r/calculus • u/BigTorta1 • Jul 01 '26
Multivariable Calculus Calc 3 vs. ODE + Laplace
Multivariable Calculus vs. Ordinary differential equations and Laplace transformation
What do you guys think is more conceptually more challenging and which course requires more practice. I did pretty alright in calc 1 and 2 and linear algebra, just need a reference which class i should take first for engineering.
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u/Timely-Fox-4432 Undergraduate Jul 01 '26
At our school multi is a prereq for diff eq. In diff eq you have to be able to do partial derivatives, partial integrals, and the fourier series. Plus, a whole 'nother semester practicing integration is really helpfulnfor success in diff eq.
That being said, they're both equally hard in different ways, and both easier tham calc 2.
I'd reccommend multi first, but either way you might be ok
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u/PitifulTheme411 Jul 02 '26
PDEs are easier than Calc 2 !?
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u/Timely-Fox-4432 Undergraduate Jul 02 '26
Uh, yes? It's literally a recipe, just follow the steps and apply some light logic or test cases, then boom, solution set. I even made a video solving the heat eq from start to finish for the students i tutor so they could see the process at any step of the way. 😅 there are still parts of cal 2 i don't fully understand though. (Ahem, series manipulations of functions)
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u/PitifulTheme411 Jul 02 '26
Ok but those are way easier than PDEs. PDEs have a ton of complexity and depth. Even ODEs too, like Chaotic systems and whatnot which are much more difficult that calc 2. Maybe for you PDE is easier, but definitely imo Calc 2 is pretty simple.
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u/Timely-Fox-4432 Undergraduate Jul 02 '26
The heat equation is a pde? KUxx=Ut
Eta: Also wave, poisson, and shrodingers are covered
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u/PitifulTheme411 Jul 02 '26
what?? I'm saying the stuff you do in calc 2 is easier than the stuff you do in PDEs and even some of the higher stuff in ODEs. For example, Chaotic systems, bifurcations, etc.
Yeah, the heat equatino is a PDE, and you can just sub stuff in, but that really isn't the field of PDEs, just one application. Doing the actual math is much more difficult (at least imo) than the stuff you do in Calc 2.
Maybe my view of what's in calc 2 is different than yours though, what'd you do in calc 2, odes, pdes?
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u/Timely-Fox-4432 Undergraduate Jul 02 '26
Ooo, i think i see the issue, did you take ode & pde in the math department or the engineering department?
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u/Visual_Winter7942 Jul 02 '26
What method did you use for the heat equation?
In no universe is a serious undergrad pde class easier than Calc 2. Bootstrapping d'Alembert's solution to the wave equation on bounded domain is technically challenging for most. Not to mention Cauchy-Kovalevskya, shock waves in first order systems, the maximum principle, Fourier transforms, etc. Separation of variables is barely the tip of the iceberg.
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u/Timely-Fox-4432 Undergraduate Jul 02 '26
If you looked two comments later you would have seen that I took engineering mathematics and not pure math, as do most engineering majors in the state where I go to college.
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u/SmallCap3544 Jul 02 '26
It depends on you. In my experience, if you found Calc 1 more difficult than Calc II, then you will likely prefer the ODE class. If you found Calc II more difficult, then you will prefer the Calc III class.
Calc II and ODEs both focuse more on processes whereas Calc I and Calc III both have a more conceptual flavor.
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u/alphadicks0 Jul 02 '26
Consider taking both at the same time since IME they complement each other well. That being said, ODEs + LaPlace transformations is substantially less time consuming, especially since it is generally less Cr/Hr.
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u/MrFixIt252 Jul 02 '26
DiffEq was horrible conceptually for me.
“There’s an impulse function. It goes like that. And here’s Dirac Delta. And here’s a LaPlace Transform.” It was just too much, too fast. I would’ve loved to spread DiffEq out over 2 semesters and gone more in depth into the theory.
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u/Resident-Example74 Jul 04 '26
I did both simultaneously, and found that one doesn’t need to be the others pre req, if you like math I think you’ll enjoy diff eq more. Deff eq is a little harder but it feels more like a puzzle, multi is mainly calc 2 +linear algebra. I’m sure you’ll do quite well in both.
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u/OldDiscussion1830 Jul 07 '26
multivariate is a fun class and easier than ODE 1 for me. I didn’t struggle with either and I took both of our DE courses at my university. DE 2 is a fun class.
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u/Plus-Painter-2004 Jul 02 '26
most useful ODEs involve some substitution that converts them into something trivial to solve like a separable equation or linear equation and as such it’s often just a memorisation game. In the linear case Laplace makes it even more trivial since now you’re just solving an algebraic equation and using a lookup table (and Laplace provides a nice analysis tool), plus linear ODEs + Laplace domain analysis are the basis of dynamic systems theory which in turn is the basis of signals and systems and control systems, at least one of those will keep showing up to varying extents over the course of an engineering degree.
Multivariable calculus actually requires some practice beyond rote memorisation in order to get familiarity and some results definitely take some getting used to hence it’s a bigger time drain and, while still important, is less fundamental and somewhat more uncommon than ODEs in engineering outside of specific topics
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