First semester physics: overwhelmed

[Mépris]

Disclaimer: I wasted a lot of time reading the forums here and elsewhere, instead of actually studying. Mathwonk, in his wisdom, once told me to "stop dancing around the fire". Now, I'm pressed for time and I need to do everything quickly, and will have to use the holidays to really study properly.

I am currently taking a mechanics as well a math methods course. In math methods, we started with some vectors and also the coordinate systems, and later on, calculus (that's where we are now). Things move quickly, and I soon realized how far more useful the tutorials are to the actual lectures.

We are using mathematics that we haven't learned yet, or haven't had the time to properly learn, in our mechanics course. As far as single variable calculus is concerned, it's fine, but last week, the teacher used something that looked like vector calculus (I could be wrong...) when teaching circular motion. He also mentioned the Taylor and Maclaurin series which we haven't covered yet.

At the same time, in our math tutorial, the tutor is teaching us about the Levi Civita, and suggested we use Arfken and Weber's book to learn vector analysis. Well, spending too much time here when I didn't have school taught me a few things about physics education...one of those is that this book is a graduate level text. Our math methods is starting from the ground up (but going quickly - it's based on the book by Bence, Hobson, and Riley), while at the same time, we're told to use a book that assumes knowledge of material we won't finish doing until the 3rd semester!

I'm also having a hard time getting an intuition of what spherical and cylindrical coordinates are. I had to complete my homework by just using formulae I found online, and I have no idea what I'm doing. I don't have an "intuition" for it, same thing with using vectors. The calculus used so far in mechanics is fine, as I've done calc before, but I still need to review it.

I went into this program knowing it would be hard work. I am not complaining about that. I just don't know where to go with this. Everybody else is as confused as I am. There are people in the 3rd semester who are taking mechanics I and math methods I (some even the lab), on top of all the other courses. For whatever reason, the requirements for courses are quite "flexible", so people can still take more courses if they want.

Anyway, it's scary to see so many persons having trouble...and after talking with them, it's evident that they are NOT stupid. There are clear issues with the organisation of the program, but I can't do anything about that now. I just need to figure out how to keep my head up, and hopefully get good grades.

In terms of schedule, I have statics h/w on Mondays (doesn't count, but need to do them to understand), mechanics h/w on Tuesdays (possibility of bonus marks), lab report and reading for Thursdays, and on Fridays, I have my math homework due. For math, 20% of my grade is from the weekly sheets. So, what ends up happening, is that I do all of my work one or two days before they're due, and by the time the weekend comes, I'm too tired to even want to do anything more. So, I haven't really been able to study more to try to understand what's going on.

So, I guess what I'm asking is what books I can use for a quick review of calculus, and how I can learn vectors and spherical/circular/etc coordinate systems. I just need an "intuition" for it, especially the coordinate systems. And how I could manage all of that work without going nuts. So far, it's OK, but it's taxing, and I don't think it will be a good long term plan. I need to change!

I would greatly appreciate your thoughts on this. Thank you.

 

[UltrafastPED]

Arfken & Weber is actually an undergraduate text - junior/senior level mathematical physics course, though it also has extra topics which are useful in grad school. It is best used as a reference book, not a textbook.

It sounds like you have skipped some coursework somewhere along the line ... in any case, the only way to learn is to do the work. Reading tid-bits here and there is not learning ... it is sampling. You may like the samples, but you still have to put in the effort to learn it.

Usually calculus is a two semester sequence for the basics, and vector calculus is an additional semester.

But most people have already learned something about vectors earlier than calculus - they are geometric objects. Coordinates are how you map vectors to a particular system of measurement; everybody learns the Cartesian/rectangular system first. This is a system of perpendicular planes. The other systems, curvilinear coordinates, are based on circles, spheres, ellipses, etc.

 

[R136a1]

For calculus, try Kleppner: https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20
For an easy book on math methods should as vectors: https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

I suggest to make a thread in the main math forum about the spherical and cylindrical coordinate thing. It's not too complicated to explain. Be sure to explain what you don't get and what your background is in trigonometry and coordinate geometry. I will be happy to help you understand this.

