I am a first year undergrad student studying computer science, and I am absolutely garbage at math. In high school, I barely passed the first 3 levels of maths, and then aced AF12 and Calculus+Vectors; which is how I got into uni (CGPA doesn’t matter as much in Canada). But the only reason why I was able to do this was because we were tested every chapter, and the expectation on us to retain everything by the end wasn’t as high. Now that I’m doing college level math, I often get stuck on trivial algebra in the middle of much more complex proofs and evaluations. It takes forever for me to process a few equations because I worry about making mistakes. Also, a lot of definitions and examples apply algebra without explanation, leaving me confused. Is there a resource or method for practicing algebra so that I don’t have to comb through 10 websites to figure out what happened? Thanks.
I just wanted to ask this here since somebody might know some. I’m looking for 80s Japanese cars in the kind of style like a Nissan cedric or Toyota mark II that were sold in Europe too and not just in Japan. I know the ones like 200sx and that kinda stuff I’m just looking for that kinda boxy shape (if that makes sense). Any answer is welcome.
I know I probably shouldve asked this in the buying thread but I felt like this might be better as a post itself since I don’t really plan on buying one right now but just want to know what cars like that there are.
Also sorry for broken English.
Recently I was thinking about what a multiplicative derivative and integral would be. I came up with:
rfdx = limh->0 (f(x+h)/f(x))1/h
which is the geometric derivative. Of course after googling it I found out about the geometric and bigeometric derivatives.
Next I tried using a different operation. Analogous to the harmonic mean, I defined harmonic addition which is
a⊕b = [a-1 + b-1]-1 and the harmonic difference a⊖b = a⊕(-b)=[a-1 – b-1]-1 And the harmonic derivative
hf dx = = limh->0 h [f(x+h) ⊖ f(x)]
h is multiplied by the difference because of the natural repetition operator.
x = x
x ⊕ x = x / 2 x ⊕ x + … + x ⊕ x = x / n
Repeated addition is multiplication, so the standard derivative multiplies the function difference by 1/h. Repeated multiplication is exponentiation, so the geometric derivative takes the function ratio to the power 1/h. Repeated harmonic addition is division, so the harmonic derivative uses 1/(1/h) * a = h * a. It’s probably skipping over a bunch of details though. Obviously after doing this I found the derivatives of the usual common functions
h[x-2] dx =1/(2x) and found how each was related to the normal derivative
rfdx = ef’/f
I haven’t been able to find anything talking about this harmonic derivative. I found sources talking about infinite families of Non-Newtonian calculi but they only ever talked about geometric and bigeometric. One site did mention quadratic and harmonic derivatives, but only in passing. Also there were a lot of papers that seemed beyond my level (calc 1 and 2, lin algebra, and general self study)
Basically I’m looking for the correct terminology and resources to look into this more. As well I’m wondering if there are any other notable generalized derivatives. Perhaps some that aren’t just
EDIT: Sorry if the formatting is terrible. I composed this on mobile during lecture lol
Tried fixing the formatting. I may have forgotten an negative sign. I’m trying to figure out where specifically I got my formula for it from. It doesn’t change the idea of the post though.
The article mentioning the quad and harm. http://planetmath.org/nonnewtoniancalculus
I think I didn’t give this article a fair chance at first. It’s seems to answer my questions. https://www.tandfonline.com/doi/pdf/10.1080/0020739790100406