Recent content by Ganesh Mahadevan

The cross product of two vectors yields a third vector, the magnitude of which is equal to the area of the parallelogram enclosed between the vectors, and the direction is the same as where the primary face of the parallelogram points to. Since there are two faces on any parallelogram, a...

I stand corrected and shall delete my reply. Thanks

Gimbals ensure that a free gyroscope can continue to point at an arbitrary point in space regardless of the movements of the structure that houses the gyro. It is l a gyroscope at this stage and not a gyrocompass. A gyrocompass is normally located on the surface of a rotating planet earth, and...

Gimbals ensure that a free gyroscope can continue to point at an arbitrary point in space regardless of the movements of the structure that houses the gyro. Remember, it is only a gyroscope at this stage and not a gyrocompass. A gyrocompass is a device very specific to orientation on a spherical...

Forget for a moment that we are dealing with a PDF. We are simply trying to compute the area under a curve. There is no way of integrating exp(-x^2) so a smart way was established by Got it. Thanks.I must have been half asleep to have got perplexed. Developing a solid of revolution from a polar...

Thanks for bringing out the dimension issue clearly.

Thanks. Let me make that "revolution" around the z-axis more specific:- ##I^2 = \int_0^{2\pi}\int_0^\infty~e^{-x^2}dx~d\theta##

Thanks. Doesnt the first integral give area and the second integral - volume ? The expression dydx gives the infinitesimal footprint of each riemann column on the xy plane. The expression ##e^-{x^2}## gives the height of the column along the z axis. That should give us volume.

I have been teaching undergrad students informally, and one of the math problems that I have always enjoyed introducing them to is how to compute the area under a gaussian curve, or to keep it simple, the area under the curve ##z=e^{-x^2}## One of my students asked me a question that has...