 

[Shivam3013]

I can't emphasize enough how much I think high school is badly taught. It is likely that you weren't given a strong enough ground in algebra, geometry and basic physics. The only thing to do now is to relearn some of that material. The good thing is that it will mostly be a review and you can go through it quickly. This may seem naive, but it's best to go over books like Lang's "Basic mathematics", "Algebra" by Gelfand, Kiselev's Geometry, Hartshorne's Geometry: Euclid and beyond, and Gelfand's "Functions and graphs". Since you have covered some of that material, you should be able to go through it quickly. Now, in calculus, since it's an important topic, don't rush through it. Get a good book like Lang's Calculus and then go through a more advanced book such as spivak or apostle. Once again, some of it may be review. After that, you should be well suited to be successful in your classes. As I said, a background in these seemingly trivial subjects is important. For classical mechanics, consider a book like K&K.

 

[Mépris]

I saw a copy of Basic Mathematics in the library. There's probably his calculus text as well. I mucked about too much in the past. I bought Apostol and it's back home. I won't have time to work through this now, but I'll try both Spivak and Apostol again over the next holidays.

I just looked at the table of contents of Basic Maths, and I've got just about everything in parts 1 to 3 down. The subjects in part 4 will be covered again later anyway. I'm not saying I've mastered the material in the book. I'm sure I can still learn quite a bit from it. Only that I wonder if it is not something I can come back to when I have more time on my hands?

I really don't think I will be able to calmly sit down and work through proofy pre-calculus and calculus texts while knowing that I can't actually do my problem sheets properly. Once the weekly sheets are an after thought, leisurely working my way through those books would not be a problem at all. Right now, if I tried that, I would definitely feel like I'm straying, if that makes sense.

 

[WannabeNewton]

Have you tried looking at Boas' mathematical methods text? It would be perfect for your needs! Good luck with the rest of your semester. I know a handful of kids in the physics department here who are taking a mathematical methods class and are struggling with getting a hang of certain things but it's all a matter of practice and solving problems; if you do enough problems involving the Levi-Civita symbol, for example, then manipulating the Levi-Civita symbol will become second nature in index based calculations.

 

[R136a1]

I saw a copy of Basic Mathematics in the library. There's probably his calculus text as well. I mucked about too much in the past. I bought Apostol and it's back home. I won't have time to work through this now, but I'll try both Spivak and Apostol again over the next holidays.

I just looked at the table of contents of Basic Maths, and I've got just about everything in parts 1 to 3 down. The subjects in part 4 will be covered again later anyway. I'm not saying I've mastered the material in the book. I'm sure I can still learn quite a bit from it. Only that I wonder if it is not something I can come back to when I have more time on my hands?

I really don't think I will be able to calmly sit down and work through proofy pre-calculus and calculus texts while knowing that I can't actually do my problem sheets properly. Once the weekly sheets are an after thought, leisurely working my way through those books would not be a problem at all. Right now, if I tried that, I would definitely feel like I'm straying, if that makes sense.

I wil advise strongly against Spivak, Apostols or even Langs calculus books. It's not what you need right now. Of course, they are wonderful books to look at calculus from a theoretical and mathematical point of view. But they eat up time. You don't have that time at this stage. Right now, you need to learn how to apply the theory, you need basic intuition and you need to be able to solve basic exercises. In that case, books like Kleppners calculus or Boas are perfect at this stage. They are very much nonrigorous, but they teach you very basically how to apply the theory to basic physics problems. This is exactly what you need at this stage.

Once you have a very basic grasp on the theory (enough to be able to understand your physics classes), only then can you go a bit more rigorous and do something like Lang, Spivak or Apostol.

 

[Mépris]

Thanks fellas.

Apparently Quick Calculus by Kleppner has lots of errors. I already know calculus, but my high school course didn't cover limits, differentiating from first principles, and stuff like L'Hopital's Rule. We did learn how to solve first order DEs by separation of variables though. I tried checking out Shankar's book, but its calculus portions might be a little too quick for me.

