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Skibidi vibes are strong in these notes, lowkey diving into the edge of analysis. We got curves flexing all over, regular and tangential, like they are the sigma males of the math world. Curve length and the dank parameter arc are here to keep it real. Complex planes are the ultimate ship for those who want to explore beyond the basics. Functions? They are the goons of this mathematical universe, scalars and vectors battling it out. Gradient and derivatives, the true warriors of optimization, making sure we do not get lost in the toilet of complexity. Dive into the Jacobian matrix, where differentiability reigns supreme.