Equality of integrals VS equality of integrands

[etotheipi]

AFAIK there are no problems up to here: $$\frac{d}{dx} \lim_{x \to \infty} \int_{0}^{x} \left[f(t) - g(t) \right] = 0$$ but yes I don't think you can generally interchange those limits to get $\lim_{x \to \infty} \frac{d}{dx} \int_{0}^{x} \left[f(t) - g(t) \right] = 0$

 

[Adesh]

so I'm not sure where your claim comes from.

People whom I know (in real life) learned by themselves, teachers only graded them.

 

[member 587159]

People whom I know (in real life) learned by themselves, teachers only graded them.

My opinion is that most of mathematics is self-study. The professor is just there to motivate the concepts and give a first exposure, or to ask questions to.

 

[Adesh]

My opinion is that most of mathematics is self-study. The professor is just there to motivate the concepts and give a first exposure, or to ask questions to.

Then what does it mean when so many people say “Rudin is not good for self-study” ?

 

[member 587159]

Then what does it mean when so many people say “Rudin is not good for self-study” ?

It means that it is a bad book to learn the material from, with which I agree. There are much better self-study books out there.

 

[Infrared]

@Adesh I generally had very good professors in undergrad and learned a lot from their lectures. I can sometimes be a slow student though, so I generally had to re-work the parts I didn't follow afterwards, but this is all on me and certainly doesn't reflect negatively on my instructors.

I think Rudin is harder to self-study because it's terse and doesn't "hand-hold" the reader. This is much less of an obstacle when you have all the aspects of a class to help you along (other students, professors, teaching assistants, homeworks, etc.)

In the future, you might want to PM a user if you have a specific question for them, instead of posting on an unrelated thread.