あ the art of doing mathematics is finding that special case that contains all the germs of generality.
goal: invent calculus
The Area Of a Circle: Intergrals Derivatives Opposites=Rectangle-ish=area under some function
dA/dx=f(x)
い So fat as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.
paradox: associate individual points in time with a velocity, but computing velocity requires comparing two seperate points in time.=ds/dt=tangent line slope=the best constant approximation for the car's velocity around that point.
う You know, for a mathematician, he did not have enough imagination. But he has become a poet and now he is fine.
for f=x^2, df=2*x*dx+dx^2=2*x*dx, then df/dx=2*x
loose feel for the shape of slopes based on the slope of graph at every single point/ function itself and precise reasoning
え Using the chain rule is like peeling an onion.
か implicit differentiation = related rates
