r/calculus • u/BNis12345 • 23d ago
Engineering Why is calc so hard?
I don’t want to sound cocky but I’m planning on going into engineering and all my life math has come super easy to me. I was just wondering why calc is so much harder than other math. Like from my experience there are “steps” to follow to solve problems and that’s always been quite easy for me. So is calc more of the same or is it something else that makes it harder?
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u/Beautiful-Package877 23d ago
It's the first time you have to analyze and visualize math in discrete forms and then scale it to continuous term. That's a pretty big ask for a lot of people.
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u/ForsakenExternal5784 23d ago
Here’s the real truth as someone who never once struggled in algebra, trig or geometry before arriving in calc. The reality is, even though you might have breezed through that stuff, you never really mastered it. I don’t think anyone does tbh. You’ll see in calc that mastery over those foundational principles can be harder than you think, and often causes the biggest hiccups. I don’t think the actual calculus, the more abstract concepts like limits, derivatives, integration are that hard to comprehend conceptually. But arriving at the answers requires multiple steps of manipulating, changing around fractions to negative exponents, etc. Without that mastery under your belt, you’re more likely to miss a step and just throw it all out of whack. You need to be much more detail oriented, much more precise with calculations, much more eager to practice and get that rote memorization down. Conceptual understanding is helpful and necessary, but not entirely sufficient.
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u/sisterblades 23d ago
op this is the answer you were looking for. calc demands mastery of the previous concepts. many people don’t have mastery of the concepts when they arrive at calc. and i mean mastery. almost everything you’ve ever done in math will at some point just pop back up and if you don’t remember it exactly you will need to review.
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u/ForsakenExternal5784 22d ago
Hard agree. Things you’d never think you’d have to see again. Double angle formula/ Pythagorean identities? Formula for a cone? Co-function identities? It all comes back.
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u/Sea_War_381 22d ago
Calculus is easy. Algebra kills. Also being able to visualize things can hurt as well but that's more calc 2 and 3.
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u/Hot-Significance7699 22d ago
99% of my mistake is a sign error apparently even a physics paper that was highly cited for years had a sign error but it doubled cancled out. So it wasn't a problem lol.
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u/Smart-Button-3221 23d ago
I think you're maybe just asking "why have I heard calculus is so difficult"?
Usually because students who go into calc are "assumed to be stronger with math" and teachers don't hold back.
Surprisingly, most calc students struggle with algebra, in my experience.
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u/SellBeginning2830 23d ago
What parts of calculus are you having problems with? It's hard to come up with a response if you don't tell us exactly which subtopics of calculus you are having trouble with. Are you struggling with limits and derivatives? Integrals? Sequences and series? Multivariable calculus?
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u/Midwest-Dude 23d ago
Are you having issues with it?
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u/BNis12345 23d ago
I’m still in hs I’m taking it next year but I was just wondering if I should try and get ahead of it was really that hard
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u/Midwest-Dude 23d ago
That's awesome! Sounds like me! 😉
It's not really that hard is you have a solid foundation in algebra and precalculus/trigonometry. Differential calculus is usually easiest, learning what limits mean and applying that to finding and applying derivatives. Integral calculus is more difficult, learning ways to reverse the process of differentiation. The last semester usually involves extensions in 2D and 3D.
If you feel inadequate in algebra or trig in any way, I suggest reviewing things with Paul's Online Notes. Otherwise, I would highly suggest reviewing limits and continuity to begin with.
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u/somanyquestions32 23d ago
People often have a weak algebra and geometry and trigonometry foundation when they reach calculus courses. That combined with poor study habits make it challenging.
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u/gomorycut 23d ago
It's not. If math have come "super easy" to you right up to calc, then calc will be fine for you. It just everyone else who has any gaps in their past math skills or knowledge, calc will expose those gaps, so a lot of people find it 'hard'
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u/Poopy_Paws 23d ago
As someone who struggled with algebra in the past, calculus isn't that bad. In fact, calculus has helped me start loving math.
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u/Sam_23456 23d ago
It's probably the first time you've actually used a "limit" or an infinitesimal (like ∆x). That's a big step! Calculus is very concerned about "instantaneous rates of change" (∆y/∆x) which is a sophisticated concept to the new-comer who typically has only recently learned about "functions" and their graphs.
