Hearing your profs say "trust me bro" a few times during calc 1, 2, and 3 is a small price to pay for deferring real analysis.
@irok1
Жыл бұрын
Facts
@najawin8348
Жыл бұрын
Counterpoint: We should just start teaching set theory in elementary school. I don't see what could possibly go wrong with this idea.
@irok1
Жыл бұрын
@@najawin8348 this is true
@najawin8348
Жыл бұрын
@@irok1 Teach them early on to be wary of the lies of category theorists.
@truthseeker7815
Жыл бұрын
@@najawin8348, actually I support this, nothing could go wrong
@mooredaxon
Жыл бұрын
I'm actually going through a calc class in high school right now: my teacher ain't even really a math guy, he just got roped into being a math teacher because he originally was going to work on computers, then decided to be a teacher, and since he had taken math for his computer classes, math was what was taught. Anyway, it really plays to his advantage, because he asks the same sort of questions you do about his own material, and so he ends up going over WHY the math works, not just how. Definitely one of my favorite people.
@MCNarret
Жыл бұрын
wish I had those kinds of teachers and profs
@TaigiTWeseFormosanDiplomat
Жыл бұрын
0.0
@Chaos_Nova
Жыл бұрын
Yea if he took computer science he def has a pretty good basis on math
@MagicGonads
Жыл бұрын
computer science is all about translating pure math into practical forms (rather than more general engineering which is still just plug and chug for the most part)
@APM_ASMR
11 ай бұрын
They legit took the Computer Science guy and threw him into a calc class teacher's position nah that's foul.
@maverickiwnl
Жыл бұрын
please never change you're mic, it is fucking hilarious and makes the video 10000x better. This shit was funny as fuck, thank you.
@ICREAMTOHANDTIE
Жыл бұрын
wrd
@thatprogrammerjack747
Жыл бұрын
Word af
@Syuvinya
Жыл бұрын
your*
@DadicekCz
Жыл бұрын
*your 🤓🤓
@hermanbrachey7653
Жыл бұрын
Lol ratio
@Lemurai
Жыл бұрын
I was super disappointed in my first calculus course at uni, there was no time in my life other than this situation where I felt like I had a better grasp of the subject than the teacher. I don’t know if he was new, but the guy glossed over trig functions in a single lesson, didn’t appear knowledgeable on how to use them, couldn’t articulate what Cos or Sin meant, seemed really nervous & confused when someone asked a question & really didn’t understand limits, which is insane because limits are based of the initial function’s people learn in college algebra. It was a complete disaster, the entire class complained at the end of the semester & he was removed (probably fired) because I never saw him again. But he really messed it up for those people who really needed to understand calc 1 before they went on to calc 2, I’m blessed that my dad is a metallurgical engineer so he taught us all these concepts at home when my brothers & I were growing up. But seriously, universities need to do a better job of investigating the backgrounds of the people they hired instead of being greedy for money.
@princehickmon2170
Жыл бұрын
You are very blessed ❤️
@treskilion-9690
Жыл бұрын
Damn, what university did this occur at if you don't mind me asking?
@Lemurai
Жыл бұрын
@@treskilion-9690 it was Clemson back in 2008
@playmakersmusic
Жыл бұрын
I feel like 90% of college lecturers either lack the passion or lack the knowledge to teach. They know how to solve questions, but they don't know how to convey it so that students can benefit from them.
@Lemon_Inspector
Жыл бұрын
They teach you what trigonometric functions are in a calculus course?
@onlineacc2717
Жыл бұрын
Bro did a math project for an english class
@MickPuff
Жыл бұрын
diffed
@onlineacc2717
Жыл бұрын
highlight reply :skull:
@onlineacc2717
Жыл бұрын
also over 500 view LMFAO this channel is blowing up soon fr
@MickPuff
Жыл бұрын
fr no cap ong 💀
@omegax1289
Жыл бұрын
Watching this video made me appreciate my math professor more. He actually spent a significant chunk of time in class going over proofs for limits and derivatives. He was really thorough and had good answers to our questions.
@Tahazif_TheCool22
Жыл бұрын
Same man, but my physics teacher did it even though it weren't needed as we were gonna understand them in deep later in maths.
@henrikbartnes8424
Жыл бұрын
Same, Tom Lindstrøm ftw
@tandemdwarf745
Жыл бұрын
my teacher for this was great. His big reveal towards the end of the derivatives unit in Honors Precalc (which covered calc 1 concepts) was the definition of a limit, and the dreaded "game" (which as he told us regularly was not a very fun game at all) wherein he would give us an equation and an Epsilon and tell us to find the largest delta that would allow us to "win" the "game", as in meet the definition of a limit and trap the function. This was limits at level 3, with level 1 being plugging in close values on a calculator and level 2 being what he called algebraic trickery, where you multiply by 1/the largest power of x in the denominator. Level 4 was in Calc BC, where we extended the concept of the game to win it every single time by actually writing out a proof.
@Neohedra
5 ай бұрын
@@henrikbartnes8424isn’t he a fellow of the American mathematical society?
@henrikbartnes8424
5 ай бұрын
@@Neohedra i googled it and he sure is
@tomtommcjohn
Жыл бұрын
Real analysis goes into almost all of the theory that builds up to calculus. It's also much harder than calculus. So the teaching order, while seemingly bizarre, makes sense in a way. You effectively memorize the building blocks of higher math, and later learn how they themselves are built. I wish they presented it that way.
@hetoan2
Жыл бұрын
it "makes sense" in a way that still doesn't make sense in any sort of computational reality of applied mathematics... Leibniz calculus is a paper method designed for paper solving of equations that describe systems. In practice, it is antiquated applied maths that really only serves to teach the jargon so people can read historical works of mathematics. even the integral symbol is what it is because of Leibniz using the ʃ (esh) character, which was available for the german printing press... the more math you learn, the more you'll see that the introduction of calculus, and even real analysis, are just fundamentally flawed. especially in the modern era where computer algebra systems hide a lot of the computational complexity from you. there exists "nonstandard analysis" which instead starts by defining what an infinitesimal is (a number that is not zero, but when squared is zero), then builds algebraically from this number. similar to how the imaginary number (a number that is not -1, but when squared is -1) is used to form the complex numbers. They are called "hyperreal numbers". For whatever reason, this is not covered, despite this being needed under the hood in the implementations of these computer algebra systems that are even hidden in basic calculator apps on phones... it is quite problematic and pervasive on a systemic level. you even defend it claiming it is necessary because you are still blinded by the undergraduate maths program...
