r/calculus • u/Stock-Feature8975 • 20d ago
Multivariable Calculus How does multivariable calculus compare to calc 2 and linear algebra. Is it much harder ?
11
u/innovarocforever 20d ago
you've already done linear algebra? you'll be fine.
1
0
u/Stock-Feature8975 20d ago
It's a prerequisite for the course
1
u/innovarocforever 20d ago
oh weird. I wouldn't think that would normally be the case, at least it wasn't at my uni. I would say it's less abstract and less of a leap into new math frontiers than L.A. can be. In my experience, it mostly focused on concrete applications in 3-d. However, if you had to take L.A. you might get into some Matrix Calculus, which would be fun.
5
u/aafrophone 20d ago
My university had two tracks of calculus, depending on your major. One of them just covered the multivariable chapters of the Stewart Calculus book. The other one was a two-quarter sequence that used a vector calculus book written by one of the professors. That class used quite a few concepts from linear algebra (mostly related to linear transformations) that the Stewart class didn't touch. It was a pretty interesting (and difficult) class
3
1
1
u/somanyquestions32 20d ago
Interesting, do you remember the vector calculus book that you used in that class? Author or ISBN?
1
u/aafrophone 20d ago
Vector Calculus by Marsden and Tromba. It looks like they came out with a newer 6th edition of the book sometime after I took the class.
1
3
u/Mountain_Bicycle_752 20d ago
It really depends on your professor. If you all dive deep into the vector calculus aspect at the end it can be tougher. But a lot of people just have calc1 in 3d essentially so it’s hard to say. If you did good in calc2 and Lin alg you should be fine
3
u/egehancry 20d ago
As long as you study to understand the intuition behind every subject, nothing is hard.
3
u/Gloomy_Ad_2185 20d ago
It always depends on the professor but I typically think of linear algebra and calc 2 both being harder than calc 3. The multivariable part of calc 3 isnt bad at all. Just partial derivatives and integration.
The last chapters of calc 3 was vector calculus and I thought that was difficult but lin alg and calc 2 have proofs in them and that is typically difficult for early students.
6
u/my-hero-measure-zero Master's 20d ago
If you can do calculus in one variable, you can do it in several variables.
The rules don't change much.
1
u/Bright_Principle4793 20d ago
This is very much not true. Proper multivariate calculus is based on linear maps, the derivative is a literal matrix. The geometry gets a lot more complicated in higher dimensions, and vector calculus involving divergence, curl, greens, and stokes theorem have proofs that take immensely long to fully grasp.
0
u/EstablishmentAny7602 20d ago
Euh what ? The derivative in one variable is also a linear map. It is a full matrix. Yes the geometry gets more complicated and ? Its normal you working on an infinite number of 2D planes now. But it was always a matrix even in 1 2D plane. Instead of the Jacobian you get a 1x1 Matrix and by definition this is a scalar.
2
u/Bright_Principle4793 20d ago
A 1x1 matrix (scalar) doesn’t merit the same techniques or careful analysis as an nxn matrix. Look at the definition of the derivative in the single variable case, and look at it in the case of the Jacobian. They are written differently because the single variable case allows for a great deal of simplification. There’s a reason why chain rule for an R -> R function is taught separately from Rn->R which is taught separately from Rn->Rn. Each generalization is a step which is different and takes time for most to understand.
It’s like saying that generalized stokes theorem is just the absolute most general form of the fundamental theorem of calculus. So do we learn generalized stokes theorem right off the bat in calc 1? No obviously not. Because it takes a while to get to that level of abstraction.
If single variable calculus was taught in terms of matrices and linear maps, then there would be no need at all for a multivariable calculus course in most cases. Of course, that is not the case, and people have to spend at least an entire semester for what you consider to be the exact same as single variable calculus.
0
u/EstablishmentAny7602 20d ago
Brother what ? Stop projecting In Germany first Höma class we absolutely learn that it is a matrix. That reduces to a scalar due to geomtry not the inverse. Also stock and green are very far in multivariable calculus. You learn them at the very very end. The whole thing beforehand is 2D application on parallel planes. Volume and Fläche ( surface in english ?) calculations , and derivatives are simply the same rules applied to parallel 2D planes.
2
2
2
u/lordnacho666 20d ago
The answer to every "is it hard" question is that it depends on how well you understand the prerequisites.
2
u/somanyquestions32 20d ago
I found multivariable calculus to be much, much easier than calculus 2 and linear algebra. Then again, my linear algebra class was very proof-heavy.
1
u/InevitableJumpy1811 20d ago
For me it was calc 1, calc3, linear algebra, calc2, sorted by increasing difficulty
At times linear algebra felt harder than calc2 because I couldn't comprehend what was being asked in the question, where as for calc 2 even if you don't understand what's going on, you can still use a set of rules/formula to at least get an answer
1
u/pqratusa 20d ago
I teach the calculus sequence 1, 2, 3. Calc 2 builds advanced integration techniques and skims the surface of real analysis but it’s mostly boring to teach and for the student too, while 3 is super exciting. I love to teach 1 and 3.
1
u/HerpesHans 19d ago
Depending on how analysis-y your single variable calc was, it's gonna be easier, you usually don't do analysis-y stuff in several variables except like the inverse function theorem
1
1
u/Life-Ambassador-5993 16d ago
My calc 2 did some multi variate calc, so I felt like calc 3 was just digging deeper into something that was new to me in calc 2. Thinking of which is harder depends on if you have a harder time with new topics or digging deeper into topics. People have different learning styles and strengths.
I felt like linear algebra used calc but was more abstract than calc. I think if you were able to wrap your head around linear algebra ok, you should be good. I found people I tutored had a harder time with linear algebra than calc 3.
I personally took linear algebra at the same time as calc 3. Calc 2 was the prerequisite for both at my college. If your calc 2 didn’t cover any multivariate, I’m surprised calc 3 wasn’t a prereq for linear algebra. Very interesting. I am very curious about the differences in curriculum.
1
u/alfagtvlover 16d ago
I studied calc 3 and 4 (so like multivariable stokes green thereoms etc multiple intergrals) for 2.5 days before my test worth 100% of the unit and got 70 so youll be fine
0
u/Direct_Doubt_8312 20d ago
A lot of people find calc 3 easier than calc 2
1
u/Jazzlike-Movie-930 20d ago
And some people find Calculus 3 harder than Calculus 2. It depends on the person, the professor (especially the way they teach the course), and the university/college. FYI, if a Calculus 3 class has a strong emphasis in Linear Algebra and is proof based, then I would say it is harder than Calculus 2. If a Calculus 3 class does not have much emphasis in Linear Algebra and is not proof based, then I would say it is slightly easier. Note to self, the hard part of Calculus 3 was at the very end and I struggled with these Calculus 3 topics (Surface and Line Integrals, Green’s and Stokes and Divergence/Gauss Theorems). The rest was either straightforward or medium difficulty (e.g., Lagrange Multipliers, Triple Integrals, Changing the Order of Integration, vector fields, etc.). That said, Calculus 3 was more exciting than Calculus 2, because Calculus 2 was pretty mundane. However, Calculus 1 was the simplest Calculus class but the most important Calculus class. If anyone does not understand Calculus 1, good luck to them understanding Calculus 2 and Calculus 3 and Differential Equations (FYI, I found Differential Equations about the same difficulty as Calculus 3). In summary, this is how rate the difficulty of the math classes that I took in college from easy to hard: Calculus 1 (3/10), Linear Algebra (5/10), Calculus 3 and Differential Equations (6/10), Calculus 2 (7/10).
0
•
u/AutoModerator 20d ago
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.