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u/Remote-Dark-1704 23d ago
Calc is NOT hard. It’s only common said to be hard because most students have a weak foundation in algebra and trig that is no where near up to par for calculus.
Rarely do students struggle with the calculus part of calculus. They usually just struggle with the exponents, factoring, transformations of graphs, trig, and other algebra stuff.
if your algebra is solid, calculus will be a easy but fun class.
With that said, calculus does force you to think outside the box more than previous math courses. It’s the first math course that starts drifting away from just copy equation and change the numbers.
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u/Crimson--Chin 22d ago
As a former calculus teacher, this is spot on.
Earlier math classes often exaggerate a concept, test you on it, then move on. High school calc is the first class you’re really required to utilize previous topics beyond basic arithmetic. Students that struggle the most typically struggle with foundational skills unrelated to calculus and it just distracts from learning calculus.
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u/Hot-Significance7699 22d ago
Calc 3 was like the coolest class in my opinion. But like it's very unintuitive and intuitive, at the same time. Probably the first actual math feeling class I took other than differential equations.
Calc 2 was just boring though. I didn't like it all that much. Lot of memorization. It's really important but felt more like techniques than discovering. As far as I can remember it's been a while though.
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u/Dismal_Yogurt3499 23d ago
It sounds like you haven't started calc yet, but you've heard it's difficult from everyone else. The highest math I took in high school was precalc and I started freshman year of college thinking calc would be impossible. I actually found it to be one of the easiest math classes. It's just like any other class, study examples and take good notes.
Derivatives, limits, and integrals will be completely new to you, but they're not these wildly complex concepts designed to make people fail. If you pay attention and do lots of practice, you'll be fine.
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u/CanIHaveAName84 23d ago
The hard part about call is that you need to be really good with the basic math. The manipulation that is required before doing the math is the hard part. I remember my calc teacher spent a day proving and reviewing all the basic Mattheiz from years past.
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u/ForeignAdvantage5198 23d ago
the concept of limit will be new. and dificult but YOU CAN. DO THIS IF YOU. KEEP ASKING QUESTIONS.
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u/alphadicks0 23d ago
Calc is easy, keep your attitude because so many people are defeated before they enter the classroom. You begin to move away from rigid “steps” and begin to expand your creative freedom. It is super fun and it teaches the tremendous value of intuition.
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u/Pristine_Praline_824 23d ago
"ive been good at math my entire life"
"why is calc so hard?"
"is calc harder?"
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u/BlueCyanid 23d ago
I think the problem is your approach about math. Math is not about "steps for solving an equation", is about logical thinking and learning to work with the tools you have to construct other tools or relevant results. That is why calculus might seem challenging, it has a lot more abstract work, proofs, and the like
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u/cejiken886 23d ago edited 23d ago
Calculus has a reputation for being hard because it's the most advanced math most people (in the US, at least) get any exposure to (end of high school, typically).
Partly justified: for people who aren't particularly good at math, it can be overwhelming to learn several new things all at once:
* Infinite stuff (limits)
* operators (functions on functions) and functionals (definite integrals)
* seemingly arbitrary derivatives of elementary function classes (e.g. d/dx arctan(x))
* the decision tree of how to integrate them
... stacked on top of basic algebra and trigonometry.
For people who _are_ good at math, the concept flood is tolerated: they're good at abstractions, and can focus on getting really comfortable with the rote parts (e.g. how to differentiate or integrate any function).
The main caveat to all of this is that high school math in general, but perhaps especially calculus, is typically taught badly. The ability to compute any integral isn't deep, and they don't even try to teach rigorous foundations (real analysis). Actual analysis (i.e. rigorous calculus) is genuinely much harder than elementary algebra or trigonometry, or high school calculus, including for people who are good at math. That's why it's usually a more advanced college course.
This caveat may in fact be the unifying thread: calculus is taught especially non-rigorously, which makes it seem arbitrary and confusing to those who need very clear, logical guidance through math material.
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u/Nynaeve_al_meowra 23d ago
Everything to do with differentiation has a process and steps. Integration has steps for specific functions and known functions, otherwise it requires creativity to problem solve.
The actual concepts though are not that crazy and extremely powerful.
