Calculus

It’s funny how important a little piece of mathematics that we teach kids in high school can be. The fundamental theorem of calculus demonstrates that if you integrate a derivative, then you get the original function back.

This simple idea tied together with a little Hilbert space and operator theory has become the keystone of my work over the past three or four years. My group and I have published paper after paper making aspects of data science and nonlinear dynamical systems better using the product of these three concepts, which we call occupation kernels.

We have brought in over a million dollars in grant money for our work, all on the back of the FTC and Reproducing Kernel Hilbert Spaces. One YIP, an NSF grant, and an AFOSR grant.

It really blows my mind sometimes. Having a solid understanding of fundamentals can really open up opportunities that others miss. I am just grateful that we had the wherewithal to put these ideas together.

What surprisingly simple idea has had a major impact on your work? Or have you been surprised to find a simple theorem leveraged to resolve a big problem in some circumstance?

EDIT: So around 300 upvotes is apparently when imposter syndrome kicks in lol. I thought this post would get a little attention, and we'd have a nice conversation about system identification. I am overwhelmed with the positive reception here. You guys are great :)

This goes for all math really. Just because your job doesn't require math doesn't mean others don't. Just think of all the things made by engineers. Cars, planes, washing machines, phones and so many more. These were all made by using math. If math were never here then we would be living in a completely different world.

but graphing is where I draw the line

Zero divided by zero is not fucking equal to zero.

Jesus H Christ on a cracker, that's the whole central fucking point of this gods forsaken course.

That is all.

After dropping out of Calculus 1 two times, taking Precalculus 3 times, dropping out of college and coming back after 7 years, I have finally completed my math requirements needed to transfer over to a 4 year university. My 20s have been an emotional roller coaster. From mental breakdowns to a failed marriage, I feel like my life's on the right track now.

I'm proud of that A, I worked hard for it dammit.

>"Introducing the new recommendations on Thursday, Dr. Rochelle P. Walensky, the C.D.C. director, cited two recent scientific findings as significant factors: Few vaccinated people become infected with the virus, and transmission seems rarer still; and the vaccines appear to be effective against all known variants of the coronavirus. > > >“The science is quite clear on this,” said Zoë McLaren, a health policy expert at the University of Maryland, Baltimore County. Mounting evidence indicates that people who are vaccinated are highly unlikely to catch or transmit the virus, she noted. > > >The risk “is definitely not zero, but it’s clear that it’s very low,” she said. >
> >One of the lingering concerns among scientists had been that even a vaccinated person might carry the virus — perhaps briefly, without symptoms — and spread it to others. But C.D.C. research, including the new study, has consistently found few infections among those who received the Pfizer-BioNTech and Moderna vaccines. >
> >Other recent studies confirm that people who are infected after vaccination carry too little virus to infect others, said Florian Krammer, a virologist at the Icahn School of Medicine at Mount Sinai. >
> >“It’s really hard to even sequence the virus sometimes because there’s very little virus, and it’s there for a short period of time,” he said.

https://www.nytimes.com/2021/05/14/health/cdc-masks-vaccines-variants.html

Hi. I'm 60 years old, and started relearning math two years ago, starting from arithmetic and going up to Calculus. I used OpenStax at first, and after finishing their math library I moved on to Tom M. Apostol's Calculus with the help of my nephew. What topics should I cover next, and what are the best textbooks for them? I would prefer something similar in rigor to Apostol's series if possible.

Hey all, just decided to go back to school a few months ago and have completed all my other gen ed courses. Been waiting to do kath so i could do them all in rapid succession.

Havent taken math since high school algebra about 10 years ago. I have always liked math and been quick to pick it up just dont remember much from back then.

My goal is to test out of college algebra (CLEP) by the end of june then take calculus and discrete math through study.com

I defintiely need a refresher on the algebra basics and am planning on using khan academy.

I am also working through the logic and fundamentals of mathematics on brilliant.org and will probably continue through some of the algebra courses on there as well.

Would you reccomend doing anything else? Thanks in advance.

Here's an example, the video itself isn't NSFW but the platform obviously is.

