Optimizing Self Study: Overcoming Learning Difficulties in Physics and Math

[CosmicKitten]

I have been out of school for over a year now. The reason for this is that I was bored with the classes I was taking at the community college (calc 2, physics 2 and physics 3) to the point that I could not concentrate on earning A's, among other issues, not quite sure why given that I had gotten A's the previous year without even paying attention or studying or doing the homework. In the past year I have been studying on my own, which I find works far better than listening to a lecture, which for me makes me too tired to concentrate on the book and stores memories of the material through episodic memory, which is a most inefficient way to learn, and, I believe, results in learning difficulties analogous to memory based trauma.

Anyway, I found that I understand things better if treated at a higher level. The particular classes I was taking were mainly about memorizing things that would be far more efficient to teach while studying harder subjects (come to think of it I don't know why calc 1 and 3 aren't taught concurrently since learning how to do it in three dimensions isn't really teaching anything new, unless I am much mistaken about the content of the curriculum or if it is just unusual that I can think in that way) and I found that, for example, reading a third year level book on electromagnetics made a lot more sense than the lower division treatment. Would anyone suggest, say, an upper division to graduate level book that treats the topics covered in physics 3 (waves, optics, modern physics) at a high enough level to actually understand well enough to remember without rote?

A while ago I bought a book titled "Mathematics of Classical and Quantum Physics" (Byron & Fuller) and only recently have I felt confident enough with my math skills to open it. I find so far that I understand everything and can remember it well, I've been reading it for about a week and I'm on the third chapter. Is that good progress? Bear in mind I have to read it on days that I am not going anywhere or doing anyhing so that I can fully concentrate, and although I have absorbed everything from each chapter before moving on to the next one I have not worked out the problems yet, I shall after I have read all the chapters but I prefer to let the material ferment in my head for a while before I attempt any problems.

What other books should I be reading? I want to study physics and chemistry and math and I am trying to save up money to take the GREs and or take graduate level classes at UCSD via extension (I am not allowed to apply for admission until I get 60 credits, that's what I get for being talked into starting at a comm. college although it seems to me the four year setup would work far better for me) and in the fall maybe go back to the comm. college and take classes in everything EXCEPT the math and science classes - I don't trust myself to get good grades in classes that require you to memorize the dumbed down way and test you on the lectures that are poisonous for me to listen to.
As for replies, if its not a problem, I would prefer responses to be PM because the moderators here like to move my threads to different forums and then give me infractions when my replies go a little off topic (which is rubbish because any good physics discussion is going to cross disciplines) I would like advice and suggested readings and perhaps what kinds of things I can do to be impressive enough to transfer to a private school or get a full scholarship to an out of state school. I have considered switching majors on paper (because my credentials as an artist and a writer are far more impressive than my credentials so far to be a physicist) and then transferring and switching back as soon as acceptance is locked (I see no point in even minoring in a subject that I have done a good enough job of mastering on my own, and that does not strictly require a degree to work in anyway) and working on the professors to let me take higher level classes.

Some other things to know:
-I have an incredibly long memory. I don't forget. Ever. Not even math that I never use.
-I can only concentrate on one thing at a time. Hence, if I have to go to class on a certain day, I can choose to either forget that class or forget about studying for the day. All attempts I have made to multitask in the least bit have failed.
-I have a hard time controlling what to focus on. If my mind decides it wants to be stuck on something else, I can forget about doing what needs to be done for the day.
-I am a 23 year old female who was not allowed to go to college until 2 years after high school, and who was not allowed to study college level physics and math until I was freed from my controlling foster/adoptive parent (sorry I really hate making these excuses but I am not lazy just so you know)
-I take 5 mg of Adderall a day. That is a small dose but if I were to take any higher I would probably get a panic attack. It helps my mood and my determination and confidence more than my attention; as a matter of fact, it may be making it worse, by making my thoughts more hyperactive; people see how fast I talk and how hyper I am and they think I am anxious or manic but I have always been like that, and my experiences with calm down pills have been awfully demotivating...

 

[Jorriss]

You don't feel confident in getting A's in classes you perceive to be about memorization but also claim to basically have a photographic memory?

 

[CosmicKitten]

You don't feel confident in getting A's in classes you perceive to be about memorization but also claim to basically have a photographic memory?

A very selective near-photographic memory, and I am almost completely out of control as to what is selected.

 

[jim hardy]

I'd say start working the problems. That'll force you to 'take charge' and direct your conscious where you want it. "Where the conscious goes the subconscious must follow."

When you find something that interests you you'll focus on that.
Best programmer i ever knew was a physics major who worked in missile tracking systems at Cape Canaveral. He branched out into industrial process control...

Pick up a book on Modern Control Systems. It's pure math applied to real things, and there's need for that talent in this day and age. At worst you'll be bored for an hour.
We used Dorf's first edition when i went through school. It's up to 12 now.
https://www.amazon.com/dp/0136024580/?tag=pfamazon01-20

 

[CosmicKitten]

I'd say start working the problems. That'll force you to 'take charge' and direct your conscious where you want it. "Where the conscious goes the subconscious must follow."

When you find something that interests you you'll focus on that.
Best programmer i ever knew was a physics major who worked in missile tracking systems at Cape Canaveral. He branched out into industrial process control...