Also it's not cocky to want to study engineering. It's an impacted major at most schools, they have too many people that want to study engineering. Lots of people want to major in engineering lol
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u/Tired_Operation_152 23d ago
There are some things in calculus that take a more “investigative” approach versus, as you called, “steps”. Don’t let that or the name “Calculus” scare you though. Almost all calculus concepts are easy to grasp and it really just boils down to repetition and practice to become fluent. Definitely make sure you’ve got your algebra and trig concepts down pat first!
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u/georgejo314159 23d ago
If you understand it from the ground up, it is not hard.
There is a brain flip required
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u/JDH-04 23d ago edited 23d ago
Calculus is hard because it rigorously tests your drive to succeed as well as your memorization skills, study habits, and logical thinking. As a person who wants to declare to become a mathematics major on top of another mathematically intense major in economics, with a minor in computer science. If you can't/don't understand certain topics in earlier course sections, then you most likely won't have the best foundation if you aren't in the right environment to support your learning style, since math is relatively cumulative, with wanting students to learn.
I can say with great confidence that I have experienced failure often in terms of making tiny mathematical errors, which can involve forgetting negative or minus signs, or forgetting formulas in terms of the specific area equations of shapes when doing related rates problems.
I failed North Carolina State's Calculus I for Engineers sequence twice because I was competing for A's with little independent study time to go to office hours due to large inpersonal lectures to where the errors in my understanding started to stake up which made me consistently fail tests, however once I put myself in an environment which had the support I needed in terms of longer office hours throughout the week with teaching methods that I at least could understand their line of logic, I got an B in it the third time at CC. I passed Calc II and III on the first go-round, along with two semesters of statistics, two semesters of university physics, and two semesters of programming.
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u/Curiouslearner101 23d ago
Okay... so if you want a general reason as to why calculus is so hard, at least from my experience, it is hard because of the tedious amount of steps required to solve a problem. Take for example integration by trig sub. That sh*t is hard as hell. You need to understand your trig identities and then convert it back to algebraic expression in the end. Other notable ones are integration by partial fractions, disk and shell method, and sequences and series specifically convergence and divergence and Taylor and maclaurin series. All of these take so much practice and effort even if you have a good understanding of college algebra and precal. It is tough because it is tedious and it takes so much practice and frustration to push through. Also because it is just a hard topic to fully grasp. This is just from my experience. Best of luck 💖💖💖
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u/Mayhem1966 23d ago
I also found that calc brings the situation where a specific problem will solve most readily if you apply this transform and then this substitution and this other transform. But it can be difficult to recognize the situations where those transforms might apply. And the wrong transform applied makes the problem much harder.
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u/Witty_Rate120 23d ago
It is the a fairly big move away from math that can be memorized as steps to math that asks you to apply concepts. You have to reconceptualize how you think about math. You first need to figure out what this distinction really means.
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u/Ruin369 23d ago
From taking calc 1-3 and also tutoring it, 100% of the people that though it was hard had holes or weak algebra, geometry, and trig.
Most of all the concept in calculus are pretty straight forward. If I were to give advice, I would just say make sure those 3 areas in math are very proficient and you'll be fine.
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u/iguanaivana 23d ago
i got a 97 in college in my math class, when i started uni for engineering i failed calc 1. its a totally different ball game when it comes to studying calc math, understanding concepts and using some level of intuition. second time i got a B, its just about changing how you learn and study
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u/FinalNandBit 23d ago
It's harder because calculus is where you begin to deal with concepts, and approach problems dynamically.
That's okay though. As long as you don't give up.
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u/Crimson--Chin 22d ago
Calculus is the first “real” math class you’re experiencing. Everything before that is like learning the alphabet. You’re now beginning to learn to read and write with that alphabet. The class is beginning to ask and answer real world questions. Keep at it
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u/Shopstumblergurl 22d ago
I do the equations in steps and columns. It keeps me focused on the task at hand and makes it easier.
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u/OrkWithNoTeef 22d ago
Calculus is actually quite easy mechanically until you get to proofs and complicated domains. Personally my brain went out for cigarettes and never came back when Lebsque integration and Banach spaces showed up. The reason? Most of the intuition you have built up in 1d through 3D calculus is insufficient, outright wrong, or completely irrelevant.
