The opening starts by showing two graphs, what appears to be the graph of y=x and y=x^2, and at the bottom of the page, there appears to be the set up for a double integral. The scene transitions and we are given a definition of the area to integrate over. (I will be writing all of the math terms in LaTeX)
$D=\{(x,y)|0\leq x\leq5,0\leq y\leq1\}$.
Now I've heard of taylor series approximations, but I've never heard of modelling people by the space of continuous functions; the domain is the set of the quintuplets (0\leq x\leq 5) and the codomain is the set of Fuutarou (0\leq y\leq 1). What we see next is some of the best applied mathematics I've ever seen in my life.
As the unknown bride is walking towards Fuutarou, she is modelled by the single integral over the domain:
$\int_0^5 f(x) dx$
The integral is a continuous sum over the domain of the function, and this expression implies that the bride does not just represent one of them, but instead, she represents all of them. This bride represents all of the qualities, good and bad, that Fuutarou has come to love and hate. A similar expression is displayed before Fuutarou.
$\int_0^1 f(y) dy$
This integral represents Fuutarou as a person. Much like the quintuplets, Fuutarou is also a sum of his parts; his good qualities and his bad qualities. Nevertheless, the bride is attracted to him.
These integrals on their own are not incredible. They are a good model for the characters, but what is amazing is the double integral we are presented with when the bride and groom combine.
$\iint_D f(x,y) dxdy$
Instead of two separate integrals, we now see the importance of the domain we were presented with before. This show is not about individual characters; it's about how the characters influence each other and work to develop themselves through each others strengths and faults. The first differential is "dx", which indicates that the integral must be integrated with respect to dx first, assuming the integral isn't separable. Fuutarou must first put in the work to understand and help the girls who may not want to be helped, but by putting in that work, he can see everything eventually pay off.
As a calculus enjoyer, the incredible mathematics brought me to this show, and I was not disappointed. I am still astonished at the amount of depth and planning that went into this opening. As I wait for the finale movie to come out, I hope to see the Laplace transform somewhere in there. If you are an aspiring mathematician, the best advice I can give you is to watch this show.
