Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)… What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it –“Epsilon-Delta”...
just to make the calculation easier. notice that i used the analytic solution from that same website so you can see the two plots are nearly identical. you can change the size of dx to make an even better fit. but yes, numerical integrations can be fairly easy---and useful. rhett ...
What are some tricks for doing substitutions ?What is the integral of dx / (x² + 4x + 7)?We know ∫1/(1+x²)dx = atan(x) + CThe trick is completing the square.x² + 4x + 7= (x+2)² + 3So :∫1/(x² + 4x + 7)dx=∫1/((x+2)² + 3 )dx= 1/3·∫...
Take plain old Dirac ‘bra-ket’ notation, the typical go-to language for calculation in quantum computing, and write it in 2D, where matrix multiplication looks like ‘plugging boxes together’ and tensor product looks like ‘putting boxes side by side’, for example: So far, things don't...