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The scipy.integrate sub-package provides several integration techniques including an ordinary differential equation integrator. An overview of the module is provided by the help command:


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is provided to integrate a function of one variable between two points. The points can be ± ( ± inf ) to indicate infinite limits. For example, suppose you wish to integrate a bessel function jv(2.5, x) along the interval [ 0 , 4.5 ] .

I = 4.5 0 J 2.5 ( x ) d x .

This could be computed using quad :


The first argument to quad is a “callable” Python object ( i.e. a function, method, or class instance). Notice the use of a lambda- function in this case as the argument. The next two arguments are the limits of integration. The return value is a tuple, with the first element holding the estimated value of the integral and the second element holding an upper bound on the error. Notice, that in this case, the true value of this integral is

I = 2 π ( 18 27 2 cos ( 4.5 ) 4 27 2 sin ( 4.5 ) + 2 π Si ( 3 π ) ) ,
Si ( x ) = x 0 sin ( π 2 t 2 ) d t .

is the Fresnel sine integral. Note that the numerically-computed integral is within 1.04 × 10 11 of the exact result — well below the reported error bound.

Jessell did not respond within several hours to an email requesting comment. He met with his lab staff and students to break the news to them earlier this week.

A leading expert in neural movement control, Jessell, a U.K. native who completed his Ph.D. at the University of Cambridge, conducted pioneering studies that identified mechanisms involved in the neural development and organization of the spinal cord. He shared the $1 million Kavli Prize in Neuroscience in 2008 , the first year that the prestigious awards were made. The foundation noted the far-reaching, foundational nature of his work: “The principles of circuit construction that have emerged from Jessell’s studies in the spinal cord are now known to apply throughout the brain, and in particular they have helped to explain, in molecular terms,how different parts of the cerebral cortex acquire their specialised character.”

Jessell’s trainees include prominent neuroscientist and president of Stanford University in Palo Alto, California, Marc Tessier-Lavigne, who did not respond to a request for comment.

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