@niikurasu2855
Жыл бұрын
thats only in the usa tho. in europe we have real analysis in the first semester of university and learn both together.
@hetoan2
Жыл бұрын
@@niikurasu2855 fwiw there's probably institutions in the usa that cover nonstandard analysis, and institutions in europe that skip it... also university here starts after college, not sure what your understanding of these terms is, but know that they are region dependent in case you mean some higher level class on analysis in general, and not the first introduction in what would be a class taken at the same time as a calculus course.
@IsomerSoma
Жыл бұрын
@@hetoan2 What he means is that right in 1st semester coming fresh from highschool we start with real analysis and proof based linear algebra (as a math major) without any introduction, but an optional prep course. What has been covered in this video (calc1) is highschool material. This is standard curriculum in germany for analysis: 1st semster: 1-dim analysis in IR 2nd semster: n-dim differentiation and topology 3rd semester: n-dim integration and measure theory In 4th semester i will take functional analysis and ODEs. In all of these courses everything is proven (but the proofs left as an excerise or theorems from other mathematical fields) and while you do some calculation the calculation/ proof ratio is ~ 30/70. Imo this is the correct approach for math majors. I have never studied none-standard analysis, but i am not so sure about your statements eitherway. You learn a lot of technical proof knowhow doing standard analysis and none-standard is more subtle thus probably way less suited for a beginner who has no experience with proof and formal logic. None-standard analysis might be the superior choice for physics students as they argue "none-standard" all the time anyway.
@hetoan2
Жыл бұрын
@@IsomerSoma standard analytical methods are the standard because they are easier. However, those proofs will always be less rigorous than constructive proofs that emerge from non-standard analysis. The standard approach relies on infinite sets and "real" numbers, which are ultimately non-constructively defined. In many ways, the non-standard approach is simply more elegant. Many of the non-constructive proofs are just waiting for the constructive version to come about to make them valid. This is literally the case for Leibniz calculus, and I don't see why non-standard approaches shouldn't be introduced early, as they are more solid logically. Also I get that you say physics is non-standard in approach because physicists gloss over the rigor because it aligns with the model and reality. However, nonstandard analysis is more in-line with pure mathematics. So really this comparison is false. For what it's worth, I am simply arguing for the expose of this topic in a general class for 1st years, which would and should also go over topics that would be relevant to other, more applied fields, such as physics, chemistry, and engineering. I'm not surprised to hear german maths education is superior to american... I can read statistics, lol. Calc 1 is also high school math, but it is not uncommon to have to re-teach this to undergrads because of the varying quality of public highschools. Many colleges here will not take high school credit because the foundations are weak. (this was not the case for my school though)
@LorxusIsAFox
Жыл бұрын
Hey, actual Calc prof here. One way to see why derivatives and integrals are opposite to each other is to remember that derivatives always represent slopes of tangent lines. Now look at a definite integral. If you extend the upper bound a *tiny* bit h, the additional tiny rectangle you get is that tiny amount times f(b+h), so that your area changes by about f(b) per unit of h. But that's the derivative of the integral showing up as f(b) again!
@Guimaster127
Жыл бұрын
Holy shit Holy fucking shit it actually works Amazing
@Nsquare_01
Жыл бұрын
😵 I'm so dumb
@themathnthug
Жыл бұрын
Dr. Peyam has another but longer way of doing it. Basically use the riemann sum definition of an integral and let the integral be of the derivative of a function. let deltax=(b-a)/n, let x subscript i=x+deltax. By the mean value theorem, there exists a f’(c) for c in the interval (x subscript (i-1), x subscript i) such that (f(x subscript i)-f(x subscript (i-1))/deltax=f'(c). Let the height of each rectangle be f'(c) -> integral=sum from k=1 to N as N->inf of [((f(x subscript k)-f(x subscript k-1))/deltax)*deltax]. The deltax’s cancel and we get the limit has N->inf of the sum from k=1 to N of [f(x subscript k)-f(x subscript k-1)]. The sum is also f(x subscript 1)-f(x subscript 0)+f(x subscript 2)-f(x subscript 1)+…+f(x subscript N)-f(x subscript N-1). All terms cancel except -f(x subscript 0) and f(x subscript N). take the limit as n approaches inf and we get f(b)-f(a) is the integral from f’(x) from a to b, thus showing the integral from a to b is the antiderivative of b minus the antiderivative of a. Also, any constants created will be cancelled out.
@crimxi7598
Жыл бұрын
Imma just comment so I can go back to this to understand it
@jackpeterson1160
Жыл бұрын
Fr
@kratostheinevitable3932
Жыл бұрын
dude i'm doing engineering and my professor is speedrunning maths like bro 🤣😭
@8stormy5
Жыл бұрын
I was fortunate enough to take Calc 1 with a professor who absolutely refused to skip the rigorous proofs. It was really freakin' difficult to follow those, but it made the concepts of calculus intelligibly and consistently build on one another. The classes also refused to skip the "this case is stupid messy and requires a ton of algebraic manipulation" topics
@linksauce_1
Жыл бұрын
Sounds like our professors are similar. There were a few times I walked out of lecture with my brain completely melted, but it was worth it
@marcusmelander8055
Жыл бұрын
Here's how I like to think about/justify the fundamental theorem of calculus Derivative = slope = rise over run = x/y Integral = area = x*y I know everyone else is complaining about calc classes but I wanted to throw that out there.
@markdave2456
Жыл бұрын
Yo dude, I was in the same boat as you because I passed calc 1,2,3 but later realized i didn't know wtf i was really doing, just manipulating symbols. I took one summer to relearn calc 1 and 2 and one winter break to relearn calc 3 all on khan academy. It was well worth the time spent because Sal and Grant Sanderson (the guy from 3blue1brown math youtube channel) explain why things are true in the first place. For example, proving all the derivative rules, the connection between area and slope, why antiderivatives give you area, how double, triple, line and surface integrals really work, and other theorems you learn in calc. Of course, I also had to learn why some concepts in algebra, trig, and linear algebra (like the dot and cross products) were also true before I had to relearn calc. Although the information gained isn't really useful to the average joe since you never really use it unless you work in a specialized field.
@andyhughes8315
Жыл бұрын
This is true. Calc 3 needs a geometric part of the course with scientific computing and graphing by hand. Not sure how I'd figure out how to graph contour maps, etc without checking a real answer.
@43333akjfkgodel
Жыл бұрын
That's sad bro, but good you relearned, you shouldn't be able to pass any course without understanding basic theory, I guess that's why in my math and physics department they make fun of engenierings
@markdave2456
Жыл бұрын
@@43333akjfkgodel not sure why you’re so rude… my teachers taught math as plug and chug without proving anything, pretty sure that doesn’t make it my fault for not understanding it the first time.