Any other alternatives? I heard only good things about Calculus Made Easy, but the edition available for free online is longer.

I will definitely go through a book like Spivak at some point, or maybe jump straight into Analysis, so I don't think it matters too much if I skimp on the details now.

As R136a1 said:

They are very much nonrigorous, but they teach you very basically how to apply the theory to basic physics problems. This is exactly what you need at this stage.

Once you have a very basic grasp on the theory (enough to be able to understand your physics classes), only then can you go a bit more rigorous and do something like Lang, Spivak or Apostol.

 

[R136a1]

Thanks fellas.

Apparently Quick Calculus by Kleppner has lots of errors.^

Apparently, some amazon review claims that, but I didn't see more errors than in a typical book. In fact, having typos is not a bad thing since it keeps you alert.

I already know calculus, but my high school course didn't cover limits, differentiating from first principles, and stuff like L'Hopital's Rule. We did learn how to solve first order DEs by separation of variables though. I tried checking out Shankar's book, but its calculus portions might be a little too quick for me.

Any other alternatives? I heard only good things about Calculus Made Easy, but the edition available for free online is longer.

Calculus made easy is going to be totally useless to you. You already know everything they say in that book, if you already did a calculus course.

 

[Mépris]

Apparently, some amazon review claims that, but I didn't see more errors than in a typical book. In fact, having typos is not a bad thing since it keeps you alert.

Calculus made easy is going to be totally useless to you. You already know everything they say in that book, if you already did a calculus course.

Kleppner's book covers more? I quickly went through the contents again, and it looks oddly similar.

Are there any other books you can suggest? I'll get the one that ships the fastest. (not in the US)

 

[PhizKid]

Kleppner's Quick Calc is a review book (hence "quick"), and doesn't go very in-depth. Here is a sample of what the entire book is like:

[Click for larger image]
http://www.picturescream.com/thumbs/20131103141639.jpg

It goes over a definition in a couple of lines, shows some sample problems, and directs you backwards or forwards in the pages accordingly, depending on if you understand a concept or not.

 

[WannabeNewton]

Again, check out Boas.

 

[Mépris]

Again, check out Boas.

Ok, I'll try to jump right into it, and fill in the gaps as needed.

If I have more trouble, then I guess I'll go for the Quick Calculus book. Thanks for the preview PhizKid. Presentation looks clear and concise!

 

[R136a1]

Kleppner's Quick Calc is a review book (hence "quick"), and doesn't go very in-depth. Here is a sample of what the entire book is like:

[Click for larger image]
http://www.picturescream.com/thumbs/20131103141639.jpg

It goes over a definition in a couple of lines, shows some sample problems, and directs you backwards or forwards in the pages accordingly, depending on if you understand a concept or not.

Yes, I agree. And I think that is exactly what he needs right now. He needs to be able to apply calculus quickly. He has no need at the moment for deep theoretical books.

 

[jesse73]

Yes, I agree. And I think that is exactly what he needs right now. He needs to be able to apply calculus quickly. He has no need at the moment for deep theoretical books.

Seconded. If he can't through one of those "quick" books to catch up on math for physics then he has low probability of getting through apostol and even lower probability of catching up on math for his physics course.

Try to go through the quick book. If that is too easy move to a harder book although i wouldn't recommend going through Apostol or Spivak if you are doing physics. Go through something like

An Introduction to Probability Theory and Its Applications by William Feller and
Principles of Mathematical Analysis by Rudin.

Apostol is an inbetweener which means if you don't want rigor don't bother but if you do you might as well do the "baby rudin" book and the probability book. Probability is useful if you want to get ready for QM along with a linear algebra book.

All of those are asides since you are likely in the middle of a semester and don't have the time to assume you are just going to go over any standard textbook over a weekend or two and much less a textbook like Apostol or Rudin.