Pick up a book on Modern Control Systems. It's pure math applied to real things, and there's need for that talent in this day and age. At worst you'll be bored for an hour.
We used Dorf's first edition when i went through school. It's up to 12 now.
https://www.amazon.com/dp/0136024580/?tag=pfamazon01-20

Yes I do need to learn some programming, I need a live person to help me with that though. I took a free programming course on edx from Harvard and I got bored right away, because of the childish computer program called 'Scratch' they decided to use. I just signed up for the MIT edx course but the python enthought wouldn't download properly.

I find that true, when I am working on problems my focus is better. It doesn't stick though unless the knowledge of how to solve them is firmly in my long term memory, otherwise it will all go into disposable short term memory. My short term memory is terrible. My working memory works really well drawing on long term memories but not short term memories. For me long term memory equates understanding it. I basically run through the problems in my head as I read through the book, as they show you how to do them, check to make sure the math is right, pick up the new procedures being introduced, and later try to run the sequences in my head without looking, and solve some problems in my head before solving on paper. I hate having to use a pencil and paper and a calculator; it breaks my concentration to get the calculator out and the pencil and paper make me want to doodle. I actually got very good at doing math in my head because of this!

 

[fluidistic]

Hi CosmicKitten,
From reading this thread I get the (maybe wrong) feeling that you believe that math and physics courses are meant to be memorized or read+memorized and as soon as they enter in your long term memory then you have learned the subject.
To me, "learning a course" is being able to solve any problem thrown at you. Sometimes I don't know the order of the chapters and I might have jumped 10 pages of a chapter but as long as I can solve the problems in the end of the chapters I'm confident I know what's going on.
You talked about a 3rd year book on EM. I don't really "read" these books. Many times I have to get a pencil and a paper under my hands to derive the formula that are presented. This is the only way one knows where and how they come from. I personally don't feel like I'm reading a book, I feel like I'm just doing an exercise or solving problems.
For example there: http://www.phy.duke.edu/~rgb/Class/phy319/phy319/node59.html, boundary conditions on a conductor. Do you know why $(\vec D - \vec D _c ) \cdot \hat n = \sigma$? (eq.10.1 or you can even take 10.2).
I know where they come from and how to derive them. If I only read them and read that they come from "inserting eq. xx into eq. yx" I wouldn't consider I really know the material given in the course. For higher than freshman level courses, reading a physics book like a novel is not going to work. In fact I would even say the same for freshman book like Halliday and Resnick Fundamentals of Physics. Solving the problems is to me the utterly most important part of the course and this is what determine whether I know the course. I'm sure I'm not alone thinking in a similar way.

I might have got a wrong impression of you though and you might study efficiently.
Also I would like to state that the freshman level EM course is not really a watered down version of the higher level EM course when it comes to the physics involved. Mathematically of course they are totally different but the physics, i.e. calculating the potential, electric and magnetic fields is essentially the same. At least for the electro-magnetostatics part.

All in all, I personally believe that being able to pass calculus 1 to 3 (i.e. solve the problem thrown at you) is very important. If you can't do that, I find it hard to believe you can understand what's going on in a upper level EM book although you might memorize what you've read from A to Z.

One more thing, calc. 3 should not be taught at the same time as calc.1 or 2. since it involves vectors, Jacobians (hence determinants which belongs to linear algebra), line integrals and other linear algebra related maths. So unless you're taking a linear algebra as well as calc.1 and 2, calculus 3 would not make much sense. Bear in mind that this is my opinion based on my own experience.

I wish you the best of luck with your studies. Don't be afraid of pencils, try hard not to doodle them. If you know how to solve the exercise because you've thought on the problem already then you should not doodle at all.

 

[jim hardy]

I hate having to use a pencil and paper and a calculator; it breaks my concentration to get the calculator out and the pencil and paper make me want to doodle. I actually got very good at doing math in my head because of this!

i understand.

Creative people ofeten have trouble concentrating. I think it's because they're so bright and ordinary school comes so easy they never have to learn to concentrate and focus. They get good grades without ever learning to exert.

Maybe one should think of that 'gift' of mental agility as somewhat of an impediment ,
in that it keeps us from developing to our potential,
and recall the story of Demosthenes:
http://itotd.com/articles/319/demosthenes-stones/

The story is this. Demosthenes lived in Athens from 384 B.C. to 322 B.C. As a young man, he suffered from a speech impediment—which may have been a stutter, an inability to pronounce the “r” sound, or both. He designed a series of exercises for himself to improve his speech. According to legend, he practiced speaking with stones in his mouth, which forced him to work very hard to get the sounds out. When his diction became clearer, he got rid of the stones and found he was able to enunciate much more effectively than before. He also practiced reciting speeches while running and speaking over the roar of ocean waves to improve his projection. These strategies must have worked, because Demosthenes achieved fame as the greatest orator in ancient Greece. He is best known for his passionate speeches urging the Greek citizens to defend themselves against invading Macedonian king Philip II.
Naturally this story is repeated often with a moral of “work hard, be persistent, and you will succeed.”

By your own statement you have avoided the exertion of working problems.

Yes I do need to learn some programming, I need a live person to help me with that though. I took a free programming course on edx from Harvard and I got bored right away,...