@moose6488
Жыл бұрын
@@markdave2456 did you take the whole courses or just what you needed to know? I think i need to do this with algebra because my prof is so plug and chug it’s infuriating
@markdave2456
Жыл бұрын
@@moose6488 the whole course just to make sure there was no gaps in my understanding
@MikeHawk-s2g
Жыл бұрын
I was actually taught the rigorous definition of a limit when I took intro to calculus. however, my teacher didn’t really understand it herself and she abandoned the topic after one confusing lecture lol
@restitutororbis964
Жыл бұрын
Been there.
@bluepi7195
Жыл бұрын
I'm planning to attend grad school for math next year, and I'll likely be teaching a calc 1 course in the near future. What do you wish you could've learned differently or more of that would've made your experience better? Stuff like rigorous proofs of the limit and Fundamental theorem of calculus are relegated to an introductory real analysis course that builds the fundamentals of calculus from the ground up in a completely rigorous manner. However, only math and maybe CS majors usually take this course.
@MickPuff
Жыл бұрын
I think the best way to teach is that there should be a clear reason and buildup to every new topic you introduce to newcomers since it is such a foreign concept. Rigourous proofs are boring yes but if someone manages to explain the reasoning behind it in an understandable maybe relatable way, i think it would entice students to want to learn more about the subject.
@camcorl7921
Жыл бұрын
Use something like Fundamentals of real analysis by Sterling K. Berberian for a more rigorous approach. But dumb it down a little bit.
@hetoan2
Жыл бұрын
Use the hyperreal numbers to define an infinitesimal, then use that definition to define what a limit really is, instead of using the epsilon-delta definition. This comes from nonstandard analysis. Math should be one done over an infinitesimal system. It is infinitely better. If you need evidence, just read that statement: "one over an infinitesimal" is "infinity". That's a joke, but it truly is way easier to learn than you'd think, and the 2x2 matrix definition allows you to also introduce early the more accurate formulation of the complex numbers as well. It is also helpful in that it's just literally how it's programmed... so it aligns with our computational tools which come from linear algebra.
@carlosraventosprieto2065
Жыл бұрын
As a student and as a future teacher, i think the most important thing to start explaining something is the context. Why was the need to "invent" calculus? How was it created? Who did it? Why is it useful? And after that: RIGOROUSNESS
@marciorjusto
Жыл бұрын
1) Remember - or teach - that Function is a model of causal relationship between two phenomena: f(x) - the "output" or "effect" - represents the evolution of one of them caused by (or used as reference for) the evolution of the other (x, or the "input" or "cause"). 2) When this relationship is continuous (like a "flow") we need tools to "break it" in measurable parts. So we start measuring the instantaneous rate of change of the "effect" phenomenon using Derivatives. In other words: this phenomenon is changing rapidly or subtle in real-time? 3) Integrals shows the cumulative "interference" of x over f(x) along the evolution until now - the net change 4) To understand the continuous behaviour of this relation, we need study Limits
@pinochet3698
Жыл бұрын
3:38 This is very relatable. As a highschool senior, I am currently taking Accelerated Calculus and AP Physics Mechanics. I have a D in Calc and an A in calc-based physics. My calculus class is incredibly dense and boring, and my physics class is fun and exciting. When my calc teacher speaks, my mind drifts (I've literally fallen asleep multiple times in her class) and my physics class is one of the highlights of my day. My physics teacher teaches more calculus in 15 minutes than my calc teacher does in a week, and I actually remember it. I really hate introductory calculus class, and I only put up with it because it is a necessary stepping stone towards the engineering degree I hope to pursue.
@tandemdwarf745
Жыл бұрын
funnily enough, I have the opposite situation, though a bit different. I'm more than qualified to take Physics C, but they wouldn't let me, so now I'm in a combined AP Physics 1/Gen physics class, which is shaping up to be just as much of a disaster as it sounds like. My Physics teacher has spent the last two weeks giving exhaustive speeches about how physics is incredibly difficult, and that he doesn't actually expect us to be able to figure it out because of how mind-bogglingly complicated it is. If you were wondering, the thing he was talking about was that even if a velocity line is flat the object is still moving. I suspect we will have covered the AP Physics material around four or five years from now at this rate. I've learned more about physics through explicit connections my calc teacher has explained or by thinking, "huh, that calc thing we learned today seems kind of like this"
@Drakonus_
Жыл бұрын
I'm majoring in Computer Science and Calculus was taught to me in the 2nd semester. The professor pretty much taught it the way you did. He also addressed the same questions that people wonder whenever they take the course. And since I had already learned Linear Algebra in the 1st semester, the behind the scenes stuff with Calculus was kind of a breeze.
@matrix9134
Жыл бұрын
bro, you hit the spot. You're literally pinpointed each problem with the world and calculus and all the people that are teaching it , are missing a lot of things and themselves need to learn it again .
@Altair4611
Жыл бұрын
Physics professors: "And then you just do the integral" The integral: Partial fraction decomposition
@Tom-vu1wr
Жыл бұрын
Yeah
@Tom-vu1wr
Жыл бұрын
It's not like it requires a clever trick
@Tom-vu1wr
Жыл бұрын
Also they r physics professors so it's not their job to teach u about solving integrals
@enozi8951
Жыл бұрын
Dude really took 3 calc lessons to make a video. Kudos!
@NEM0_1
Жыл бұрын
I took a calculus course in high school for 2 semesters and by the end of it even my teacher was confused. Literally asked me what grade I thought I should get. I got an A.
@christian_swjy
Жыл бұрын
"you probably re-learn it in university anyways." I always taught myself this when I was in high school, and it was a mistake. The lecturers won't bother teaching why things go a certain way because you have learned it in high school anyway. They will go straight to solving problems, skips multiple steps then show you the final answer, leaving you confused.
