4/14/2011
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What is an ODE?
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Where do ODEs come from?
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The harmonic oscillator
Supplement lecture: ODEs
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Damped variations
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The Lorenz attractor
What is an ordinary differential equation?
An ordinary differential equation is an algebraic relation which
relates a function with its derivatives.
For example, for a function f, the following equation is an ordinary
differential equation:
f’(x) +f(x) = 0
Just like when you had a quadratic equation, for example
x+1 = 0
you needed to find the solution (x=-1), here you will need to find
the solution, i.e. f(x), for all x

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4/14/2011
2
What is an ordinary differential equation?
Example of a first order ODE
Solution method: separation of variables:
Solution is an exponential
Where do ODEs come from?
In numerous engineering problems, the constitutive equations result
from the laws of physics, and are given in the form of ODEs
For example: a spring:
For example: a spring:
Newton’s law:
Leads to the following ODE