ANECDOTE - i hope it doesn't bore you...

Here's how i got started programming. It was before the IBM PC .
We had a sociopath in management who took delight in torturing people.
Monthly expense accounts were his favorite tool. He'd find a tiny yet obvious addition error, strike a diagonal line across the whole page with a magic marker and return it. That meant you had to re-transcribe the entire thing, and re-check every addition. I'm mildly asperger's and often swap digits or mis-key the calculator... so it was a problem for me.
It took a couple hours to rewrite and double check a form. Pure mean spiritedness on his part, he even looked like Mr Potter from "It's A Wonderful Life"(Lionel Barrymore)..

I shared your disdain for rote transcription and menial arithmetic.
And i had a TI-99 home computer. And a printer.
So i brought the computer to my office and wrote a Basic program which prompted me for expense-able items day by day. It stored them on a 5 inch floppy disk.
On demand, it printed them in the exact same format as on the company expense account. And it did all the arithmetic. So i knew there were no addition errors.
Now all i had to do was transcribe to the company form. Also i knew that any mistake was an error of omission not an error of addition... i'd simply missed an entry.

I added one more feature to the program - with one keystroke i could adjust every entry for which no receipt was required up or down by 1%. You see, i knew darn well he knew where any mistake was. By changing everything i made HIM repeat HIS tedious checking of my arithmetic.
AND i could have the new form back to him in ten minutes. Ha Ha Ha Ha Ha Ha! i deprived him of his pleasure. Well it worked. After three cycles he started sending my forms back with a sticky-note indicating the problem, instead of a magic-marker swipe.

And I learned how to handle input, strings, arrays, formatted print, Ascii special characters and disk I/O in Basic.
END ANECDOTE ----------------

Moral of THAT story - We need motivation. We learn by doing.

So quit making excuses and get to work making something that you can look at a year from now and say "I did that well! ".
Even if it's only this with every supplementary problem worked:
https://www.amazon.com/dp/0071635122/?tag=pfamazon01-20 !

 

[CosmicKitten]

Hi CosmicKitten,
From reading this thread I get the (maybe wrong) feeling that you believe that math and physics courses are meant to be memorized or read+memorized and as soon as they enter in your long term memory then you have learned the subject.
To me, "learning a course" is being able to solve any problem thrown at you. Sometimes I don't know the order of the chapters and I might have jumped 10 pages of a chapter but as long as I can solve the problems in the end of the chapters I'm confident I know what's going on.
You talked about a 3rd year book on EM. I don't really "read" these books. Many times I have to get a pencil and a paper under my hands to derive the formula that are presented. This is the only way one knows where and how they come from. I personally don't feel like I'm reading a book, I feel like I'm just doing an exercise or solving problems.
For example there: http://www.phy.duke.edu/~rgb/Class/phy319/phy319/node59.html, boundary conditions on a conductor. Do you know why $(\vec D - \vec D _c ) \cdot \hat n = \sigma$? (eq.10.1 or you can even take 10.2).
I know where they come from and how to derive them. If I only read them and read that they come from "inserting eq. xx into eq. yx" I wouldn't consider I really know the material given in the course. For higher than freshman level courses, reading a physics book like a novel is not going to work. In fact I would even say the same for freshman book like Halliday and Resnick Fundamentals of Physics. Solving the problems is to me the utterly most important part of the course and this is what determine whether I know the course. I'm sure I'm not alone thinking in a similar way.

I might have got a wrong impression of you though and you might study efficiently.
Also I would like to state that the freshman level EM course is not really a watered down version of the higher level EM course when it comes to the physics involved. Mathematically of course they are totally different but the physics, i.e. calculating the potential, electric and magnetic fields is essentially the same. At least for the electro-magnetostatics part.

All in all, I personally believe that being able to pass calculus 1 to 3 (i.e. solve the problem thrown at you) is very important. If you can't do that, I find it hard to believe you can understand what's going on in a upper level EM book although you might memorize what you've read from A to Z.

One more thing, calc. 3 should not be taught at the same time as calc.1 or 2. since it involves vectors, Jacobians (hence determinants which belongs to linear algebra), line integrals and other linear algebra related maths. So unless you're taking a linear algebra as well as calc.1 and 2, calculus 3 would not make much sense. Bear in mind that this is my opinion based on my own experience.

I wish you the best of luck with your studies. Don't be afraid of pencils, try hard not to doodle them. If you know how to solve the exercise because you've thought on the problem already then you should not doodle at all.

Oh, yes it does in fact appear you are quite mistaken. When I said that long term memorization equates understanding... What I meant was, I don't know if understanding it puts it in my long term memory, or if having it in my long term memory causes me to somehow understand it better, but I know that for me the two go hand in hand. I mean, if its been in my head for a whole, I can more easily apply it. You might say my memory works better the longer ago, rather opposite to that of most peoples; the knowledge does not rot but rather ferments. That is my impression anyway.

I tend to understand concepts very quick, too quick as a matter of fact so I become bored and although I have a basic understanding of the material I don't remember all the finer details of the equations as well. This is ironic because I tend to remember equations and constants better than most people.

