Improving Your Analysis Skills: Tips and Resources for Self-Study

[Pseudo Statistic]

Getting "better" at analysis

I didn't know where to put this exactly...
I've been stuck somewhere in calculus... I mean...
I've been trying to advance, but recently I haven't been enjoying it as much-- mainly because I guess I don't truly understand the content; it seems as if I'm looking for a short explanation and a bunch of formulas/methods to remember.
I'm not much of a proof guy or an analysis guy... so I guess that's the main contributing part to my problem. (I don't even know the epsilon-delta stuff!)
So, I was curious, can anyone point me to some resource, free online book, or even textbook (not to expensive) for trying to go from plug-and-chug math to analysis?
Or does anyone have any specific advice that might help me?
Thanks a bunch.

 

[quasar987]

You haven't made it clear what is your current situation and what are your exact goals.

I've been stuck somewhere in calculus...

where?

I don't even know the epsilon-delta stuff!

Are you supposed to?

So, I was curious, can anyone point me to some resource, free online book, or even textbook (not to expensive) for trying to go from plug-and-chug math to analysis?

I haven't heard of a smooth road. You just got to take an analysis textbook and go over the material step by step. and that means not read the second chapter before you understand the first.

 

[d_leet]

I didn't know where to put this exactly...
I've been stuck somewhere in calculus... I mean...
I've been trying to advance, but recently I haven't been enjoying it as much-- mainly because I guess I don't truly understand the content; it seems as if I'm looking for a short explanation and a bunch of formulas/methods to remember.
I'm not much of a proof guy or an analysis guy... so I guess that's the main contributing part to my problem. (I don't even know the epsilon-delta stuff!)
So, I was curious, can anyone point me to some resource, free online book, or even textbook (not to expensive) for trying to go from plug-and-chug math to analysis?
Or does anyone have any specific advice that might help me?
Thanks a bunch.

I know what you mean, I'm a high school junior now, but I took AP Calc last year so I've been taking classes at the loacl university since, I'm taking complex analysis now and when we learned limits with complex numbers it was the first time I ever had to use the epsilon-delta definition of a limit, and because they don't teach it in the high school calculus classes it was the first time I'd ever have to use it, it was hard but after going and asking the teacher about it I think I understand it now. As for analysis I'm in somewhat the same situation as you I;m trying to find a fairly readble analysis textbook to teach myself a bit from, but all the one's I've seen seem to be too far above my current knowledge, but I guess the only option is to just pick a book and go over the material until it makes sense and if doesn't then you could always ask here or one of your math teachers...

 

[JasonRox]

I know what you mean, I'm a high school junior now, but I took AP Calc last year so I've been taking classes at the loacl university since, I'm taking complex analysis now and when we learned limits with complex numbers it was the first time I ever had to use the epsilon-delta definition of a limit, and because they don't teach it in the high school calculus classes it was the first time I'd ever have to use it, it was hard but after going and asking the teacher about it I think I understand it now. As for analysis I'm in somewhat the same situation as you I;m trying to find a fairly readble analysis textbook to teach myself a bit from, but all the one's I've seen seem to be too far above my current knowledge, but I guess the only option is to just pick a book and go over the material until it makes sense and if doesn't then you could always ask here or one of your math teachers...

I found that for the epsilon-delta limit definition limit that it is better to work backwards and not forward.

It's like backward logic. You probably know this already, but when I was told about this, it made it easier to solve for some cases.

 

[d_leet]

I found that for the epsilon-delta limit definition limit that it is better to work backwards and not forward.

It's like backward logic. You probably know this already, but when I was told about this, it made it easier to solve for some cases.

I'm sorry but I don't understand what you mean? Do you mean having a good knowledge of calculus and how it works before you learn the epsilon-delta definition?

 

[quasar987]

Here's a thread where I explain thoroughly the definition of limit and work out a specific exemple in some details. I should have also included a picture illustrating the geometrical representation of epsilon-delta convergence as it greatly helps grasping the how and why of epsilon-delta.

https://www.physicsforums.com/showthread.php?t=54175&highlight=limit

 

[JasonRox]

I'm sorry but I don't understand what you mean? Do you mean having a good knowledge of calculus and how it works before you learn the epsilon-delta definition?

I meant proofs regarding the epsilon-delta definition.

 

[Pseudo Statistic]

You haven't made it clear what is your current situation and what are your exact goals.

where?

Are you supposed to?



I haven't heard of a smooth road. You just got to take an analysis textbook and go over the material step by step. and that means not read the second chapter before you understand the first.

Well, my exact goal is to get myself up to understanding multivariable calculus.
At the moment I'm stuck somewhere inbetween integral & differential calculus and multi-var calculus, but as I said I don't really understand the stuff much with my lack of background... I mean, I know the techniques and such, but I can't prove things...
Can you recommend any analysis textbooks in particular? I'm looking for something not TOO costly.

I know what you mean, I'm a high school junior now, but I took AP Calc last year so I've been taking classes at the loacl university since, I'm taking complex analysis now and when we learned limits with complex numbers it was the first time I ever had to use the epsilon-delta definition of a limit, and because they don't teach it in the high school calculus classes it was the first time I'd ever have to use it, it was hard but after going and asking the teacher about it I think I understand it now. As for analysis I'm in somewhat the same situation as you I;m trying to find a fairly readble analysis textbook to teach myself a bit from, but all the one's I've seen seem to be too far above my current knowledge, but I guess the only option is to just pick a book and go over the material until it makes sense and if doesn't then you could always ask here or one of your math teachers...

True... after looking around the forum a bit I found "Zakon's Mathematical Analysis I".
It looks good... but the only problem is the set theory stuff is confusing the crap out of me. :\ It's hard to remember what symbol means what.
By the way, you don't know how lucky you are that you had the chance to take an AP Calculus class and take courses at a university.

Here's a thread where I explain thoroughly the definition of limit and work out a specific exemple in some details. I should have also included a picture illustrating the geometrical representation of epsilon-delta convergence as it greatly helps grasping the how and why of epsilon-delta.

https://www.physicsforums.com/showthr...ighlight=limit

Hey, thanks... I'm sure this'll help. :D

 

[CMoore]

For an excellent introduction to elementary analysis, I would suggest https://www.amazon.com/gp/product/0521288827/?tag=pfamazon01-20 by K. G. Binmore. The author provides numerous examples, his proofs are clear and answers to ALL problems are in the back of the book. It is thus a great choice for self-study. You can get it used on Amazon for about $15.

 

[Jeff Ford]

Zakon's not too bad. It does take awhile though, especially if it's your first time with some of the notation. I haven't read the Binmore text. It sounds like it could be a good supplement for self study while taking Calculus.