"dx" here is still an infinitesimal change in x. To see why it's there, we should think of the integral as a signed area and as the limit of Riemann sums. We recall that to compute a left Riemann sum of f(x) from x=a to x=b with n intervals, we let the following be true:...
The entire game is now to use Shannon entropy inequalities and “entropic Ruzsa calculus” to deduce a contradiction from (1) for small enough. This we will do below the fold, but before doing so, let us first make some adjustments to (1) that will make it more useful for our purposes...
Relativity is a known false in science as EM is the actual attraction repulsion, “power” and rate of that power (i.e. voltage and amperage without limits). Einstein finally admitted there can be no electrons as they repel and this is Brought to the forefront...
To analogize to calculus, if human reasoning is a Riemann sum, machine learning may be the integral that results as the Riemann calculation approaches infinity. Human doctors do the best they can with what they have, but whatever the ECG algorithm is finding in the data, those studying the ...
I didn’t fully succeed; but I think the approach I outline below is in principle feasible. The manifold I will work on is a cylinder , where is a smooth compact manifold, and the metric on is just the sum of the standard metric on the first coordinate and : (I have experimented...
1. Describe the Fundamental Theory of Calculus 2 2. What is the purpose of applying the Fundamental Theory of Calculus to a given function or integral? What is the role of mitochondria in a cell? What does calculus mean and what is it used for?
The integral of x^2 is \frac{x^3}{3} plus a constant. Integral The fluent of a given fluxion in Newtonian calculus. Integral Lacking nothing of completeness; complete; perfect; uninjured; whole; entire. A local motion keepeth bodies integral. Integral Essential to completeness; constituent, ...
Each of these forms of averages represents given information in a data set. For instance, the median represents the number found in the middle of the list after arranging the list either in ascending or descending order. Mode is the number that is the most repeated in the list. Finally, ...
RiemannsumA number of scholars have recently maintained that a theorem in an unpublished treatise by Leibniz written in 1675 establishes a rigorous foundation for the infinitesimal calculus. I argue that this is a misinterpretationViktorBlåsjö...
Wouldn't the concept of Dirac delta function be simpler by the use of basic measure theory? In fact, Lebesgue measure in not even needed: You can use Radon measure theory a la Buck's Advanced Calculus. In a naive sense, any partition of the real line (x-axis, say) would give wei...