Calc 3 vs. Differential Equations

[Freyster98]

I want to start by saying that I know this may be perceived as a "stupid" question, but I'm quite curious...

What class more difficult...Calc 3 or DE? I'm into my final week of Calc 3, and next week I start DE. I decided to take both during summer sessions as I did this for Calc 1-2 last summer and loved the pace of the classes during the summer. I am doing well in Calc 3, and am curious as to how difficult DE will be in comparison.

Also, are there any basics from previous courses that I should get good at before I start DE?

 

[The|M|onster]

I took both classes simultaneously and found that I put more time into Calculus III. If you are doing well in Calculus III, then you should be fine in Differential Equations. As for preparation, I'd recommend brushing up on linear algebra, particularly material on eigenvalues. It will come in handy when you start solving systems of equations and higher order differential equations.

Also, you probably should have put this in academic & career guidance

 

[HallsofIvy]

It's not a matter of one being more difficult than the other- Topics from Calculus III are used in Differential equations (partial derivatives, exact differentials, etc.). Calculus III can be taken at the same time, but that is harder. Calculus III should be a prerequisite for Differential Equations. I would also strongly recommend Linear Algebra as a prerequisite.

 

[Monocles]

The difficulty ranking I usually hear (can't say if I agree with it yet because I haven't taken Calc 3 yet) is Calc 2 is harder than Calc 1 which is harder than Calc 3 which is harder than Diff Eq.

I'm taking Diff Eq. right now, without having taken Calc 3, and I've definitely found it easier than Calc 1 or 2 so far. I think it requires a little more memorization than Calc 1 + 2, but less problem solving skill.

 

[mathwonk]

i think often calc III is harder class than DE, simply because it has more topics crammed into the same time frame. of course that is just a comment on the way our courses is structured here. anyone could cram more topics also into DE and make it harder too.

there is at least one extremely easy topic in DE, namely how to solve linear, constant coefficient, differential equations. the answer is that if the roots of the correspondingn polynomial are c1,...,cn, all distinct say, then the solutions are e^c1t,...,e^cnt.

pretty much anyone can learn that. to understand it better however it definitely helps to have some linear algebra.

still this example also motivates the linear algebra. e.g. if you write down the matrix for the operator D (differentiation), acting on the space of polynomials of degree at most n, with basis the monomials x^k/k!, you will see a typical "nilpotent" jordan matrix.

if you do this for the span of the exponential functions above, you will see a typical diagonal matrix. and if you do it for the space of products e^ct.x^k/k!, letting k vary but not c, you will have a typical jordan matrix.

the moral is that on a suitable space of functions, D is absolutely the generic linear operator (with split minimal polynomial).

 

[Asphodel]

Calculus 3 is usually multivariable calculus with some extras thrown in like vectors or such depending on where you take it. It's usually a snooze fest.

DE is not that bad in some ways, but more hardcore than what you've probably seen before. It can be very easy or very hard depending on how you approach it...the problem is, learning how to approach it usually comes well after taking it.

 

[Nick M]

I'll be taking Multivariate and Diff-Eq this year to finish up my Engineering mathematics sequence as well.

We're using McCallum/Hughes-Hallet/Gleason for the Multi text - not sure about the Diff-Eq text unfortunately. We used these texts from Wiley for PreCalc, Calc I, and Calc II... I really enjoy learning from them.

In Linear we used the text by David C. Lay... a much different approach to learning than the Calculus sequence. I got an A-, but it was like reading an encyclopedia rather than a text that walked you through the material.

Having already taken Physics I & II w/Calculus, I'm eager to take Multivariate to better understand the nitty-gritty E&M material that we slogged through such as Flux.

 

[Freyster98]

Calc 3 will definitely help you better understand the E&M calculations. I took Physics 2 ( which included topics such as flux ) before I took Calc 3, and I wish I would have taken Calc3 first to help me better understand the 3-D calculations, but in the end it all works out I guess.

To the points on Linear Algebra...I haven't taken that yet, and will probably only end up taking it if I decide to minor in Math ( I'm a Dual Mech/Aero major ). Hopefully my teacher doesn't make the assumption that people have taken it already.

 

[Asphodel]

Calc 3 will definitely help you better understand the E&M calculations.

Can you even take E&M without first studying multivariable and vector calculus? They're required at my school...

 

[RasslinGod]

DE is easier because it's very systematic. Liek you'll know how to solve the problems easily from recognizing patterns.

 

[Freyster98]

Can you even take E&M without first studying multivariable and vector calculus? They're required at my school...

The E&M we did was just a part of the Physics 2 class I took. It wasn't an entire class dedicated to E&M, so we just covered basics.

 

[Asphodel]

Ah, you mean freshman general physics level, not Griffiths / etc.

 

[Howers]

DE is definitely easier. I feel I could have done that course in first year.

 

[Freyster98]

Thank you for all of your input. My apologies for putting this in the wrong forum. I have a feeling I'll be using this forum a lot in the coming years.

 

[Vanadium 50]

This is strongly dependent on the course and the instructor. Neither Calc 3 nor DE has a fixed curriculum (my undergraduate school didn't even have 3 semesters of calculus; the class after Calc 2 was DE) so the difficulty depends on what is covered. Either class can be easy; either class can be a bear.

That's why other people's experience at other universities really isn't all that relevant.

 

[PhilosophyofPhysics]

I had a tougher time with Calc III than with DE.

 

[Mathemaniac]

Some of these posts surprise me; I got B's in both (disappointing grades; I should have worked much harder that semester than I did) and was taking them at the same time, but I worked much harder in my DE class than in my Calc 3 class. Also, my older brother who used to be a math major failed his DE class, while he got a B in his Calc 3 class (he was taking both at the same time as well).

This could have something to do with the fact that DE was completely new to me, while I was already fairly familiar with a lot of the topics in Calc 3 from my general physics courses. As for my brother, though, I don't know.