Anyway, in my calc 2 class anyway, what they taught was techniques for finding out whether a series converges or diverges, and also L'Hopitals rule, and basically how to solve improper integrals. I could not find a list anywhere of improper integrals tables, you know for the trigonometric functions, the tables on Wikipedia were a load of redundant formulae and none of the ones I needed, I sought tutoring and although I understood everything well enough to interrupt the teacher before they were done explaining, I could not effectively remember any of it. Why? Because spoken word and any activity involving social interaction for me just doesn't encode in an easily retrievable mode. I should have asked for a piece of paper with all the formulas to memorize -- I can figure out my own explanations better than the teacher can explain them, that way it won't be by rote - or gotten a book that explains everything well enough, but I couldn't find one and was probably too stressed to search effectively. At the same time I was studying differential equations on my own, and I apparently understood them well because I got to thinking about the n-body problem and discovered that it could be approximated in a way using power series - my only problem area in calc 1 - and that was before I read later in the book and found out this was called the Euler method.

Also, I find compulsory homework to be problematic. It puts you in the wrong state of mind - rush it and get credit instead of learn it - and takes away time from working on your own problem areas.

Linear algebra is easy - I am a very visual thinker, so matrices make sense to me. Learning about the angular momentum tensor helped me to understand them better.

And the third year electromagnetics book cleared up curl and divergence and gradient for me. These were not taught in the time I was in that physics 2 class, I think they should be taught very first thing. Apparently they can't be taught at that level because they require knowledge of calc 3? You know what, they should just load up the students on math and hold off physics classes until they can teach them in more mathematical depth. Also, the textbooks and class notes (purposely perhaps?) left out a lot and I guess you had to pick up that knowledge from the teacher? Which is too bad because as I mentioned earlier I have a deficit in oral comprehension. So I try to tune it out to avoid distracting episodic memories but then I see stuff on the test I KNOW I didnt see in the class notes. Either that or I couldn't concentrate (I was not medicated at the time not that that's any excuse) or I suddenly have test anxiety and I have NEVER had test anxiety before. I in fact scored 34 on yhe ACT, 35 in math, and in my previous physics classes I got the highest or second highest score on most of the tests, suffering only labwise (I don't work well with others, provided I can even get others to be my lab partners)

As I read this book, I find myself rather impatient with some sections, and at times jumping to understanding things before they are even revealed.

 

[ZapperZ]

A while ago I bought a book titled "Mathematics of Classical and Quantum Physics" (Byron & Fuller) and only recently have I felt confident enough with my math skills to open it. I find so far that I understand everything and can remember it well, I've been reading it for about a week and I'm on the third chapter. Is that good progress?

I find this hard to believe.

One just doesn't "read" such a text as if it were a novel. I lost count how many times I hear students telling me that they understood the material when they read the text, but found it difficult to solve the homework assignments. To paraphrase Mary Boas's message from her book, you only get a superficial understanding of the material by simply reading books or hearing lectures. The only way to have a deeper understanding of the material is to solve various problems, and to practice this often. From what I've read, you seem to have an aversion to doing that.

Secondly, you are not a very good judge on whether you have mastered or understood the material. You may claim that you have understood "everything", but how do you prove such a thing? I've read books on performing surgery and I believe I've understood everything. Piece of cake! Shall I take out your appendix?

Zz.

 

[CosmicKitten]

i understand.

Creative people ofeten have trouble concentrating. I think it's because they're so bright and ordinary school comes so easy they never have to learn to concentrate and focus. They get good grades without ever learning to exert.

Maybe one should think of that 'gift' of mental agility as somewhat of an impediment ,
in that it keeps us from developing to our potential,
and recall the story of Demosthenes:
http://itotd.com/articles/319/demosthenes-stones/By your own statement you have avoided the exertion of working problems.ANECDOTE - i hope it doesn't bore you...

Here's how i got started programming. It was before the IBM PC .
We had a sociopath in management who took delight in torturing people.
Monthly expense accounts were his favorite tool. He'd find a tiny yet obvious addition error, strike a diagonal line across the whole page with a magic marker and return it. That meant you had to re-transcribe the entire thing, and re-check every addition. I'm mildly asperger's and often swap digits or mis-key the calculator... so it was a problem for me.
It took a couple hours to rewrite and double check a form. Pure mean spiritedness on his part, he even looked like Mr Potter from "It's A Wonderful Life"(Lionel Barrymore)..

I shared your disdain for rote transcription and menial arithmetic.
And i had a TI-99 home computer. And a printer.
So i brought the computer to my office and wrote a Basic program which prompted me for expense-able items day by day. It stored them on a 5 inch floppy disk.
On demand, it printed them in the exact same format as on the company expense account. And it did all the arithmetic. So i knew there were no addition errors.
Now all i had to do was transcribe to the company form. Also i knew that any mistake was an error of omission not an error of addition... i'd simply missed an entry.

I added one more feature to the program - with one keystroke i could adjust every entry for which no receipt was required up or down by 1%. You see, i knew darn well he knew where any mistake was. By changing everything i made HIM repeat HIS tedious checking of my arithmetic.
AND i could have the new form back to him in ten minutes. Ha Ha Ha Ha Ha Ha! i deprived him of his pleasure. Well it worked. After three cycles he started sending my forms back with a sticky-note indicating the problem, instead of a magic-marker swipe.

