APPLICATIONS OF DIFFERENTIAL EQUATIONS - ANIL. S. NAYAK
WHAT IS A DIFFERENTIAL EQUATION????
A differential equation is a mathematical equation that relates some function of one or more variables with its derivatives. Differential Eqn. are broadly classified into : Ordinary and Partial Differential equations
HISTORY OF DIFFERENTIAL EQUATIONS
In mathematics, the history of differential equations traces the development of "differential equations" from calculus, which itself was independently invented by English physicist Isaac Newton and German mathematician Gottfried Leibniz. “Differential equations began with Leibniz, the Bernoulli brothers, and others from the 1680s, not long after Newton’s ‘fluxional equations’ in the 1670s.”
Example: A population grows at the rate of 5% per year. How long does it take for the population to double? Use differential equation for it. Solution: Let the initial population be P 0 and let the population after t years be P, then [Integrating both sides]
Solution Cont. At t = 0, P = P 0 Hence, the population is doubled in
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
ATOMIC PHYSICS
TIRE MODELING
MECHANICAL VIBRATION ANALYSIS
EARTHQUAKE ANALYSIS