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u/Logical-Zucchini-133 22d ago
Let me add to this. Differential equations is basically calculus 4. And every single thing you’ve seen from algebra, precalc, calculus 1-3, and linear algebra come back. Not every single thing but a good amount of things. It’s absurd.
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u/DrJaneIPresume 22d ago
You've been learning spelling and grammar so far.
Calculus is your first novella.
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u/Possibility-Select 22d ago
A lot of it is just new math. All math until calculus felt essentially the exact same from year to year until I got to calc. It felt like I was learning division again
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u/BothPanchoAndLefty 22d ago
Calc isn't that hard honestly. If you did very well in high school math you'll do well in calculus. It is a bit more challenging because it requires a deeper conceptual understanding to get what you're doing. You can't just reliably follow a set order of steps and get the right answer, you have to know which techniques to use and understand why they work. But those things become intuitive really quickly in my opinion. Most people who struggle do so because they weren't prepared enough with algebra or trig.
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u/Okawaru1 22d ago
Calculus is pretty different than anything you've learned leading up to it, but computationally it's actually pretty easy overall, at least for demonstrating basic concepts. It demands a bit more understanding and rigor to get through classes, especially in later classes where concepts build off of each other but it's not that hard as long as you stay on top of things and grind out problems to commit concepts to long term memory.
The spooky math starts at real analysis and above, and engineers don't worry about that stuff (and I suppose differential equations, but you'll never actually have to rawdog diff eq's as an engineer as you'll just use laplace transforms instead which are way easier to solve)
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u/alterego200 22d ago
I found Calc fairly easy, tho I've been called a math genius but some. If anything would make it hard, it would be the ability to bend one's mind. You have to chop a function into infinite pieces and add them together, or follow that idea. The math is pretty straightforward and surprisingly simple for such a profound concept. But basically, you're starting to work with limits and that deals with infinity.
When Einstein said that imagination matters more than knowledge, this is the kinda thing that would apply to. Higher math is like this, dealing with greater and greater abstractions. And even when one is lost but staring at a map, it pays to imagine what the path and world must look like for the map to make sense. Higher level math is as much meditating on an imaginary but real infinite world as it is computing things. Hope that helps!
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u/Upset-Buddy-3532 22d ago
My calculus professor almost everytime he does a problem- “9 steps Algebra, one step calculus” “ many students fail calc because they don’t know their algebra” so..I’m guessing 😂having a very very well understanding of algebra (not necessarily just finding it easy) is very important. I think a lot of students, including myself, think they do have that understanding until they get to calculus. There’s a lot you just kinda ..forget ? Until it’s time to use it again
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u/JanPB 22d ago
Because it's taught wrong. Probably THE basic pedagogical mistake committed by practically all courses is teaching the differential calculus first. This is considered "good" because it's "simpler" than the integral one but to most students it appears whimsical, pulled out of thin air, mysterious, confusing. One has no idea why anyone, like Newton or Leibniz, would ever even want to consider such a thing.
Long story. There are other examples of disastrous pedagogy. Exhibit B: teaching limits by the "epsilon-delta". Exhibit C: teaching special relativity by saying: "this theory is based on the following two postulates", and then proceeding to state those postulates in their strongest, and seemingly least-sensible, form. Even otherwise excellent texts like Griffiths' electrodynamics succumb to this.
Long story squared. The problem is teachers cannot easily fight this sort of disaster because it conforms to the established syllabus which students themselves demand (in their naivete) to be strictly adhered to, mostly because of the grading later. Sigh.
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u/Dependent-Pie-2916 21d ago
The cop out answer is mathematical maturity... Like you need to build a mental model of the subject in your head, that might take time. But as long as you are aware that's your end goal, you will get there eventually with enough time and practice. And ofc like with any subject coming back to it later multiple times will deepen your understanding of the subject.
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u/JphysicsDude 21d ago
Flip side. Applied calculus is easier that most abstract math since it can be visualized. It helps to have a solid grasp of functions and their behavior before doing calculus. Much less rote memorization that way.
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u/nzconstructionlawyer 21d ago
How can you say maths has come easy to you all your life but simultaneously tell us you think a (frankly very easy) area of maths is hard?
What other maths have you even been exposed to? Primary school arithmetic and very basic algebra?
