How important is tedious 2, 3 page long integration in physics?

[xdrgnh]

I'm taking QM next semester and I'm studying Griffiths to get a leg up. I've noticed so far that a lot of the problems aren't hard per say but instead just require the integration of annoying functions. The kinda of stuff I hated to do in Calc II because I got a Disgraphia. As a matter of fact I hate most things done by hand. So instead I just write out the integral and use Wolfram to solve it. I believe I understand most of the derivations and even do the derivations by myself even if they are long. I can't stand though doing practice problems where I got to do a lot of integration by hand. Am I committing a huge physics sin by doing this?

 

[Raioneru]

When I took QM a couple years ago, most weekly homeworks had many equations to derive. If you don't like doing that kind of stuffs, theoretical physics is not for you. And trust me, somethings just can't be understood just by reading/looking at them, some of the steps you take to derive these equations teach you WAY more than the actual result. (in QM, many times the result is mostly known, the steps to get there are what matters imo)

The Homeworks were pretty time consuming (which is why we had a week to work on them) but the Exams usually took 50mins. In such a short amount of time, there's not much time to think about stuffs, so having spent time on the previous homework teaches students how to recognize the situation they are presented with.

I mean, it's fine if you don't like doing that, cause I'm pretty sure you won't have the choice

 

[xdrgnh]

Did you use Griffiths? Most of the problem in Griffiths ar not deriving but more or like find this wave function, normalize this wave function, what is the probability of so and so. Derivations I don't mind because I see a point to them. Mechanical calculations I like also if they are not time consuming.

 

[WannabeNewton]

The important part is setting up the integral based on the given physical system. Sure the actual computation of the integrals might be tedious and might offer no insight but if they show up on a test and you aren't used to solving them you're going to be out of luck because you won't have Wolfram by your side.

 

[TomServo]

Yes you are committing a sin, for two reason:

1) Big ugly integrals are a part of QM exams and you need to get better at doing them by hand (there are shortcuts you can take)

2) Physicists should keep their analytical skills sharp. We're not engineers.

 

[cjl]

2) Physicists should keep their analytical skills sharp. We're not engineers.

Speaking as an engineer, analytical skills can be useful in engineering as well. I really don't understand why many physics majors don't understand that...

 

[Lavabug]

I second TomServo. I remember my QM1 final had a question that involved 4-5 pages of integrals if you chose the "safe" brute-force approach and didn't spot the trick, but if you knew how to integrate you would make it out alive.

IMO, for a STEM major, there is no excuse for not knowing how to do integrals of basic transcendental functions, and eventually being able to do most of them fairly quickly (with tricks like using graphical methods when possible, keeping things tidy, knowing your trig. Read something like "Street-Fighting Mathematics" for examples)

Speaking as an engineer, analytical skills can be useful in engineering as well. I really don't understand why many physics majors don't understand that...

I think the implication was not that it's not useful as an engineer, but rather that it's rarely used on the job in most typical situations (I'm being more or less specific about integration here). As opposed to scientific research, which is what a physics degree is meant to prepare you for, at least on paper.

I have a sibling who studied engineering and literally prides himself about not having had to do an integral in 15 years. Also knew an engineering grad who went into an astrophysics masters (out of pure interest) that I shared an apartment with, who scoffed at the utility of being proficient at integration. He came to me whenever he needed a 1st order ODE solved. It might come as no surprise he was an anti-SR quack, but that's another story, and I always give engineers the benefit of the doubt despite running into ones like these.

 

[TomServo]

Speaking as an engineer, analytical skills can be useful in engineering as well. I really don't understand why many physics majors don't understand that...

My engineering friends (and I have more engineering friends than physics friends) are always talking about how they don't use advanced math once they get their BS and are working, or if they do advanced math then they just use a package for it. Obviously some engineers will continue to use their analytic skills (meaning pen and paper analytical math) but they seem to be the minority among all "engineers."

 

[TomServo]

:::looks around, sees nobody asking:::

Okay, I'll ask. What is anti-SR? Yeah, I could Google it but you never know with acronyms.

 

[Nabeshin]

:::looks around, sees nobody asking:::

Okay, I'll ask. What is anti-SR? Yeah, I could Google it but you never know with acronyms.

From the context, the guy doesn't believe in special relativity.

 

[lurflurf]

Integration by hand while fun is a waste of time. That said can you post some examples? I do not recall Griffiths having as many tedious integrations as other books. Three pages is a lot unless you count the rough draft or write very large or something are you talking about something like
$$\int \! \frac{\cos(a x)}{x^8+b^8} \, \mathrm{dx}$$
Often early in an integration we know the form, and the rest is calculating constants that appear.

 

[WannabeNewton]

Just use a QM book with conceptually difficult problems (be it mathematical or physical) as opposed to long tedious calculations.

 

[symbolipoint]

I'm taking QM next semester and I'm studying Griffiths to get a leg up. I've noticed so far that a lot of the problems aren't hard per say but instead just require the integration of annoying functions. The kinda of stuff I hated to do in Calc II because I got a Disgraphia. As a matter of fact I hate most things done by hand. So instead I just write out the integral and use Wolfram to solve it. I believe I understand most of the derivations and even do the derivations by myself even if they are long. I can't stand though doing practice problems where I got to do a lot of integration by hand. Am I committing a huge physics sin by doing this?

This is just a wild idea ---- but does the disgraphia diminish if you use a dry erase board or chalkboard? Also, does a visual or mechanical guide help to control it? Maybe the presence of ledger lines on paper, or use of a straight edge or ruler while writing symbolism? or is this irrelevant?

 

[symbolipoint]

Yes you are committing a sin, for two reason:

1) Big ugly integrals are a part of QM exams and you need to get better at doing them by hand (there are shortcuts you can take)

2) Physicists should keep their analytical skills sharp. We're not engineers.

Does that mean, a person with disgraphia cannot become a physicist?

 

[TomServo]

What is disgraphia?

 

[lurflurf]

http://en.wikipedia.org/wiki/Dysgraphia

 

[Mandelbroth]

Integration by hand while fun is a waste of time.

In physics, I'm inclined to agree with this. Unless you feel the need to appreciate the math, you aren't necessarily obligated to do the calculations by hand because things like Wolfram Alpha can compute the integrals for you.

That being said, I think it helps me understand the ideas better to understand exactly how the ideas came about, so I wouldn't exactly say doing the integrations manually is a complete "waste of time."

Out of curiosity, if you're comfortable answering this, does dysgraphia only hinder actual written material, or do you also have trouble with formulas "written out" in your head?