Is Differential Equations a Hard Class #shorts

Is Differential Equations a Hard Class #shorts

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[JP-xmqf]

A good teacher is the difference between understanding and failing

[jeremiahwilson]

I think the hardest thing about differential equations is that it’s not very intuitive. Most professors just give you the formulas needed to solve certain DEs because “it’s what works” but there’s no real natural intuition behind them.

[noobgt]

Having a really good teacher is the hardest part

[TheEvilUmpire]

Agreed. Things you wanna brush up on before taking differential equations:
1. Integration techniques (as mentioned)
2. Infinite Series (Taylor Series)
3. Maybe look into recursive relations a bit, but don't go crazy. If you see generating functions turn back, lol.
4. I can't recall why, but I recall "roots of unity" being mad important.

Other than that, I recommend learning how to write clearly with both hands simultaneously. If you've never experienced a crippling hand cramp before, you likely will during hw or worse yet, an exam. Those problems go on for days! Stay organized. Signing up for ODEs was really intimidating. I was surprised at how much I enjoyed the subject. I can't believe I'm saying this, but Differential Equations was a real confidence booster. I feel like Calc II (Integration) was way harder.

While I'm here, book recs:
"Differential Equations" by Shepley L. Ross (3e) has a really nice passage about using differentials. It's full of gems like that.
"Differential Equations: Theory, Technique, and Practice (Walter Rudin Student Series in Advanced Mathematics)" by Simmons is possibly the best technique focused text I've read. I really wish there was a book like that for combinatorics.
"Differential Equations with Applications and Historical Notes" by Simmons is another classic.

[elieddy]

I think the hardest part of diff-eq is just the memorization. If I didn't make flash cards for all the different methods and when to use them, I definitely wouldn't have passed

[HDitzzDH]

My experience with it was that it seems to have been just about memorizing a bunch of techniques for solving them depending on how the DE looks. If it's structured like this then it's a Bernoulli's Equation, if it looks like this then it's separable, like this and it's Exact, Integrating Factor etc. Initial value problems (determining the constant) was pretty easy, but determining interval of validity could get pretty tedious sometimes, especially if you had a bunch of substitutions because then apparently you need to find the domain for each substitution.

[Kovici.]

This year, i discover that i love maths but i feel little sad because my level of maths is not that great, i am not good at study at all, i failed multiple times in school but somehow i completed my school and now i took admission in college, i m doing my best, i start from zero, i start with a 6th standard book (square roots, cube roots, basic algebra and equations, basic trigonometry), after make my base strong i will do further, thank you sir, (this comment is not relevent to this video but .... just want to express my emotions 😂)

[brett]

Understanding it from an applied perspective is always helpful!

[sgc]

Back in my chemical engineering days('68-'72), the Chem E department taught us DE and didn't leave it to the math department. They taught us DEs as would be most appropriate to what we needed.

[jessstuart]

Differential equations are hard, until you learn the right substitution to use.

[sidpit]

Keep reviewing!! That's what got me through this class

[allenruddlesden]

It was very hard with my tenured, incredibly lazy and low quality teacher. But thank goodness I found your channel! You made it fun and intriguing, wouldn't of passed without you.

[von]

Currently taking different equations and it’s the first time I’ve felt that I was in a genuinely hard course. Granted I am taking it online and my professor only gives us brief videos showing very basic things and then expects us to solve much more complex questions, so that could also be a large factor.

[Taylor-rxyb]

I definitely agree, especially with the teacher part. I think differential equations, as well as linear algebra, are courses that are really deceptive in a sense. What I mean by that is that your first encounter with the subject is very different from what the subject is really like. I would imagine that this is due to the fact that, at an introductory level, the proportion of math students to physics or engineering students is low, and though I love proofs and rigor, very few students taking the course have to interest or mathematical maturity to approach the subject as a mathematician would, neither would many math majors at that point but still (also lot of math majors at my university would push differential equations off until their junior or senior year so they would at least have a better chance with rigor). This is all to say that I found my first differential equations course very hard because the way it was presented to me was like a set of steps that seemed unnecessarily complex and I think that as someone who likes more rigorous math that was hard to figure out. It was also boring because when the math is what you find interesting very little motivation is gained from the subject being applicable. However, I am now taking graduate-level PDE courses and can say that my entire disposition regarding differential equations is very different, so much so that I may specialize in a field related to differential equations.
Sorry for such a long comment, but that was an accurate depiction of my experience.

[darkrising]

DE can be extremely hard depending on how in depth the professor goes during lectures. The same goes with Linear Algebra. People who say these courses were easy are lucky (or unlucky) that they probably got a light version of it.

[pipertripp]

IMO, what makes differential equations hard, but also incredibly rich is interesting, is learning how to apply them to real problems. The mechanics of solving them can be learned by rote given enough time and desire to learn. But lets face it, the mechanics (while important to learn and understand) are not how we actually work with differential equations in the "real world". We solve them using numerical techniques, on computers, because there is almost never an analytical solution. I'd love to see a course that just specializes in presenting problems and then applying differential equations to describe a model of the problem which can then be solved numerically.

[amandasoto]

Due to quarantine I don’t have a professor giving me class. In the curses pages there’s just a list of YouTube links to specific topics. I’ve found differential equations to be easy but occasionally tricky. Problem comes with math modeling and verbal exercises which easily through me off. Thanks to this class I found you channel which overall has help me tremendously.

[tabhashim]

I would disagree on integration. You hardly do it other than in separable equations or integration factor, but in both cases they are usually pretty simple integrals since that is not the point of the class. For everything else you practically don’t need much integration.

I think the most important thing for differential equations is to be able to visualize solutions and build a gut feeling for them

[ricaulcastellon]

You have to be really good at integration.

[baher]

with the amount of resources we have today online, I think DE is not that difficult, it does require lots of practice. Meaning, if you get stuck on a concept, you can always get an answer online.