I managed to pass calculus 2.... wooo...I am free of countless nights of studying, for now........Also, let this be a lesson: don't give up

This is the hardest math class I’ve taken so far in college. Cal 2 was much easier than this. I didn’t quite understand sequences and series in cal 2 but after much practice, it became easy to get. I got an A in both cal 1 and cal 2, but cal 3 is different.

It was easy at first until “Multiple integration and vector calculus”. I don’t understand geometry and it has been my weak point in math since highschool. I don’t get the 3D surfaces and how to find the endpoints to the integral. I also don’t know how to interpret the question with a diagram. Finals are next week and I’m exhausted. I can get an A in the class based on my homework grades, previous exam grades and how well I do on the final, but this is the toughest math class for me.

Many know about the card The Ultimate Nightmare of Wizards of the Coast Customer Service, hereby abbreviated as TUNWCCS, from the parody set Unglued. The effect is to pay X+Y mana plus two red mana to deal X damage to Y targets. (For all intents and purposes, we'll assume Z is part of Y, as players are just additional targets.)

Those who have taken calculus may remember those optimization problems where we find the maximum of a function with respect to some constraint. For example, optimizing the area enclosed by a fence with a certain amount of money to buy fencing. Well it turns out that maximizing the total amount of damage from TUNWCCS is basically the same problem.

In particular, the total amount of damage dealt D is given by D = X⋅Y. If we have M mana total to spend, including the two red mana, then we are subjected to the constraint that X+Y+2 = M. Solving for Y and plugging into our original equation, we get that D = X⋅(M-X-2). Taking the derivative and setting it equal to zero, we get that the optimal choice of X and Y are X = Y = (M-2)/2, and the maximum total amount of damage that TUNWCCS can deal is D = (M-2)^(2)/4. In particular, the number of targets chosen and the amount of damage to deal to each target should be equal to maximize the total damage.

And they say pure math has no real world applications.

edit: Some of you have mentioned that the modern versions of this card are Comet Storm or Strength of Tajuru. These cards are slightly different since the first instance of damage/first counter is free.

Let D be the total damage or total number of +1/+1 counters. Then let Y be the number of times the multikicker cost is paid. Then in this case we have D = X⋅(Y+1), and again we have the constraint that X+Y+2=M. Again solving for Y and plugging into our original equation, we have D = X⋅(M-X-1). Again taking the derivative and setting it equal to zero we get X=(M-1)/2, then solving for Y we get Y=(M-3)/2, and the maximum damage/number of +1/+1 counters is D=(M-1)^(2)/4.

For example, if M=7, we should have X=3, and Y=2. In other words, to maximize D, we shou

the may 4th one was so much easier f$ck college board

I'm an undergrad majoring in Computer Science, but when one of my parents asked me what calculus even is, the best answer I could give was the study of derivatives and integrals. For people that don't have a math background, this answer doesn't really help much so I was wondering if anyone has a better explanation.

I have a STEM background, math-heavy. I now have to study Economics very quickly, both Micro and Macro. It's written in plan language, and, at first blush, the assumptions of Neoclassical theory seem weird - people don't have explicit and consistent utility functions that can map any basket of commodities to a single numerical Real value, or even ones that can consistently organize the sets of possible baskets by preference or indifference.

However, these formulations started to make sense to me once I tried to phrase them as mathematical statements - I'm getting the impression that they're an effort to take a very complicated and messy reality and express it into tidy, mathematically rigorous models. You don't really answer the question you set out to, but you answer one about something that's somehow close to your target while being much easier to measure and model and operate with.. It's the resource-allocation equivalent of physics' infamous "perfect rigid sphere through a frictionless void on a perfectly straight inclined plane with infinite friction coefficient and no slip or rolling resistance being released at time t=o with velocity v=0" as something that is utterly deranged and surreal at first glance, but is a useful first approximation on the long road to "how should I build the brakes on this car so it can go down the steepest hills with roads on them at a fluid yet safe traffic speed" or "how do I design the rails and wheels on these drawers so that they slide down into place when released and slow down smoothly at the end so that they close just so".

Sorry for the detour. TLDR, what I mean to ask is: what are good textbooks on "economics for STEM-trained dummies" or "economics in math-speak" or "good luck writing any of this digitally without generous helpings of AMS-LaTeX"?