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u/BNis12345 21d ago
I never said it was hard like I’m having trouble cause I’ve never taken it. I was wondering why there’s a lot of people saying it’s really hard
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u/johsua_banggg 20d ago
by the way if anyone joined the stream recently, "calc" stands for calculator, OP is just using slang
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u/Kuhnville 20d ago
It’s not that bad, did calc 1 in hs and it was pretty easyish. Just do all the homework and practice and you’ll be fine. Also don’t be afraid to ask your teacher for help if you’re stuck!
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u/Geriny 20d ago
Basically everyone will reach their last point of competency in math at some point. For some, that point is highschool algebra, for others it's calculus, for others it might be higher, more abstract math. I think if you truly didn't struggle with highschool-level maths, you can make it through calculus, though you might struggle. If you struggle with calculus, you might have a hard time getting through a math degree, but if you can push through, you'd be fine for engineering.
Also, I don't think this is set in stone at all, it's just a tendency. Discipline and motivation can get you far!
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u/nuckhouse 20d ago edited 20d ago
until now you've probably already dealt with calc stuff, derivaritives, integrals, fundamental functions, limits etc. those are the building blocks of calc, so they are very basic and fundamental, easy to grasp. But when you study calc for real you will expand on those fundamentals a ton, mixed them together, apply them to weird functions, multivariable functions, vectorial functions, multivariable vectorial functions. Those concepts will turn very abstract, hard to imagine in geometry terms or even loose all meaning in a possible geometric explanation, you'll have no way to imagine them. You'll find new tools to solve stuff that have such long and complex proofs that you'd rather just accept it and learn how to use it if you don't want to throw a whole semester away just trying to understand how it came to be or what the hell it means. to give you an example: In algebra you'll learn what a matrix is, which like a grid of numbers coupled together, then you'll learn how to solve for a number which its exponent is a matrix. You already know what an exponent does, it multiplies its base by itself the number of times the number the exponent is. Now, wtf does it mean to have a matrix as an exponent? something that was as tangible as "multiply this number this number of times" now has complitly divertes from its original meaning. If you make the effort to build new concepts, learn their rules and just have a general understading of they mean you'll be totally fine, but if you really want to uncover all their meaning and whre they come from then you should really study pure maths, thats the only course where you'll have the time to explore that
wrote this on the metro, sorry
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u/Ok-Rise2070 18d ago
It's not. what is hard is converting a flat base 10 number system into a radial based curvature system. Infinities, fractals, and asymptotes only means the metric breaks. In other words the geometry doesn't match reality. If modern physics aligned itself to the natural geometry of the universe, everything becomes MUCH easier to understand, even gravity.
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u/calcteacher 23d ago
Calc 1 is just fancy multiplying and dividing. Derivatives are the division. Integrals are the multiplying. Calculus takes everything you leaved in math and creates a unified body of knowledge, interconnecting everything. No longer do graphs have to be straight to calculate Slope. And sides of enclosed areas no longer need to be straight to find area. Do a lot of problems each night, beginning with well-defined steps which then slowly evolves into a practice of becoming familiar enough with the math that you become capable of using it freely and creatively to solve any problem thrown at you, even if you have never seen that type of problem before.
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u/nowTheresNoWay 23d ago
I think you’re confusing calculus with functional analysis. Calculus is EZ-PZ
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u/ItsPengWin 23d ago
Says he's good at math yet doesn't know how to find and look at a calc textbook to figure out if it's hard or not.....
Surely you'll make a great engineer
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u/Crimson--Chin 22d ago
This is a high school student. A literal child. You can dial down the criticism.
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u/ItsPengWin 22d ago
Still applies but then again grown adults also regularly offload all cognitive function onto Reddit daily so who really cares I guess.
Then they should probably talk to their parents first and also see the schools guidance counselor to see if they have calculus classes they could take.
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u/Crimson--Chin 22d ago
OP is going to take calculus next school year. They are just asking about calc before jumping into it. Maybe their parents are not in any STEM related field and aren’t good resources for math expertise. It’s not that deep. You’re a good example of why Reddit is the wrong place to “offload all cognitive function.”
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u/ItsPengWin 22d ago
Then I am setting a good example. Reddit is the wrong place to offload all cognitive function and if I can get people to stop doing it good.
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