And I learned how to handle input, strings, arrays, formatted print, Ascii special characters and disk I/O in Basic.
END ANECDOTE ----------------

Moral of THAT story - We need motivation. We learn by doing.

So quit making excuses and get to work making something that you can look at a year from now and say "I did that well! ".
Even if it's only this with every supplementary problem worked:
https://www.amazon.com/dp/0071635122/?tag=pfamazon01-20 !

I tried Schaums before. I found them very not ADHD friendly. Maybe different now that I'm medicated...

That's why I have to study harder problems. Is it odd that I can carry out most of the entire Euler Lagrange equation in my head but not memorize that other stuff?

As for programming... Not sure I quite got that story, nor would I find swapping keys like that funny unless it were a prank played on that particular individual that I HAAAAAATE (not going to say who she is or she will probably try to get me arrested again for 'slandering' her... But she probably doesn't frequent this site anyway.) And yeah I'm mildly Aspergers too.

I did a bit of programming on a graphing calculator for a calc 1 class (in high school, but a small one with no AP tests, idiot bastards made me take it again in college instead of letting me test for credit out of it, you can only pass out of as high as precalc which some engineering majors had to retake and they were fresh out of high school too having taken calc 1 AND calc 2 while in high school, how pathetic, I would NEVER hire them to design a bridge, no wonder that towns infrastructure was shot... Can't blame them though, the high school class was garbagety. Spent the entire first quarter reviewing trigonometry, barely covered integrals by the end of the year, and that teacher, like the one in college, was a condescending louse. I studied ahead in the book as much as possible, but I was also very depressed so I don't think that studying was very effective. )

I somehow got away with checking out a book on nuclear physics a book on vector calculus, and a book on molecular spectroscopy while I was 19 and still under control of the abusive person I mentioned. I had no internet, nothing to distract me except a television I seldom watched, so I studied all day and wrote stuff down that made no sense later and in two or three weeks I picked up most of calc 3, linear algebra, a bit of ODEs, and a bit of quantum mechanics. And then I was told to take the books back and pick up something at the library 'worth reading'... like Twilight. But when I got back to studying a couple years later I remembered it all surprisingly clearly.

 

[CosmicKitten]

I find this hard to believe.

One just doesn't "read" such a text as if it were a novel. I lost count how many times I hear students telling me that they understood the material when they read the text, but found it difficult to solve the homework assignments. To paraphrase Mary Boas's message from her book, you only get a superficial understanding of the material by simply reading books or hearing lectures. The only way to have a deeper understanding of the material is to solve various problems, and to practice this often. From what I've read, you seem to have an aversion to doing that.

Secondly, you are not a very good judge on whether you have mastered or understood the material. You may claim that you have understood "everything", but how do you prove such a thing? I've read books on performing surgery and I believe I've understood everything. Piece of cake! Shall I take out your appendix?

Zz.

I do not have an aversion to doing problems, I just prefer not to do them until I feel that I fully understand everything. Plus, this book does not even have answers to the problems to make sure you know how to do them.

That I believe is part of the problem with many lower division classes. They make you do problems for credit, which takes away from your study time so you don't know quite how to solve the problem but you're in a rush to get it done so you do three quarters of the problems and get half of them wrong but still get full credit. And then get a failing grade on the test but if its a high F you can still pass from the homework and attendance credit (this is more typical of c.c.'s than four years or so I am led to believe).

All I know is that this book seems so much clearer to me than the other, easier books I have read. I certainly don't read it like a novel; if I did I would have finished it in one or two days. I look at the problems as they go step by step and sort of make up my own rules on how they work (and by making up I mean most of the time ripping off whoever discovered how to do it that way but it sticks better if I feel like I'm making it up haha) and I check all of the work from step to step (THIS is how I learned much of what I know about calc 2 and 3) and if I don't get why that step follows I agonize over it until I do and this can sometimes be distracting or cut a marathon study session to a screeching halt, so I attempt to take back the reins by searching on the internet...

And then there are times I get Eureka moments that I enjoy a little too much (like today I was all "aaaahhh I discovered how m by n matrices relate to what they discussed about isomorphic vector spaces I have an even better idea now of what matrices are all about!") Which are certainly encouraging but also distracting...

 

[jim hardy]

while I was 19 and still under control of the abusive person I mentioned.

Soounds like maybe you've had a time of it.

The science books you read are above my level. So i can't address your original question.

Your difficulty in slowing down to focus is all too familiar... i addressed that in myself with myriad self-help books... now that was in interesting journey!

This may sound strange, but i found a lot of comfort in reading Jodeph Conrad's "Tales of the Sea", a colllection of his short stories. Every one is a character study. I gained insight into my own strengths, weaknesses and behaviors from it. Sorta helped calm the storms, if you will.
Good luck and hang in there .

old jim

 

[Jorriss]

That's why I have to study harder problems. Is it odd that I can carry out most of the entire Euler Lagrange equation in my head but not memorize that other stuff?
.

No, not odd at all. You have a normal memory. You remember some stuff, and not the other stuff.

But I am not quite sure what "carrying out most of the entire Euler Lagrange equation" means.

