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I just had one problem in reading it - the somewhat inconsistent use of fonts - often in the same line was not pleasant. The numeric zero ('0') in particular looks like character 'oh' ('o').
It's fortunate that we so seldom need to solve cubic or higher order polynomial equations. Quadratic equations come up in physics all the time, because it's very common to have a constant acceleration. But when does one ever come across a constant jerk?
It's fortunate that we so seldom need to solve cubic or higher order polynomial equations. Quadratic equations come up in physics all the time, because it's very common to have a constant acceleration. But when does one ever come across a constant jerk?
I always wondered why that is for a long time (in basic physics that at least). It wasn't until grad school that I understood that position and velocity are enough to uniquely determine a trajectory on a manifold.
Earlier quoted context omitted.
I always wondered why that is for a long time (in basic physics that at least). It wasn't until grad school that I understood that position and velocity are enough to uniquely determine a trajectory on a manifold.
This is super interesting, is this generalizable to n-dimensional manifolds?
It's fortunate that we so seldom need to solve cubic or higher order polynomial equations. Quadratic equations come up in physics all the time, because it's very common to have a constant acceleration. But when does one ever come across a constant jerk?
I've worked with several.
It's fortunate that we so seldom need to solve cubic or higher order polynomial equations. Quadratic equations come up in physics all the time, because it's very common to have a constant acceleration. But when does one ever come across a constant jerk?
Nice write-up! Incidentally I ran all the exercises through ChatGPT which seems to have completely crushed them, with work shown. Forget about assigning grades via math homework, it only took a few minutes (though I should go through and check it by hand I think). [edit looking at the answers in more detail it seems to go down some strange rabbit holes that probably were not what the author intended] Also, if one wan…
It's fortunate that we so seldom need to solve cubic or higher order polynomial equations. Quadratic equations come up in physics all the time, because it's very common to have a constant acceleration. But when does one ever come across a constant jerk?