@mehraneh1554
Жыл бұрын
this is why i failed university calculus
@PythonDad
Жыл бұрын
I think you're overestimating the typical student's psychological readiness (and willingness) to spend any amount of time dwelling on topics like the epsilon-delta definition of a limit. This is something that goes deeper than just not wanting to think hard and carefully. I also think that there is basically no solution to this problem except to elevate high school math--at least in the United States--to a higher level across the board. But there are barriers to this unrelated to intrinsic student aptitude. One is a lack of qualified teachers who want to work for U.S. high school teacher salaries. The real shame about this one is that it deprives willing students of an opportunity to prepare themselves more. Not everyone is an excellent self-studier, especially when they are in high school. Another is political resistance to standardizing mathematics education, the standards of which presently vary wildly by state. The residents of the states that need it the most are also the least likely to support such a standardization (y'all know who I'm talking about). Most parents see neither need nor benefit to requiring their kids to learn more math in high school. One possible compromise is a trade vs. academic tracking system, but American parents also all want their kids to be the the most special-est in the room so they don't want their kids to go the vocational route. There is no such stigma attached to this in countries that already use this type of arrangement. On top of that, many students who have decided not to go to college view trade schools as an escape from studying even though they will still be taking classes with exams to pass (often with very high grades, such as over 80%, 85%, or 90%, you can't just get a D and call it a day). In many such fields they need to be proficient with certain mathematical skills. Many unmotivated high schoolers seem to think that vocational training is just following someone around holding their hand all day until they just understand how to do the job and that there is no sense of urgency attached to the program completion time. People who should advise them on this such as their parents, teachers, guidance counselors, etc. rarely take the time to explain what it is really like. As a result they wind up being as unprepared for a college algebra level class they need to take to be a plumber or an electrician or whatever as is a university-bound student for intro calculus. Tl;dr The only real solution is to convince the shitkickers that better high school math education is needed.
@CHOCOLATIONZ
Жыл бұрын
4:43 I’ve pondered this question for quite some time. And then i heard someone said derivatives is the operation of subtraction and division which corresponds to slope function and integrals is the opposite operation: addition and multiplication which corresponds to the area under the curve.
@evanbright6105
Жыл бұрын
Wow ive never thought of that
@asapvarg
Жыл бұрын
Hold up that actually kinda makes sense 😳
@evanbright6105
Жыл бұрын
Is that the actual reason or just speculation?
@nestorv7627
Жыл бұрын
It makes sense in a way, but that's not the whole story. The reason why integration is the opposite of differentiation is more of a matter of how antiderivatives relate to the area of a function
@Celtics-x4w
Жыл бұрын
@@nestorv7627 h
@blablabla7796
Жыл бұрын
I get your point and I felt the same way. The entirely of Calc 1 made me feel like a complete idiot because of all of my classmates could jump through hoops like monkeys on demand while I still questioned why sin became cos. Almost flunked the class but after college I feel like I’m part of the 1% that still uses calc from my class while my former classmates couldn’t use calc to save their life. But I have to ask, what is the alternative? Is there really much utility in going through the algebraic tricks needed to produce some of the more obscure derivatives? At the end of the day, calculus is a tool to achieve a goal much like algebra. Should we have spent a few more months on the foundations of calculus?
@qu3nt0r
Жыл бұрын
Bro's channel consists of Valorant gameplay. And there is just this. And I just realized I gotta do this shit in grade 12. I have no idea how agebra works, I just use recognition. And my teacher barely teaches it. 💀
@shep2004
Жыл бұрын
As someone who has taken Calc I and is currently taking Calc II, the biggest thing that can make the difference with actually understanding the subject is definitely the teacher/professor, thankfully I had an amazing professor in Calc I who made sure to explain WHY everything was the way it was instead of just saying "Do this and this, and you get this", him explaining those essential concepts has made my understanding of Calc II so much better. I personally think high schools should give options to kids where they can take classes to better understand Algebra as well, cause if you don't really understand Algebra, then you are going to STRUGGLE in Calculus.
@pandatolomeobipa
Жыл бұрын
3:12 me: it's not that difficult, I just learned it two weeks ago! 3:16 always me: HOLY SHIT, WTF IS THIS !!!
@mohnazaidi4666
Жыл бұрын
I'm not sure if anyone has pointed this out yet, but integration IS NOT the inverse of derivatives! Derivatives look at the rate of change of something (i.e., this is why the derivative of a linear equation is a constant = the rate at which the line changes is constant). The second order derivatives are usually called concavity, but they are simply measuring the rate of change of the rate of change, and so on for higher order derivatives. If you look at the limit definition, it is simply taking a slope! lim as h->0, (f(x+h) - f(x))/h, right? But note that h is defined as some distance from x. So, x2 is simply x+h, and x is, well x. Then delta x is (x+h) - x = h, just like in the denominator. The numerator is the function evaluated at x+h (which is x2), making this your y2. Similarly, the function evaluated at x is y1. So, you are simply doing the standard slope formula of (y2-y1)/(x2-x1), as the distance between the x2 and x1 values becomes VERY small. The extra condition of making the distance "very small" is justified because the tangent to a curve gives its rate of change at that point, hence, the limit definition of the derivative is simply finding the slope of the tangent line at the point x! Integration is the area under the graph, which is correct. However, that graph can be shifted up or down by any constant value C (it doesn't have to be at 0). So, if my curve is a sinewave centered at y = 1000, my area covered by the curve would be no different than the area covered by a sinewave centered at 0. If you understand this concept, you will understand that integration gives you a RANGE of possible functions (essentially, it gives you a function that can vary infinitely by a constant). So, if I take the derivative of sin(x) + 1000, I'll get cos(x), just as I would if I had done sin(x) - 100, or sin(x) + 35, etc. When I integrate cos(x), my answer is sin(x) + C, where the C signifies an infinite variation of the sin(x) functions - notice how this is not an inverse?! An inverse is, for example, multiplying 4 by 2, then dividing by 2, returns back 4. So, division is an inverse of multiplication (same with addition and subtraction). Finally, consider integrating a second order derivative twice: suppose our second order derivative gave us sin(x). Then, integrating it once will give us -cos(x) + C. Integrating this again will give us -sin(x) + Cx + C1! That means that not only are we getting an infinite constant shift, but ALSO an infinite linear function shift! Hopefully, this helps you understand derivation and integration better, and why integration IS NOT an inverse of derivation :) Best regards, Your friendly neighbourhood Math teacher ^_^
@Djenzh
Жыл бұрын
Bro sounded like he wanted to cry at the end of the rant 💀
@i-win
Жыл бұрын
The issue with bring theoretical math all the way to first year is that it'll throw a bunch of students off, particularly for those who just want to use calculus. What's best is for students to be able to choose whether they want the rigorous math treatment right in first year, and know what they'll learn or miss out on. Of course, there are unis that do this already
@mrqz3146
Жыл бұрын
Currently at midterms. Going to take my first calculus class next semester. Shits looks scary af. My highschool was as shitty as it could be in terms of math.