Really look into a quick book like

https://www.amazon.com/dp/0393969975/?tag=pfamazon01-20

Calculus is funny when you query for advice on textbooks because people will give you recommendations for advanced textbook irrespective of what your current level or constraints are. I imagine it would be analogous to a premed student asking for a secondary text for his intro physics II class and getting recommendations to look at Jackson and if that is too opaque to look at griffiths.

 

[Mépris]

I'm in Europe, so only 3 weeks into the semester. I've heard of Baby Rudin. I tried Spivak before, and didn't really like it, and I preferred Apostol. Also, the latter seems to get to the calculus part faster. But as you've all said, for my intents and purposes, a pure math book is not suitable.

I'll keep those books in mind for later.

In other news, I have better intuition of vectors now, so spherical and cylindrical coordinates are my only problem. Hopefully I solve this this week itself.

 

[Physics_UG]

Thanks fellas.

Apparently Quick Calculus by Kleppner has lots of errors. I already know calculus, but my high school course didn't cover limits, differentiating from first principles, and stuff like L'Hopital's Rule. We did learn how to solve first order DEs by separation of variables though. I tried checking out Shankar's book, but its calculus portions might be a little too quick for me.

Any other alternatives? I heard only good things about Calculus Made Easy, but the edition available for free online is longer.

I will definitely go through a book like Spivak at some point, or maybe jump straight into Analysis, so I don't think it matters too much if I skimp on the details now.

As R136a1 said:

Your HS calc class didn't cover limits? Calculus is pretty much the study of limits. Differentiation and integration and infinite series are based on limits.

I would agree that Boas is a good place to start.

 

[Mépris]

Update:

I bough Quick Calculus and went through most of the book. I also borrowed Boas from the library.

I ended up surviving first semester math. I really underestimated the value of good habits, like studying daily. I studied very haphazardly until the end of the semester, and it shows. At any rate, I ended up doing fine in my exam (equivalent of an A-, according to wikipedia). I dropped marks on series, line integrals, and a vector calc proof where using tensor analysis would have been a life saver. Judging by my grade, I'm assuming those are the only places where I lost marks. I have not yet decided if I will retake it or not. It depends on how quickly I learn the topics I dropped marks on. Retaking has no effect on my "GPA"; only the best grade is counted. And when I asked older students, they said the retakes wouldn't appear on my transcript.

I guess my lab was one of my most annoying courses. It's around 3 hours long, and I have a lab report (and preparing for the next lab) due every week. It doesn't help when your partner works very differently to you. He's less diligent than I am, to the point where he'd always start his half of the work the day before it was due. I will have a similar lab course next semester, in addition to an oral exam about each lab. I need to find a very methodical approach to this course. I.e, specific blocks of time dedicated to the same tasks, such as "prepare for lab", "start writing and put up diagrams" and "describe how data is processed", etc.

I always had that lab hanging over my head and felt such relief when I would finish the report, and again, when I finished the experiment. Then rinse, repeat.

 

[Mépris]

I'd like to thank everyone in this forum (especially this subforum) who's helped me out over the years. There's been many of you, and I genuinely appreciate the time you took to write and share your experiences.

It's sad, but it took me years to finally admit it to myself, but I was just scared. Scared of failure. Scared of not being good enough.

I was too used to have everything come easy to me, and when I hit a wall, I didn't know what to do. It paralysed me. I felt like I couldn't live up to my potential, and I got more depressed. More missed deadlines, more failed classes. I gave up too easily, too quickly. Truth is, I had lost confidence in my abilities long before I even started university.

It would have been nice if I had listened earlier. I would have been wrapping up my bachelor's thesis right about now.

But it is what it is. It took me a long time to find the wisdom to put the advice I had been given to practice. I just wasn't ready to come to terms with reality, and this is what caused my troubles.

This is not an easy field. Like everything, it takes work. I know that now.

I'm now ready to accept the consequences of what I did and did not do. I feel less pressured, and more zen. I now know that I can do this, and finish my degree. I am now committed to this, and it's time to work hard. Harder than I have before. And if I fail, so be it. It will be with the knowledge that I tried.

Again, thank you to everyone here who has helped. It is much appreciated.