 

[WannabeNewton]

Who cares about memorization in the context of physics and math problems? Why the constant memory rhetoric? It doesn't matter if you can memorize the Euler Lagrange equations in your head (one can easily look those things up); this is a useless trait and you focusing so much on it only takes away from you focusing on traits that actually matter when it comes to solving physics and math problems. I think in order to get any proper advice, there has to be a shift away from all this prolonged memorization chatter and go on to how one can properly absorb concepts and subtleties and subsequently apply them to proofs and physics problems. These kinds of things come with practice not memorization.

 

[micromass]

I do not have an aversion to doing problems, I just prefer not to do them until I feel that I fully understand everything. Plus, this book does not even have answers to the problems to make sure you know how to do them.

That's exactly the problem, isn't it? You can't understand anything unless you do the problems. It's not like reading a text again and again makes you understand it. You can only understand if you do the problems. If you didn't do problems yet, then you don't have a full understanding of the topic. You'll have superficial understanding at best.

And books which have answers are really unnecessary. You should be able to do problems and know that you did them correctly.

All I know is that this book seems so much clearer to me than the other, easier books I have read. I certainly don't read it like a novel; if I did I would have finished it in one or two days. I look at the problems as they go step by step and sort of make up my own rules on how they work (and by making up I mean most of the time ripping off whoever discovered how to do it that way but it sticks better if I feel like I'm making it up haha) and I check all of the work from step to step (THIS is how I learned much of what I know about calc 2 and 3) and if I don't get why that step follows I agonize over it until I do and this can sometimes be distracting or cut a marathon study session to a screeching halt, so I attempt to take back the reins by searching on the internet...

So you just "make up rules"?? That sounds like a recipe for disaster. How do you know your rules are valid in general? How do you know when to use which rule? Why do the rules even work?? It sounds to me that you're just memorizing a book without actually learning the material very deeply. And making up rules is a very bad thing (unless you can prove the rules to be true).

 

[CosmicKitten]

Who cares about memorization in the context of physics and math problems? Why the constant memory rhetoric? It doesn't matter if you can memorize the Euler Lagrange equations in your head (one can easily look those things up); this is a useless trait and you focusing so much on it only takes away from you focusing on traits that actually matter when it comes to solving physics and math problems. I think in order to get any proper advice, there has to be a shift away from all this prolonged memorization chatter and go on to how one can properly absorb concepts and subtleties and subsequently apply them to proofs and physics problems. These kinds of things come with practice not memorization.

Hey, I'm not the one who thinks memorization is all that important, it's the schools, or at least the schools I went to. I can understand the process and the meaning behind it completely, and then get a D on the test because I didn't remember the formula in perfect detail. Same goes with almost everything I self taught, given just a few reminders of the formulas and stuff I can solve just about everything but since you are usually not allowed to have access to such details on an exam that makes me sad knowing I wouldn't be able to ace the exam unless I do.

Of course, if you truly understand the formula, then the details and everything else follow naturally. But elementary level textbooks don't contain the full derivations and explanations required to understand the formula well enough to memorize it without rote. If a calculus formula was derived using partial differential equations or even higher level math, then that should be taught before one is required to memorize it, unless they are to be pigeonholed into a career that doesn't require much understanding or thinking, as I imagine is the goal for most community colleges and the insidious 'cooling out' process that they carry out, am I correct in that assumption?

I went to a four year college for one semester (I left and went back to a community college because I had to move and the latter was the only option available to me where I moved, and the four year college, having no physics majors, was not worth staying at anyway) and the classes were not in fact taught at a higher level. As a matter of fact, I found the physics 1 class very easy, because I was not required to do homework for a grade, I only had to worry about the tests (its too much of a strain on my attention span to have to worry about homework for a grade every night plus I get too tired in the head from sitting through lectures to concentrate) and I got the highest or second highest grade in the class on nearly all of them, without doing the homework or studying (not that I didnt try, but I simply couldn't concentrate, especially with all the other things I was worries about at that time of my life). I was able to figure out problems I had never done before in the time given to take the test. Plus the teacher never covered most of what he should have covered; it was mostly stuff I remembered from high school, and I had a similarly easy time in that class as well. Electromagnetics and optics are a little less intuitive however, especially regarding laws that require a higher level of math than is taught to fully understand the rules, and thus rote memorization, or a higher level book to supplement the class (provided you have time after the homework which I try to do during lecture since I am too tired to do by the end of lecture) is required.
In short, I had a hard time in comm. college because I WOULDN'T memorize by rote. Not sure if wouldn't or couldn't actually, perhaps a little of both... I wasn't failing, I mean a high D on the tests can be brought up to a B with homework and attendance and labs, but that to me was unacceptable. I'm still not sure how I could do so poorly... And yes I studied and got tutoring too. It was always the case in math in high school that I got A's without understanding anything because I almost rotely memorized the rules. Luckily I was able to look back on it later, when I wasn't forced to do homework, and find that I could suddenly understand everything at a level I didn't while I was in the class. Most people I think would forget it altogether?

 

[CosmicKitten]

That's exactly the problem, isn't it? You can't understand anything unless you do the problems. It's not like reading a text again and again makes you understand it. You can only understand if you do the problems. If you didn't do problems yet, then you don't have a full understanding of the topic. You'll have superficial understanding at best.