@tgclericoll572
Жыл бұрын
its all fun and game until the instructor asks you to pull double and half angle formulas out of your ass on test day
@stevematson4808
Жыл бұрын
Honesty is so RARE in discussions about calculus.
@sahijrandhawa5480
Жыл бұрын
THE DESMOS PART IS WHAT WE ARE DOING RN HAHAHA. LMFAOOO
@tarikeld11
Жыл бұрын
I loved calculus in high school, it always made sense to me and I think they explained pretty well why e.g. the integral is the area of a function
@adityaranjansahoo6261
Жыл бұрын
I just Understood integration as Summation of Very Tiny Parts of area comprising into a bigger one where the initial and Final ranges may be fixed or not...That's it!😬
Integrals defining the area of a function is an easy concept to grasp in high school, but that was not his point. He was pointing out that somehow the area a function between x=a and x=b is given by just plugging in a and b into an antiderivative of that function and taking their difference, and this is almost never given a proper explanation in high school nor intro calc in college. I personally recall the summer right before I took real analysis when I started wondering why that was so. I had to look up proofs of it online and I was surprised how easy it was to prove so, that even a calc 1 student could understand it
@skit_inventor
Жыл бұрын
This guy needs a 3b1b's essence of calculus dose asap 🗿
@thatwaffledweeb9822
Жыл бұрын
mickpuffi believe you could be one of the best math teachers on youtube if u continued this gen z way of teaching. so please do make more. if you struggle to find where to start, you can do the NSW Stage 6 Math Adv or math ext syllabus
@umomiscool1754
Жыл бұрын
I love his other vidoes too ❤️
@watermelons2921
Жыл бұрын
everything you want to know is covered in the first semester of university calc. an integral is an infinite series of rectangles and a derivative is a secant line between two points "infinitely close together" (x +/- delta). If you take the two points defining your secant line and multiply the distance between them by the height of the function somewhere inside that range of points then you get an approximation of the area contained under the curve between those two points. The approximation gets better as the points you choose (again, x +/- d) get closer together. That's why you get the ftc telling you that the derivative is the inverse of calculus. proving it rigorously is for mathematicians and i promise it won't help you apply it to anything unless you're a mathematician or a theoretical physicist.
@bob38028
Жыл бұрын
Good comment. I was thinking the same thing. Rigorously proving this stuff would take forever as a student, it's better to just learn it and then naturally come to an understanding of Calculus as you go!
@Ralleighen
Жыл бұрын
I did cherish these five minutes and fifty-one seconds of calculus. It was interesting to hear your perspective on the subject, and I liked that you indicated curiousity. I like calculus, and I also would like to understand the relationship between slope and area under the curve. Calculus is genuinely fun and I think that math is just awe inspiring when you consider its long tradition. It's a gift, passed down from generation to generation and added to, traveling with time along the existence of our species. I will continue to learn more and cherish it. Thank you!
@waldwz
Жыл бұрын
Me a 2nd year in engineering 1:46 *tf's that*
@blackburgundy1659
Жыл бұрын
During middle and high school, I always followed formulas, saw a polynomial and thought "Oh I'll just plug it in a formula" and I get the answer a lot of the time. I never understood what those formulas meant. Come my first year of college, I took a remedial math course, and my professor summed up all 4 years of highscool math in a few months, not only that but he explained EVERYTHING perfectly, he explained how formulas were derived, explained why operations worked the way they work, etc. So now when I come accross a polynomial or anything, I don't blindly plug them in a formula anymore, I actually do the long math to make sure I get everything right,
@HA7DN
Жыл бұрын
My fist calculus class in highschool (grade 11, for 16-17 year old students) actually started with epsilon-delta, and we had quite a few advanced integrals at the end of it. Even at uni level I could use most of that.
@relaxedamphibian2933
Жыл бұрын
I would a rather a “just trust me bro” than a whole ass proof on most of the shit I learned in cal II 😭
@imhopelesslyaddictedtofent4266
Жыл бұрын
Ive been pounding my head against a wall the last 3 days because I feel like i’m just memorizing and regurgitating rules and formulas without it being clearly explained why they work. I can’t find a source that explains the proofs in a way I can comprehend. I’m glad this problem isn’t exclusive to me.
@vinesauces4023
Жыл бұрын
MORE MATH please/// f them gamer Valorant videos bra...
@DL-zv5xc
Жыл бұрын
It's been about a year now, and the only concepts I remember are the ones that were explicitly talked about in 3blue1brown's calculus series. I feel like I've learned NOTHING from those classes, and rather were helpful at nailing down the topics I learned in those videos.
@asterbot7736
Жыл бұрын
Okay this may sound slightly different, but I have to point out just knowing how to do the computations is a big win for when you actually learn the concepts rigorously. For example, I would always try my best to learn and answer questions about limits/derivatives/integrals, why they come together, but no matter what my high school courses only cared that i knew HOW to do them(obv i tried researching beyond the scope of my course) But in uni when you finally learn the rigorous stuff(like epsilon-delta proof) you see how amazingly everything fits together, and at that point you don't have to worry about learning HOW to do stuff, because you already know it, but instead WHY stuff happens. It's the same thing with other stuff in math too, you need to just sometimes grind through it before the puzzle starts to come together. And if you weren't fluent in computation you probably wont be able to give the theory behind it time. Grinding on problems to just get good at computation is underrated Like you got fluent in basic arithmetics (addition/substraction...) before you actually started applying them in word problems right? Same analogy.
@dovilacus
Жыл бұрын
In the introductory course on calculus I learned integrals from the Riemannian integral, which defines it as a limit that leads to the area under the function. I'm surprised that in 3 courses you haven't been taught that, maybe it's different in the US?
@ec6895
Жыл бұрын
Na I'm in the US that's how I learned it too and it wasn't even on a university but rather a community college
@harveyboi3917
11 ай бұрын
Man the limit definition of a derivative formula is the biggest abomination I have ever seen. I took AP Calc in high school and my teacher skipped over that mess and went straight to the power rule because "it's a waste of time." I never knew what he was talking about until two years later taking intro calc in college. Using this formula takes me 10 minutes to do what power rule can do in 10 seconds. And of course I had to "Show my work" so I couldn't sneakily use power rule instead of this shitty thing.
@NguyenNguyen-xp3yc
Жыл бұрын
It's just the way U.S. education system see Math as some sort of application Math so they just teach you how to "use" Math as a tool by plugging in number into provided formulas. Your job as a Math "learner" (user) is to know what formula to use without even understanding that formula. Sometime they might explain those formulas but in a very brief ways or say "it's too complicated" as an excuse. Same thing for the Sciences that use Math.
