[M4A] Late-Night Boyfriend: Homework

Transcript

Oh, hi baby. Is it bedtime already? Oh, oh shit.

I need to, uh, I need to get this homework done because it's due in just a few days. Is it okay if I just sit here and do it? I promise I won't make much noise.

Yeah. No, no, don't stay up on my behalf. I'll just keep working when you're sleeping and I promise I'll come to bed at the same time.

Yeah. I'm just in a good flow and I just need to concentrate. Okay, baby.

Delta, delta x, yeah. Delta x, delta y, uh, delta, delta, no. Delta y, uh, delta x, yeah.

Leibniz, E-Y-I-E, lie, lie. I feel like it's L-I-E-B-N-I-Z. Leibniz notation.

Gradient, flow, multivariable, multivariable calculus is, um, several inputs, one output, several, one input, several output nodes of function. So, there's one output. Yeah, it's been a big yes.

Multivariable, uh, multivariable. Calculus is, does it need, yeah, it needs two or more inputs. These can be x-y coordinates, but they aren't restricted to strictly, well, let's, they aren't bound to strict, to being strictly, um, bound to being strictly geometric, Cartesian, oh, I've got this one.

Let's see. They're bound to being strictly geometric representations of, uh, relations. For example, one might, um, predict, let's see, or something continuous, um, as one might predict the outcome of, uh, an ecosystem, um, fox population as a function of predator count versus prey count.

This is, uh, what, uh, alter, uh, system, is it a system of family, or a system of, yeah, uh, 139, uh, blah, blah, blah, blah, blah, 3, 39, uh, oh, here we go. Let's, uh, this is a lot quicker, um, oh, hang on, is this not multivariable, oh, yeah, I'll just call it system of, no, system of crystallized linear algebra, right, yeah, I'll just call it family, oh, fuck it, maybe it'll subtract me, family of equations. These are often used by biologists in their job, in their work, yeah, I hope so, maybe I'm just talking out of my ass.

Oh, that's good coffee. Oh, okay, okay, that's multivariable, put a pin in that for now, uh, next up, um, oh, oh, fuck, I can't remember, what's the name of it, I don't know, uh, brain not working, um, exponential, no, it's not exponential, it's, blah, blah, blah, blah, it's partial, partial differential, differential equations, that's what it is, not partial, oh, okay, I'll make another, partial comes later, partial equals small multivariable equivalent, now, differential equations are, um, they are, differential equations are relationships, um, between any function and its, does it have to be a function? No, surely not, an equation doesn't need to be, to represent a function, it can represent a parametric curve, or, or some other type of mapping, I'll just, just stay within a curriculum, don't go too far, don't go too far, uh, differential equations are relationships between any function and its derivative, parenthesis, S, for example, um, a function may be defined as, uh, maybe define, let's try easier, for example, we might observe that, uh, um, that there is a relation between the rate of, uh, let's start more concrete, let's add some bones to this, we might observe that there is a relation between a function's current value and its falloff, as is the case in radioactive half-life, or any other types of half-life, half-lives, half-lives, that shit looks weird, oh, whatever, um, if we observe that a material's decaying properties are as such, f derivative equals, uh, e to the x, I think that's a valid one, right, I will try, then we can solve this by using, hang on, now it needs, um, I don't know, f of x equals f derivative of x multiplied by e to the xth power, ah, fuck it, I'll just write that, then we can solve this by using methods of differential equations, should I, should I write what differential equation is in Greek?

Professors love that. What is equation in Greek? Is that even, or is it Arabic? No, that's algebra, ugh.

Now, parentheses are not too self-right, etymology and margin, what was I, oh, okay, uh, okay, to be continued, that's a good start, let's see, 3 out of 10, no, 2 out of 10, okay, well, partial differential, assuming we've got a bunch of meat and bones on there, now that we've explored, now that we've explored, uh, single variable differential equations, it's time to expand, that's a good word, into higher dimensions, wait, hang on, it doesn't need to be dimensions, does it? Dimension, well, technically, ugh, I don't like this, into, and expand into, expand using more than one variable, oh, okay, what's a typical partial differential, oh, okay, ugh, okay, so, so for partial differential equations, I'm almost out of paper, fuck, oh my god, I need to buy more, I need to spot this, my god, okay, so partial differential equations are a bit, are generally tougher to solve, whereas we as mathematicians tend to rely, parentheses, and revel in the comfort of the known, or at least in finding the known in partial differential equations, we must be humble and accept that even the unknown is, that the method for finding the unknown might be unknown, um, to elaborate, let's consider the following, sine of x plus cosine of y equals sine derivative of y, if we were to use traditional or conventional methods of integration, with, .