Differential Equation in Engineering
Chemical reaction by Economists
A population of living creatures normally increases at a rate that is proportional to the current level of the population.
The electric current move through conductor by the potential difference that accrue in circuit
Done By :
Maryam Abdulnoor
Nooria Ibrahim
Shifaa marouf
Bahara Masoud

REFERENCE
Andrewartha, H. G., and L. C. Birch. 1954. The distribution and abundance of animals. University of Chicago Press.

Davidson, J., and H. G. Andrewartha. 1948. Annual trends in a natural population of Thrips imaginis (Thysanoptera). J. Anim. Ecol. 17: 193-222.
Wikipedia
www.math/circle.com
Full transcript