@felipefred1279
Жыл бұрын
Bro, I am doing cal1 and I know how to solve derivatives, but I have no clue what is a derivative. I truly want to understand, right now I just feel applying formulas and shit.
@tcpnick6895
Жыл бұрын
I liked the end of the video because I literally got an A in calculus just to be able to say I got an A in calculus and look smart in front of my friends. In truth I learned VERY little and can absolutely NOT do any calculus equations because I have no fucking idea whats happening.
@byzantinefish9192
Жыл бұрын
I don't understand algebra 1. If this is what I have to learn in the future, then I think I'll just become an alcoholic. Like, I don't want to, but my mom is going to kill me for not getting good grades, so I'm going to need something to forget I got killed
@AustinFeltron
Жыл бұрын
Our calc 1 class did epsilon delta proof of limits on day 2 lmao our teacher is great though
@parmisiguess
Жыл бұрын
i was so lucky to have such good professors for both my calc 1 and 2 classes. i’m not pursuing any further math than calc 2 because my major doesn’t need it but even tho i don’t like higher math, these two professors made me appreciate it more and understand what the hell these processes mean
@15symph8
Жыл бұрын
Thanks bro, my dad constantly reminds me to start form scratch and this vid really shows me why I've been sinking into a chaotic process in learning. But calc is hard to learn by yourself... I'll try and organise my learning a bit.
@tactical_slime4608
Жыл бұрын
Education system: How to get people to hate math speedrun WR
@HAe76
Жыл бұрын
Jesse we need to cook math
@nivmizzetjt2858
Жыл бұрын
Took my first quiz today on limits. My prof hands it out, about 5 questions of some solid limits ( few curve balls nothing I didn’t expect.) then as I’m on problem 3 she says “you have one more minute” 😳 I did the fastest algebra a man could humanly do. I barley get the second problem done. Half the class waits for her out side the class room to confront her on why she never gave us a time limit (pun) and she walked out making no eye contact and says “welcome to calculus”
@lukewalkerr2d2
Жыл бұрын
Ah yes, the "calculus is hard because I make it hard for you" approach
@boygenius538_8
Жыл бұрын
Complain about her to the department head. That's scummy.
@PrismaticCatastrophism
Жыл бұрын
I enjoyed math in school, but now I'm so glad that I decided to study medicine
@eliteteamkiller319
Жыл бұрын
Integrals are like asking for a running total. So you're adding things. Differentiation is like asking, "How is this thing getting bigger or smaller?" so it's like subtraction. That's kind of why they undo each other. Remember that dy is kind of like a small interval between values of why. y2 - y1 => Δy => dy. If you let the difference between y2 and y1 approach the infinitesimal, you get dy (this is lazy talk for intuitive purposes). Thus the derivative dy/dx is kind of like the difference in y over the difference in x. Or rather, how y changes with respect to x. So derivatives are essentially fancy subtraction. As for integrals, you are summing up all the infinitesimal dy's or dx's. . One other way to think of it, which you will see later in calculus, is that differentiation gives you a lower dimension while integration gives you a higher dimension. For example, take (4/3)pi*r^3. What is that? That is the volume of a sphere. What happens if you take the derivative? You get 4*pi*r^2. Guess what that is? A _constant_ times the area of a circle. You turned a 3D circle into a 2D one, except you have that multiplied constant. Now, take 4*pi*r^2 and take another derivative. What do you get? 8*pi*r. What's that? Well that's 4 times 2*pi*r. And what is 2*pi*r? That's the circumference of a circle. So what's important here? (4/3)pi*r^3 is a _cubic_ function. 4*pi*r^2 is a _squared_ function (a parabola). And 2*pi*r is a LINE. That's right, it's a linear function (just connected together into a circle. Think y = mx + b, except m = pi, x = r, and b = 0. So what happens if you go in reverse? Let's integrate 2*pi*r. What do we get? Using the power rule, you get 2*pi*r^2 * (1/2) + C = pi*r^2 + C. So now we have almost the same thing as when we went backwards. The difference is that instead of some constant C, we had a coefficient of 4. But the point is, you're getting back the same type of function, with the only difference between the coefficients and constants. But you can change a constant into a coefficient anyway. For example, 5 + 26 = 31, but also 5 *(31/5) = 31.
@heavenpad-
Жыл бұрын
actually explained the epsilon delta def better than any of my professors so far in a fucking meme vid
@militantpacifist4087
Жыл бұрын
Calculus is easy. It’s the algebra that is difficult.
@jcnot9712
Жыл бұрын
I took calc 1 during the summer and my teacher spent ample time going through the rigorous proofs for several concepts (including the limit proof you showed) instead of assigning us exercises to practice computations. Needless to say, I ended up dropping calc 2 on the fall and taking it the following spring ‘cause I had no clue what I was doing. Got an A the second time around at least lol
@Stashix
Жыл бұрын
I had all this in Uni. Thanks for reminding me that 10 years later I remember absolutely nothing.
@majdsaleh_
Жыл бұрын
I like to watch math vids in ×2 speed ,it's a different experience 👌🏻
@ahmadahi9591
Жыл бұрын
Yes fr I still don't know if one day I'm going to get it or if I'm going to have the answer to why as a CS student I have to study 3 calculus courses 😭 All I want is learning programming to hopefully one day I'll be a programmer but having to take several Math courses is making my university life a hell I no longer care about my degrees I just want to be happy😢
@peterpeek
Жыл бұрын
Ur teacher looks like the head of math department in my old school, Andrew Joslin lol
@scuzyprod.1611
Жыл бұрын
At least you guys play with desmos, all we did in my goofy ass country is write shit down 💀
@danzz7583
Жыл бұрын
think if they tried getting the students to understand calc in a more rigorous fashion it'd take up the entire school curriculum and the souls of both the teachers and students LOL
@nomic655
Жыл бұрын
I never really understood the ε δ definition. It kind of makes sense, but also kind of doesn't. Despite it being out of the course material, from all I could study of it I understand it as a sentence that describes where the y value of a function will go, according to where the x value moves. Kind of like the rate of change, but instead of describing how, it describes the end result. Still, I think limits should have a far more simplified definition that students can actually understand, instead of a wacky sentence everyone ignores. Limits are undoubtedly the most insane jump from algebra to calculus, which leaves geometry behind but somehow still finds it at the end. They shouldn't be reduced to a tool we use and accept without properly understanding it. Differenciation made perfect sense for me tbh. As an algebraic, geometric and physical concept, once you understand limits it makes sense and you can already find applications for it. Integrals are weird. They kind of make sense as antiderivatives, but I don't want to sit down and guess what antiderivative am I looking for, or try to learn extreme methods to do it. This solidifies the weakness differenciation as a one way process. As a geometrical concept, I understand them as a limit of a sequence of rectangles, but I don't see the connection with derivatives. I can't understand why are we told that there's a connection between the two, without actually telling us about it.
