What's the use of breaking my brain over long problems of higher order derivatives?

Main Question or Discussion Point

I've got mathematics as one of the courses in my engineering programme. I love maths. However i don't enjoy working my guts out to ''if...then prove that...'' problems which are kind of brain teasers and brain teasers only. Their solutions often involve leibniz's rule of higher order derivative of products of two functions. I've been working on them for a week now but i fail to understand how does an engineer or a physicist needs it to work so hard.

What sort of engineer or physicist do you want to be?

If you become a structural engineer you will regularly be dealing with fourth order differential equations.

Second order differential equations play a vital role in most areas of physical science. They are more common than £1 coins.

I've got mathematics as one of the courses in my engineering programme. I love maths. However i don't enjoy working my guts out to ''if...then prove that...'' problems which are kind of brain teasers and brain teasers only. Their solutions often involve leibniz's rule of higher order derivative of products of two functions. I've been working on them for a week now but i fail to understand how does an engineer or a physicist needs it to work so hard.
If you're building the bridges that I'm driving over, I really want you to be able to work hard to get detailed and complex calculations absolutely right.

Here's a video of a famous bridged designed by someone who didn't do their calculus homework! Carnage starts at 1:00.

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I find the opening post very ambiguous. Can you give an example of a type of problem to which you are referring or explain what you mean more clearly?

Their solutions often involve leibniz's rule of higher order derivative of products of two functions. I've been working on them for a week now but i fail to understand how does an engineer or a physicist needs it to work so hard.
Think of it as lifting mental weights. If you do it enough, then you'll find it easy after doing it 1000 times (at which point someone will just put more weights on the machine).

Also, for the type of work that I've done (i.e. astrophysics and extreme financial mathematics), being able to do these problems quickly and easily is extremely important. What you want to get to the point of doing is to look at a problem, and immediately figure out how to solve it.

If you're building the bridges that I'm driving over, I really want you to be able to work hard to get detailed and complex calculations absolutely right.
There are reasons for studying math, but this isn't one of them. Any major engineering project that depends on a human being to get a calculation absolutely right is doomed, because doing precise calculations is something humans are terrible at but machines are good at.

If you were doing this in the "real world" you'd get a computer to do the calculation. Now you need humans do know when the computer is spitting out non-sense, but that's a different skill.

However, construction workers use machines to build skyscrapers, but if you want to improve your health and skills, you still should lift weights by hand, even though if you work in construction you'll have a machine do it and they can do it better than you can.

You're right. However I'm concerned with the trend in academic maths that's put into an aerospace engineering course. The kind of questions we need to prepare for the test involves churning our mind to prove an eqn is right assuming the validity of a given condition. I don't see any link btwn real life aerospace problems and working to find nth derivative of a long trigonometric fuction.

You will need a good deal of trig in conformal mapping.

Since you are in aerospace and dislike maths so much can you offer a non mathematical reason why the air flow faster over the top surface of a wing than it does over the bottom?

Here is a real life engineering trig formula that you might use:

Can you differentiate it? Integrate it?

$${E_p} = \frac{{{E_a}\cot \beta + {E_b}\cot \alpha + ({N_b} - {N_a})}}{{\cot \alpha + \cot \beta }}$$

AlephZero
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I don't see any link btwn real life aerospace problems and working to find nth derivative of a long trigonometric fuction.
If you are stilll at college, what do you know about "real" life" aerispace problems and what it takes to solve them?

I agree some of the learning process might seem lilke learning to do circus tricks, but you need get to the stage where you can handle the basics correctly withiout even thinking about it. For mote people, the only way to get there is lots and lots of practice. Things like Leibnitz rule as basic as "2+3=5" IMO.

Proof type questions might not be directly applicable to anything but they develop a mental muscle that helps everywhere, especially engineering.

Working with high-order derivatives builds some intuition when working with lower order ones. I see many people in my class plugging and chugging simple formulas in there calculators. You should be able to look at simple derivatives, integrals, linear 2nd order ODEs, etc and know how they behave. No need to run to a calculator or MATLAB every time you see a math formula.

At least in the mean time you'll be expected to know mathematics to learn other concepts in your future classes. If that will continue to mean anything post-graduation, I suppose thats up to you. You aren't going to school for job training.

I've got mathematics as one of the courses in my engineering programme. I love maths. However i don't enjoy working my guts out to ''if...then prove that...'' problems which are kind of brain teasers and brain teasers only. Their solutions often involve leibniz's rule of higher order derivative of products of two functions. I've been working on them for a week now but i fail to understand how does an engineer or a physicist needs it to work so hard.
As an engineer, it's part of your university education, therefore you need to understand it to complete your university education so that you can get a job.

It's okay though, once you're in industry unless you become the guy that checks that the computer isn't spitting out nonsense then you'll probably never have to see any more calculus.

Because doing hard, abstract problems creates the neutral networks that allow you to do hard, abstract problems. Even if you never have to do that problem again, the next time you come across something vaguely similar, your brain will say, oh that looks familiar... heres the thought processes I used last time.

There are reasons for studying math, but this isn't one of them. Any major engineering project that depends on a human being to get a calculation absolutely right is doomed, because doing precise calculations is something humans are terrible at but machines are good at.
You still have to program the machines, and that takes the kind of logic developed through "if... then prove that..."

You still have to program the machines, and that takes the kind of logic developed through "if... then prove that..."
Only a very small amount of engineers will be involved in programming the machines.

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It's probably true that for any given topic, one can find a job where they will never use it. ("But teacher, when am I going to ever use this?") It's also true that the longer the list of things you decided not to learn becomes, the less likely it is that you will get the job of your choice.

Why does a Kung Fu master have his pupils balence a rice bowel on their head for hours? Surely that's not something they will encounter in hand to hand combat.

It's okay though, once you're in industry unless you become the guy that checks that the computer isn't spitting out nonsense then you'll probably never have to see any more calculus.
Depends on the job. Where I work not being able to do calculus is basically the same as not being able to read.

The other thing is that when big money is involved (i.e. tens of billions of dollars), people become very, very, very interested in making sure the computer isn't spitting out non-sense.

chiro