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Integral is a fancy way of saying that you're continuously summing up something. So if you had a discrete function like this: _|_ , when you sum it up over time, you would get zero until the curve starts, and then a constant value till infinity. For a continuous function there are no breaks in it, so we would get a smooth transition as shown. If the jerk is like the discrete function, then the acceleration is like this one.https://anand-hari-natarajan.com/wp-content/uploads/2018/10/ball.jpgballA smooth ball on a smooth table to help the imagination flow. Courtesy of Google Images.https://anand-hari-natarajan.com/wp-content/uploads/2018/10/floatingball_gettyimages-148173972.jpgwhite ballCourtesy of Google Images.https://anand-hari-natarajan.com/wp-content/uploads/2018/10/screenshot-2018-10-20-at-10-47-30-pm.pngcurve 3https://anand-hari-natarajan.com/wp-content/uploads/2018/10/screenshot-2018-10-20-at-10-47-00-pm.pngcurve 2https://anand-hari-natarajan.com/wp-content/uploads/2018/10/screenshot-2018-10-20-at-10-46-28-pm.pngcurve 1This is an example of a curve similar to one called a "normal distribution". It exponentially increases, reaches a maximum value and they exponentially decays. If this curve were to be squished horizontally to a very small set of "x-values" it would be the curve we want.https://anand-hari-natarajan.com/wp-content/uploads/2018/10/screenshot-2018-10-20-at-10-13-37-pm.pngvector field 2This is an example of a vector field. Since we are representing it using two axes, the "X" and "Y", we need two directions to draw a vector, one in the top-down and another in the right-left. To write a vector field, brackets like are used. The first variable in the brackets talks about the right-left dependency and the second, the up-down dependency. This vector field can be written as F = meaning, the right-left or horizontal component of the vector increases equally as you go along the X-axis, and the top-down or vertical component doesn't change no matter where you go in the X-Y plane.https://anand-hari-natarajan.com/wp-content/uploads/2018/10/screenshot-2018-10-20-at-10-13-16-pm.pngvector field 1F = This is an example of a vector field. Since we are representing it using two axes, the "X" and "Y", we need two directions to draw a vector, one in the top-down and another in the right-left. To write a vector field, brackets like are used. The first variable in the brackets talks about the right-left dependency and the second, the up-down dependency. This vector field can be written as F = meaning, the right-left or horizontal component of the vector increases equally as you go along the X-axis, and the top-down or vertical component doesn't change no matter where you go in the X-Y plane.2020-10-17T11:21:54+00:00monthlyhttps://anand-hari-natarajan.com/2016/12/06/welcome-to-order-in-entropy/https://anand-hari-natarajan.com/wp-content/uploads/2016/12/461651246.jpg461651246https://anand-hari-natarajan.com/wp-content/uploads/2016/12/entropy-is-disorderliness.pngentropy-is-disorderlinessCourtesy of Google Images.https://anand-hari-natarajan.com/wp-content/uploads/2016/12/1entropy.gif1entropyCourtesy of Google Images.https://anand-hari-natarajan.com/wp-content/uploads/2016/12/unknown-1.jpegunknown-1Courtesy of Google Images.2017-11-30T20:12:40+00:00monthlyhttps://anand-hari-natarajan.comdaily1.02024-03-11T10:57:54+00:00