Going into 3rd yr, how much should I know about inf. series?

[Ascendant78]

Ok, I'm finishing my AA at a state college this semester and transferring to a university for fall. One of my friends who already transferred told me I need to learn about sequences and infinite series (though I haven't been able to follow up with him since). For some reason, our calc teacher that instructs calc II & III never covers it. I did learn a bit about MacLaurin and Taylor's formulas through OCW, but I really don't know much beyond the general idea of them. I haven't used them in problems or any of that, but I'm not sure how much I need to learn at this point? Does anyone have any decent sources for material I should know by the time you finish calc II (multivariable calc)? I want to learn it but I already have so much on my plate that I don't want to go overboard and have it cut into my other studies.

While we're at it too, how important is linear algebra? I know it is a preferred course for most grad schools and I saw some OCW for it, but I haven't had time to look at it yet. Will it be useful at this point or should I just wait until later when I can take it as an actual course and put my time into other studies?

 

[johnqwertyful]

This is such a weird question. Is it important? How would we know, DO you need to know it? I mean also, why would you ever elect to know less? Learn the stuff, it really isn't hard.

 

[Ascendant78]

This is such a weird question. Is it important? How would we know, DO you need to know it? I mean also, why would you ever elect to know less? Learn the stuff, it really isn't hard.

Why is it a weird question? He said he hit a brick wall in a course (I believe it was Thermal Physics but not 100%) because of not knowing that material. I don't want the same to happen to me because teachers expect me to know material that I'm not familiar with yet.

As far as "how would we know," are you not a physics major? If not, why are you even responding? I'm not sure what in my post made you decide it was a good idea to post such a standoffish response...

As far as "electing to know less," this makes me think even more so that you are not a physics major. I can't make more hours magically appear in a day. I am taking Physics II, ODE, and Calc III at my college and studying some additional Physics II (MIT OCW), computer programming, relativity and astrophysics, learning Latex, learning Ubuntu, having to work part-time, and having to make time for my 10 month old daughter in between. So yes, when you have as much to study as I am right now, you can't just "elect to know everything." I have to prioritize based on order of importance, which is why I asked for someone to help me know what is important regarding series and sequences going into my 3rd year.

 

[johnqwertyful]

I really wasn't trying to be standoffish. It's just that you didn't say what you were talking or what you were studying or anything. ARE sequences and series important for your classes? Look at the syllabuses. Google the topics, look into them a little bit. It shouldn't take more than an hour to get a good idea of what is needed.

To answer your question in a hopefully less standoffish manner, as someone in upper division physics, I need to use series constantly and they are important to me.

 

[johnqwertyful]

I guess the point I'm trying to make is that you should read up on the classes beforehand. Read the syllabus, google the topics. Spend an hour getting acquainted with the material before the class starts. It'll help you figure out what you need to know, and go from there.

 

[Ascendant78]

I really wasn't trying to be standoffish. It's just that you didn't say what you were talking or what you were studying or anything. ARE sequences and series important for your classes? Look at the syllabuses. Google the topics, look into them a little bit. It shouldn't take more than an hour to get a good idea of what is needed.

To answer your question in a hopefully less standoffish manner, as someone in upper division physics, I need to use series constantly and they are important to me.

Apologies for misinterpreting your initial post and thank you for the follow-up.

Anyway, I have gotten an idea of how the formulas work and a few ways to apply them. I just wanted to ask because I didn't want to waste time studying aspects of it I may never use as a physics major. For example, my physics professor said I won't ever use at least 30-50% of what I learn in math courses. So, he said the only things worthwhile to brush up on from previous courses is core concepts or things that I already know apply to physics. He said the rest you just brush back up on when you need them in physics courses down the road. So, I'm just doing my best to make sure I don't waste my time studying things that I won't ever need down the road is all.

 

[johnqwertyful]

Also to let you know, there are plenty of math, engineering, chemistry, etc. majors on here (and even a lot of people that are not currently in or have never been in higher education). You might be one of those people. I had no idea if you were a physics, math, engineering, or basket weaving major. No idea what classes you were taking.

I apologize if I came off standoffish.

 

[Ascendant78]

Also to let you know, there are plenty of math, engineering, chemistry, etc. majors on here (and even a lot of people that are not currently in or have never been in higher education). You might be one of those people. I had no idea if you were a physics, math, engineering, or basket weaving major. No idea what classes you were taking.

I apologize if I came off standoffish.

Yes, I do realize after looking back at my post I never did indicate I was a physics major. That was my fault, sorry about that.