Is there a legit really really good reason to learn it? If there is, what is it? Thanks!

edit: thanks for the comments. I should learn calculus then.

I'm starting to learn it, and while I can do pretty well, I take a way longer time than I should. it's not the concepts that confuse me, I'm just slow. I'm honestly thinking about asking for accommodations for it during tests, but would that have an impact on my future? Like in what field would it be important to be able to do these problems fast?

I would like to have a textbook with good practice problems and also teaches you some things about calculus. Can anyone help me?

Things like derivatives were originally used to describe physical objects, and now they are widely used in economics. how did this happen? I'm not sure if theres a clear answer but i'm wondering

In other words: assuming I already know basic arithmetic, where should I start the "journey" to learning calculus? What is absolutely vital, and what can be bypassed? About how long would it take? (Obviously, it's different for everyone; but are we talking weeks, months or years?)

Batman vs. a Silverback Gorilla with guns conveniently coming from all of its everywhere BUT THE GORILLA GETS A MONTH OF PREP

Prep.....that magical word that gets used so much for so many things and yet is defined almost as frequently as it is taken into consideration, and that is to say....basically never. Prep time is most infamously used in threads revolving around a few characters (DOOM) and most people generally understand super geniuses will do super genius stuff when given time to prepare but I have a few problems with "prep" and the way we use it and for this example I will be using Iceman.

What is Prep?

Prep is rarely defined in a thread more than simply "X amount of time to prep" but not what the person is allowed to do with that time. There are a lot of very important things to know for what "prep" time means.

• Where can the person go when they have prep? Are they in their home world or their opponents world? Iceman in Marvel has more resources and friends than he would in the Hidden Leaf Village.
• What information do they get access to? There aren't any books in the Baxter Building or the X-Mansion about Naruto so are they provided with some kind of dossier on their opponent or do they need to spend time doing recon and learning about their opponent.
• Can they alter the field of battle? If Iceman knows he is going to fight someone in the middle of the desert but has months to prepare, could he make a giant above ground pool to supply him with extra water and moisture?

There are so many undefined terms of what Prep is that it is hard to factor in what a person could even do with the time. A character like Iceman who is not a super genius who could spend time building a death laser may not have much to do with prep time.

What do People do with Prep?

This is why I chose Iceman over Doom, and I know, that's a bummer for everyone, but this is really what got me thinking because for characters who aren't geniuses what can they do with prep time!? With genius characters most people will basically fill in whatever answer is needed to win because they assume with time to prepare geniuses will figure it out. However for characters who aren't geniuses, it is harder to think what would they do, given the time to prepare.

For example, if you give Iceman 6 months to prepare to pass a math test, would he learn calculus in time to ace it?

Now we go back to the above section for a moment to say, well, what resources does he have? Beas

Is this class hard and should I try to prepare for it ahead of time? I have never taken a calculus class but I got a 86 on the ALEKS Math Placement test. Is there anyone who can give me some insight on this class?

Also if anyone has the textbook I will pay for it, if I really will need it.

So next year I'm taking AP Calc AB but here is the kicker my lazy ass has not done any math work since online school started. And I'm skipping pre calc to do Calc AB I know this isnt a great set up but what topics do I need to nail down during the summer before the start of calc.

Edit: forgot to include what math I am in right now. The math course is math 3 here is a link to the khan academy course. The normal progression after that would be pre calc

I have a student in one of my sections of calculus this year who, while incredibly lovable, has some absolutely jaw dropping ideas about how he thinks the world works. He is probably good for one “Wait, WHAT?!” moment every week and here are some highlights.

“Wait, aren’t diabetics allergic to caffeine?”

“Do you know what I just found out? Thomas Jefferson was the biggest slaveholder in Massachusetts!” shortly followed by “But I thought ALL of the Founding Fathers were from Massachusetts?”

“Mr. L, have you ever realized that we haven’t even discovered all of the letters yet? Like, there are sounds no one has ever thought to make yet so we have no idea what those letters will even look like!”

“You know that scene in The Dark Knight where the Joker burns all the money? Were those real dollars?”

“But if FDR was in a wheelchair, then how did he run for President?”

Anyone else have a student like this? What are some of your favorite student quotes of all time?