@coreymonsta7505
Жыл бұрын
One way to think about continuity is to relate it to the informal definition that says you can draw the graph without lifting your pencil. Technically, there are continuous graphs that are strange and you can’t really map the informal definition onto them well, but just ignore those for now. Ask yourself how you can mathematically define what it means to be able to draw the graph without lifting your pencil. You’d want that for any y value f(x), and interval about that y value I_y, that there will exist an interval about x, I_x which maps into I_y. Think about I_x as where you actually do the drawing of the graph. If no I_x exists then where can you ever draw the graph without lifting your pencil?
@nomic655
Жыл бұрын
@@coreymonsta7505 You're a bit confused mate. I never actually said I have a problem with continuity. It was actually one of the most logical concepts and I never understood why were we taught it so late in our school. Until then every function we used was continuous and we took that for granted. Afterall, the pencil definition is kind of neash. It can't be proven, by any means, and it explains continuity in a form clearly inferior to it's actual definition. All you need to know is what limits actually are. Which even further shows why the ε δ definition needs an upgrade.
@kj_H65f
Жыл бұрын
Wow this is so true. For me it was now over 20 years ago, I had to take calc I two times before actually understanding what a derivative was in an intuitive sense. Literally after getting through twice, while mid way into calc 2 I finally got it. And it was because I talked to my uncle who was an engineer and he gave me real world usage of what integrals and derivatives are used for, and it suddenly made intuitive sense. And now I realize I wasn't bad at math, I did poorly because of how I was taught.
@kaiquesilva535
Жыл бұрын
Well, my professor for cal 1 and 2 really made and effort and I actually understood calculus... seven years later...I’m an engineer and I can’t remember anything bc softwares do the heavy calculations lol to be honest I only used it during college
@MarkQub
Жыл бұрын
speak louder i cant hear you.
@nonsenseproboy
11 ай бұрын
im watching this while working on calc homework due tomorrow
@Xenomnipotent
Жыл бұрын
Keep the same mic and talk louder
@zebastianengelska6831
Жыл бұрын
I agree fully that calculus is basically only complicated algebra that you have not learnt before
@maxe624
Жыл бұрын
Isnt the point of precalc to make a baseline for the algebra?
@priangsunath3951
Жыл бұрын
3b1b and Khan academy fr carried my junior and senior years that shit was my life support
@qylov_d2639
Жыл бұрын
Very good content . I did AP Calc AB and it was pretty comprehensive
@fortescuegr7573
Жыл бұрын
Rofl, just your wait. If you go in electrical engineering or physics, Green Theorem is waiting for you. Still to this day, I have not a single f**** clue what is going on with this theorem and how it is link to line integral. In fact, all the advance technic to resolve integral in scalar or vector field are just pure magic. You just plug number in a integral, you do yoyo trigonometry trick to get a standard function and than *Magic*, it spits out a value that you don't even have a single clue if it is correct or not.
@fortescuegr7573
Жыл бұрын
@edntz in engineering? No problem, fundamental are nice to have however the very advance stuff isn't used in the job. In pure science like physic, sadly you need to understand deeply the math
@joshbosh3603
Жыл бұрын
i like how this video still didn’t help anyone understand
@quynguyenkhanh5983
Жыл бұрын
My brain is expanding but my ears are bleeding
@guitar_jero
Жыл бұрын
F’(eet Wexler) = f(eet Wexler)
@justaskaulakis8202
Жыл бұрын
In Lithuania we learn this in 12th grade
@notawesomebread
Жыл бұрын
4:56 I'm confused. Are you saying that in your integral calc class, you only did integrals simple enough to be solved with the reverse power rule? Those methods you crossed out aren't optional, they're required depending on how complex the derivative is, and you can't just reverse product rule everything. An intro integral calc course should have at least covered u-sub and integrating by parts. Did you even do Riemann sums?
@DotNetDemon83
Жыл бұрын
My pre calc class was nothing but trig. Calculus 1 was taught by a guy getting in his Ph.D. In animal genetics. Calculus 2 was taught by a high school teacher getting his Ed.D. I switched majors after limping through these classes. To this day, I still have not used calculus.
@dechair3113
Жыл бұрын
Honestly can't relate to this. What's your undergrad? I'm in eng so it might be more in depth then a sciences undergrad
@onlineacc2717
Жыл бұрын
Does he know?
@sitty7
Жыл бұрын
I hated calc 1 because of the amount of work we had to do as students. The homework problems were usually insanely long, as the problems aimed to introduce you to either algebraic manipulations or just more chain rule stuff. I had to retake calc 1 because my first instructor literally said nothing about what derivatives are. I didn't understand the concept of derivatives or how some equation can turn into another just be adding dy/dx. All I learned from that class was to put my equal signs in a line for organization... I didnt even learn what derivates are for until calc 2. As for calc 2, calc 2 is probably the hardest calc class. Integrals are fairly easy as you have most of the memorization done from calc 1, but the trig integral stuff and the washer/ring rotation over an axis thing was a nightmare. You'll be fine so long as you're paying attention in class and spending reasonable time studying. I have personal beef with calc 3, which is entirely about determining whether a function converges or diverges. So. Fucking. Pointless. "OOh it's not pointless how can you say that?!?!?!? Electrical engineers depend on w-" I dont give a shit, it's pointless for 99% of people, dare I say 99.99%. And electrical engineers aren't going to remember the 10 different converging/diverging tests and whip out some scratch paper to determine whether a complex/annoyingly long function approaches a number or inf. No, they'll use a fucking online graphing platform. It frustrates me to this day that I wasted money and time to learn that pointless shit. Calc 4, otherwise known as vector calc, was chill. That was the only 100% online math class (no lectures) I've taken and I actually did well (no I didn't cheat, the exams were in-person). I feel as though vector calc (the beginnings of it at least) should be taught in calc 1 or 2 (instead of that pointless washer stuff) as it will be beneficial to the many students who will also be taking physics around that time too. To all those who are currently in the calculus series, remember, struggling is part of the process. You're not the exception. Avoid complaining and that pointless frustration feeling and just keep on walkin through that mud. Calculus is a very complex subject. You're literally joining the top 1% in terms of math knowledge (assuming you're going through the whole calc series). One thing that always kept my mind at ease whenever I came across difficult times revolving around my math and even physics classes was that humans are literally built to handle these problems. We come across many complex math-related situations (basketball, baseball, driving, I mean hell, even running) in our lives that we do without even thinking about. You're no different, you just need time. To those who, like me, were piss-poor at math through their high school career and hated anything to do with numbers, then you also probably know you don't hate math. You just hate your math experiences. Like I had just mentioned, don't go into your homeworks/study sessions aggravated because you have to do math now. Go into them because you want to learn, because you want to be good at math. Accept what you don't know, even if it's simple algebraic stuff. In all honesty, algebra is the hardest part of calculus. Ask any calc professor this and they'll likely agree. It's what students have the hardest time with. And for the love of god, if you have questions, ask. Even if it's "What's 1+1" drop your fucking ego and just ask. That's the whole point of you joining lectures anyway, for you to learn. I wish you all the best. Remember, one step in front the other and you'll eventually make it.