 

[johnqwertyful]

Apologies for misinterpreting your initial post and thank you for the follow-up.

Anyway, I have gotten an idea of how the formulas work and a few ways to apply them. I just wanted to ask because I didn't want to waste time studying aspects of it I may never use as a physics major. For example, my physics professor said I won't ever use at least 30-50% of what I learn in math courses. So, he said the only things worthwhile to brush up on from previous courses is core concepts or things that I already know apply to physics. He said the rest you just brush back up on when you need them in physics courses down the road. So, I'm just doing my best to make sure I don't waste my time studying things that I won't ever need down the road is all.

The nice thing with series are Fourier and Taylor series. I wouldn't worry about Fourier just yet, but Taylor series are very helpful. Calculus is about making approximations, then taking limits to make them exact. Convergence. Taylor series let you approximate "nice" functions very well. Now mathematicians (such as myself, I confess. Although I am studying a lot of physics) like to take limits, get analytic solutions, worry about what "nice" means. But as a physicist, you should just know that you can turn "ugly" functions into polynomials approximately.

For instance, for small x, (1-x)^n "=" 1-nx

 

[AlephZero]

The idea that you can claim to have done Calc II and III without even knowing about Taylor series seems unbelievable to me. But hey, there are plenty of unbelievable things in the US education system.

So, I'm just doing my best to make sure I don't waste my time studying things that I won't ever need down the road is all.

I think you have a basic decision to make here. Are you trying to do the bare minimum to get some sort of degree certificate, or are you trying to learn something? Those are two different objectives - but without being judgmental, it's your choice and your life, not mine.

 

[Ascendant78]

The idea that you can claim to have done Calc II and III without even knowing about Taylor series seems unbelievable to me. But hey, there are plenty of unbelievable things in the US education system.



I think you have a basic decision to make here. Are you trying to do the bare minimum to get some sort of degree certificate, or are you trying to learn something? Those are two different objectives - but without being judgmental, it's your choice and your life, not mine.

Don't ask me why we never dealt with Taylor series. I haven't completed Calc III yet, so maybe I'll run into it later on, but I didn't remember seeing it in the syllabus and it was never so much as mentioned in Calc II.

As far as the bare minimum, the exact opposite. I spend countless hours studying physics. I use OCW in conjunction with my courses. I also use OCW for courses that aren't required but will compliment my major. I am teaching myself Ubuntu and computer programming because I know both will be useful at some point (maybe not so much Ubuntu, but I'm at least learning the basics anyway). I try to read published articles in the field when I have the spare time. So, my objective is to optimize my studies. I already spend the majority of my days studying. I don't have the time to spend studying additional things that I will never use/need.

Besides, what point would there be to learning something I will never use? If I could learn C++, which will increase my value as a potential employee, but instead I spend that time learning some math that doesn't get used in physics, I just wasted my time that could've been spent more productively.

Ideally, I would love to attend MIT for grad school. As such, I am always studying at this point, save for 2-3hrs a day I spend with my family. Since my studies take away from them, yes, I want to optimize my studies. So no, I'm not lazy and looking to do the bare minimum. I am an over-achiever to the extreme, both in and out of my classes. With so much to learn though, I have a hard time prioritizing sometimes.

 

[Ascendant78]

Just to add... I have spent a bit of time looking at sequences and series. We did cover some of the concepts in that section, like convergence/divergence and estimating values (though we used the trapezoid and Simpson rules). However, the majority of the section we never touched on. Like I had already said, we never once touched on anything that looked like MacLaurin or Taylor series. Anyway, looking at the content, I at least do have an idea of some of it. We just used different methods and skipped over a lot apparently.

 

[retro10x]

I learned infinite series in depth as soon as we finished integrals in first year calculus. In multivariable and vector calculus we were assumed to be familiar with them and used them to discuss many other features like convergence and especially Taylor Series (one of the most, if not the most, useful mathematical tools a physicist has). Infinite series are used in upper year physics course, not incredibly often (from what I have seen) but are definitely a pre-requisite. Linear Algebra is even more fundamental than series and should be learned as soon as possible, the basics anyways. Courses as early as 2nd year assumed we were quite familiar with eigenvalues, matrices, determinants etc.

 

[romsofia]

Fourier series is important to know, but you will probably be taught that in your QM class. You should have a firm grasp on Taylor series if you want to be successful though, because in physics you apply a concept called perturbation theory which will be easier for you to understand if you know your series very well.