4/14/20111•What is an ODE?•Where do ODEs come from?•The harmonic oscillatorSupplement lecture: ODEs•Damped variations•The Lorenz attractorWhat 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) = 0Just like when you had a quadratic equation, for examplex+1 = 0you 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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4/14/20112What is an ordinary differential equation?Example of a first order ODESolution method: separation of variables:Solution is an exponentialWhere do ODEs come from?In numerous engineering problems, the constitutive equations result from the laws of physics, and are given in the form of ODEsFor example: a spring:For example: a spring: Newton’s law:Leads to the following ODE