@sitty7
Жыл бұрын
@edntz You already answered your question - learn to understand a problem rather than memorize. I was literally in the same boat as you, so I completely understand your concern. Been bad at math all my life until second year of college. That's when I, as you said, learned to understand more than memorize. For math specifically, learn to understand what the problem is asking. Every math concept and question has real world value. Learn to understand what your math questions are asking. It's easier to answer a question you have some idea on than a question you have no idea what it's asking, wouldn't you agree? Also, as I stated above, ask questions. Never be shy, never feel like you're asking a dumb question, never feel like you're wasting time. Those feelings and thoughts have no value in a world of learning. Another piece of advice I can give is, practice practice practice. Cliche, I know, but it's true. It can be painful, yes, but it's what needs to be done. Study an hour or two per day for your math subject so it doesnt feel like you're putting too much in one day. Don't drop a homework problem until you understand it. Homework problems are almost always similar to problems you'll see on tests, so be sure to study your homework problems. Also, do your homework even if you feel like slacking, just do it. Half-credit is better than no credit (still though, try not to slack 😅). So to recap: 1) Learn to understand math questions and concepts rather than memorize (study the formula's, maybe look up some history on the concept). Specifically, understand the "key terms" in the questions. 2) Ask questions, ask questions. Make time with your instructor if you need to or hit up a school tutor (if that's a thing there) 3) Practice, practice, practice, and do your homework. Many of my math instructors would use homework problems for test questions. 4) Lastly, no need to stress out or get frustrated. Just chill, take a breather, look at the wall for a few mins or a poster or whatever. Hell, take a walk if you need to. The important thing is that you keep trying. Math is not easy, and getting frustrated will only make math more difficult. Instead, realize that you're in the process of learning and try to overcome this obstacle. Think of it as you leveling-up your brain with every question you answer.
@HampusTman
Жыл бұрын
While high school calc is pretty trivial and shallow, it does make actual university calculus seem a lot less scary, as it's not completely new concepts. Then multi-variable calculus comes and fucks you up
@HistoryOfEnergy
Жыл бұрын
I took calc 1-3, diff eq and linear algebra before Covid then dropped out, came back to finish engineering degree this year and remember nothing. I want to go back and relearn the proper way (I never did proofs besides in Lin alg) but don’t have time between work and classes. Great video
@hashtags_YT
Жыл бұрын
That f(x+h) - f(x) all over h part is sooo true, learned it in physics this year before we even began learning about derivatives in math and felt my brain actively dissolve
@nestorv7627
Жыл бұрын
How so? It's just the rise over run formula from algebra 1
@hashtags_YT
Жыл бұрын
@@nestorv7627 What do you mean? I meant that we hadn't learned it prior anywhere else and this was my introduction to derivatives
@sek5372
Жыл бұрын
@@hashtags_YT that's because that's the intended idea of a derivative. The definition of a derivative comes from the rise over run equation (y2 - y1)/(x2 - x1). Just that by adding h that approaches 0, f(x + h) - f(x) wouldn't be 0 since h is approaching 0 and never at 0, then dividing it by h will give you the slope of an exact point at a curve. Then the power rules and other derivative rules are generalised versions of the definition of a derivative to make things easier to compute.
@hashtags_YT
Жыл бұрын
@@sek5372 Yeah, I get it now, but I had absolutely no clue when we began. I had no idea what a limit was, or that you could even calculate the slope of a non linear function. And that was on top of my physics teacher not being good at teaching and more or less just writing down the formula and an example on the board before calling it a day. It wasn't until the very next day that I was properly taught that stuff in my math class that it actually began to make sense.
@mez3932
Жыл бұрын
Get a worse mic or talk louder
@tomburgess8485
Жыл бұрын
you legit just explained calculus to me better then any of my lecturers ever did
@ek6352
Жыл бұрын
I remember it was the start of class 11. My teacher taught calculus starting with differentiation (yeah, not limits) and i was on the verge of crying. I felt like smashing his bald head with a baseball bat. He basically explained nothing. After the classes, I didn't even understand what derivatives actually are. Teachers really need to teach calculus properly.
@StockHonda
Жыл бұрын
As soon as you started you lost me
@TheRealNickG
Жыл бұрын
If you have already successfully mastered the first two calculus courses, you have made it through the toughest part of what they call "engineering calculus". Seriously, congratulations if I understood that correctly because calc 2 is the hardest "non proof" class ever. Calc 3 is not so chaotic and much more focused and obvious unlike the unmedicated ADHD calc 2 curriculum. Last is differential equations, which is "hard", yeah, but it's just a lot of algebra and mostly a logical extension of the other classes. And that's the secret of the whole thing. That's it. You can now literally go on campus and decide which degree you want. You actually interested in how the proofs work? Major in math. Want to use the maximum of this math without having to learn much more until at least grad school, if you even decide to go? Check out chemistry and physics and mechanical engineering. Willing to learn a little more math and interested in computing and programming? Computer science and engineering and software engineering might be a good idea. My point is to stop belly aching about what you don't know because for the first time you are faced with the idea of math that's actually useful. You've put in 85% of the work to be qualified for more advanced upper division physics classes. Why stop now? 🤔🔥😎
@TrandusNinja
Жыл бұрын
Is that so? In my first calculus class we had all the "basic" derivatives and "basic" integrals (exponentials, logarithms, trig, square roots, and combinations of those). We had proofs for the fundamental theorem of calculus and had a mention of the formal limit definition
@aydin5978
Жыл бұрын
I'm happy I took AP calculus courses at my high school. Having a full year for what is typically a semester course really let us go through more material and actually build on everything from precalc.
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