And books which have answers are really unnecessary. You should be able to do problems and know that you did them correctly.



So you just "make up rules"?? That sounds like a recipe for disaster. How do you know your rules are valid in general? How do you know when to use which rule? Why do the rules even work?? It sounds to me that you're just memorizing a book without actually learning the material very deeply. And making up rules is a very bad thing (unless you can prove the rules to be true).

By making up rules, I mean I figure out my own process for doing them, because I have a hard time paying attention through the steps given sometimes, or a hard time memorizing them. I can't even articulate what goes on in my head most of the time, I am very visual and I try to visualize what they are describing, and I check all the units if they are using units to make sure they provide the desired thing that is to be measured, whether it be meters, meters squared, meters per second times mass (momentum), momentum times distance which is the same as energy times time (units of Planck's constant or 'action') since these can be treated as pseudo-variables that can be canceled out or raised to a power. This aids understanding and memorization, and is a problem area for most students if I am not mistaken? What is the main problem area for most students anyway?

I will in fact spend a little too much time focused on things like that. Even if the problem is clearly laid out I feel like I am missing something if I don't see how all those work at first. Sometimes I see right away, and forget...

 

[Jorriss]

Of course, if you truly understand the formula, then the details and everything else follow naturally. But elementary level textbooks don't contain the full derivations and explanations required to understand the formula well enough to memorize it without rote. If a calculus formula was derived using partial differential equations or even higher level math, then that should be taught before one is required to memorize it, unless they are to be pigeonholed into a career that doesn't require much understanding or thinking, as I imagine is the goal for most community colleges and the insidious 'cooling out' process that they carry out, am I correct in that assumption?

This sounds like you are making many excuses. You should probably take a step back and realize that these grades imply you do not understand the material as well as you believe and also understand that you do not need partial differential equations to have a very solid grasp on intro physics.

 

[CosmicKitten]

This sounds like you are making many excuses. You should probably take a step back and realize that these grades imply you do not understand the material as well as you believe and also understand that you do not need partial differential equations to have a very solid grasp on intro physics.

I think I was in fact overthinking. Instead of listening to the teacher and picking up on the 'dialect', so to speak, of that particular class, I just observed the class notes and old test questions, did the homework problems (which did in fact include the answers so you would think I would know what I needed to work on?), and looked in the book, having thought that everything I needed to know was there, or apparently not knowing what I needed to know. If they would only put everything on one big sheet of paper and let you have at it *sigh*

First question on a test I scored 41 on from Fall 2011 Physics 196 (E&M):
On the x-y plane, the electric field is uniform and is given by E = 400i (N/C) (E and i are vector quantities). Point A has coordinates (-1, 1) and point B has (2,0) if the electric potential at point B is 300V then what is the potential at point A?

First off, does it even make sense that there is electric potential in a uniform field? Maybe yes but at the time I was used to thinking of electric fields as growing stronger the closer one moves to the source, this kind of electric field is unnatural and impossible to occur in real life and maybe that's what threw me off, I mean if you took the divergence of it you would get zero just like with a magnetic field (they didn't teach divergence in that class, shame it would have solidified a few concepts for me) but anyway if I just took the antiderivative of the electric field and got 400x, 400(2) - 400(-1) = 1200V, this also doesn't make sense, because clearly the voltage cannot equal 300V unless x equals 3/4 which it doesn't but why is this supposed to make sense anyway it's electromagnetical lala land in the fantasy world where an electric field has zero divergence. It should have been a no-brainer to realize that 1200V is just a difference and that it must equal 300V - V_A (V_B - V_A since that's the way I did it) and oh look we get -900V which is not in the answer options. Say we take V_A - V_B: 400(-1) - 400(2) = -1200V, V_A - 300V = -1200V, V_A STILL equals -900V. No clue what I did wrong here...

Second problem, ok the electric field this time is 3(x^2)i, which does have divergence and I guess it could be from a pair of same charged plates. Antiderivative of 3(x^2) equals (x^3) and the task is to find the potential difference between x=1 and x=3. That would be (3^3) - (1^3) = 27-1 = +26V. But that was marked wrong; maybe it was -26V?

Problem 3 is... electric potential V(x,y)=2xy-(x^3), so in units of V/m, you must find the electric field at (2,1)... the x derivative of V(x,y) is 2y - 3(x^2), the y derivative is 2x, so the field would be E = (2y-3(x^2))i + (2x)j, to plug in (2,1) into that would get -10i + 4j, which I marked but according to the teacher is the wrong answer.

And then there are problems I'm not sure whether I got right or wrong because the cat went potty and blurred out the red x or check, and a picture I was required to draw field lines and equipotential surfaces (how does the teacher decide it is worth 2 out of 3 points? No clue...) and although I thoroughly understood capacitors even back then, I screwed up an entire 18 point problem because I... looks like I multiplied the voltage by the area of the plates and divided by the separation distance... ugh I knew even then that you are supposed to multiply area by distance and those other two constants and not bother with voltage for the other capacitance equation that you use when you are given area and distance but not charge, the equation was even written on the cheat sheet the teacher allowed us to make, how did my reasoning lapse so badly? The rest of the work that followed was fine apart from the grossly oversized value of capacitance I got for the first problem... stress, I guess, I even saw something was wrong right before I had to turn it in and so had no time to fix it.

