▲ 4 r/askmath
What math notation did you come up with and use on your own?
i have a shorthand for single integrals i call "reverse prime notation". all it is is the same prime you write for derivatives, but placed before the function instead of after. it looks like this:
'(f ± g) = 'f ± 'g
'(f ⋅ g) = 'f⋅g - '('f⋅g')
'(f ⋅ g) = f⋅'g - '(f'⋅'g)
'(f / g) = 'f/g + '('f⋅g'/g²)
'(f(g)⋅g') = 'f(g)
heres what it looks like in practice:
8. ∫ exp(x)⋅sin(x) dx
'(f ⋅ g) = 'f⋅g - '('f⋅g')
f = exp
g = sin
'exp⋅sin - '('exp⋅sin')
exp⋅sin - '(exp⋅cos)
'( exp(x)⋅cos(x) )
'(f ⋅ g) = 'f⋅g - '('f⋅g')
f = exp
g = cos
'exp⋅cos - '('exp⋅cos')
exp⋅cos + '(exp⋅sin)
I = '( exp(x)⋅sin(x) )
exp⋅cos + I
I = exp⋅sin - (exp⋅cos + I)
I = exp⋅sin - exp⋅cos - I
2I = exp⋅sin - exp⋅cos
(exp(x)sin(x) - exp(x)cos(x))/2
exp(x)⋅(sin(x) - cos(x))/2
i like it because it 1. represents the "opposite" of the derivative by being on the opposite side of the letter, and 2. makes it much easier to scan through identities to potentially use when solving a problem.
i am curious to see if anybody else has a personal pet notation they use, if so please share
u/completely_unstable — 14 hours ago