And here's one problem where I did the integral right but I just forgot to plug a and 0 back into take the antiderivative from a to 0.

So like I said I massively screwed up on a couple of things but mostly NOT because of not understanding it well enough, but rather... test anxiety? I am not one to normally get test anxiety either...

 

[Jorriss]

I think I was in fact overthinking.

This is not often the case.

First off, does it even make sense that there is electric potential in a uniform field?

Yes, it does make sense.

You know that $$\nabla\cdot{\bf D} = \rho$$ but do you really know what it means? This is not inconsistent with a uniform electric field if one is looking at a region that contains no charge or if there are discontinuities in the boundaries which is often the case with idealized problems.

Second, suppose a uniform electric field can't exist. One could certainly construct a field that varies very little over space and might be approximated as uniform. A student of physics should be able to appreciate the necessity of approximation.

But in any event, its moot. You must of seen the scenario that leads to uniform fields.

 

[AlephZero]

First question on a test I scored 41 on from Fall 2011 Physics 196 (E&M):
On the x-y plane, the electric field is uniform and is given by E = 400i (N/C) (E and i are vector quantities). Point A has coordinates (-1, 1) and point B has (2,0) if the electric potential at point B is 300V then what is the potential at point A?

First off, does it even make sense that there is electric potential in a uniform field? Maybe yes but at the time I was used to thinking of electric fields as growing stronger the closer one moves to the source, this kind of electric field is unnatural and impossible to occur in real life and maybe that's what threw me off, I mean if you took the divergence of it you would get zero just like with a magnetic field (they didn't teach divergence in that class, shame it would have solidified a few concepts for me) but anyway if I just took the antiderivative of the electric field and got 400x, 400(2) - 400(-1) = 1200V, this also doesn't make sense, because clearly the voltage cannot equal 300V unless x equals 3/4 which it doesn't but why is this supposed to make sense anyway it's electromagnetical lala land in the fantasy world where an electric field has zero divergence.

I'm sorry, but that doesn't suggest "test anxiety" to me. It just shows woeful lack of understanding of the basics.

There is nothing unphysical about this field, and (if as you claim later in the post) you "undestand" capacitors, you would know a physical situation that would produce it - at least, to a good approximation.

 

[WannabeNewton]

First question on a test I scored 41 on from Fall 2011 Physics 196 (E&M):
On the x-y plane, the electric field is uniform and is given by E = 400i (N/C) (E and i are vector quantities). Point A has coordinates (-1, 1) and point B has (2,0) if the electric potential at point B is 300V then what is the potential at point A?First off, does it even make sense that there is electric potential in a uniform field? Maybe yes but at the time I was used to thinking of electric fields as growing stronger the closer one moves to the source, this kind of electric field is unnatural and impossible to occur in real life and maybe that's what threw me off, I mean if you took the divergence of it you would get zero just like with a magnetic field (they didn't teach divergence in that class, shame it would have solidified a few concepts for me) but anyway if I just took the antiderivative of the electric field and got 400x, 400(2) - 400(-1) = 1200V, this also doesn't make sense, because clearly the voltage cannot equal 300V unless x equals 3/4 which it doesn't but why is this supposed to make sense anyway it's electromagnetical lala land in the fantasy world where an electric field has zero divergence.

I completely agree with Aleph. This isn't test anxiety. First off, the field of an infinite sheet of charge is uniform and in real life this is a brilliant approximation to actual charge sheets. Secondly, just because the divergence of an E field is zero doesn't mean it is unphysical. In electrostatics if your charge density is compactly supported then the E field has vanishing divergence outside of the compact support. There is nothing crazy about this, it comes right out of the formulas even. There is no shame in not teaching the differential form of Maxwell's equations in a first course in EM and clearly they only confused you MORE for this exam. Just because it "seems" more complicated doesn't mean it makes things any clearer and makes you any more capable of acing an exam just because you know what it looked like.

Don't over think things and don't belittle your classes for being too "simple" because if you don't have a handle on the "simple" things then you shouldn't be jumping ahead to the more complicated things. You can even memorize the form of maxwell's equations in my signature below but that won't help you at all for your EM exams. Many times, the simpler math allows for much more physical understanding.

 

[CosmicKitten]

This is not often the case.


Yes, it does make sense.

You know that $$\nabla\cdot{\bf D} = \rho$$ but do you really know what it means? This is not inconsistent with a uniform electric field if one is looking at a region that contains no charge or if there are discontinuities in the boundaries which is often the case with idealized problems.

Second, suppose a uniform electric field can't exist. One could certainly construct a field that varies very little over space and might be approximated as uniform. A student of physics should be able to appreciate the necessity of approximation.

But in any event, its moot. You must of seen the scenario that leads to uniform fields.

That is d/dx + d/dy + d/dz (by d I really mean partial derivatives but I don't know how to make that kind of d) multiplied as a dot product. That is the x derivative taken of the unit vector in the x direction (which is i) and so on, and added together and made into a scalar. Anyway, the dot product of d/dx with 400i is obviously zero. Divergence indicates going outward from a source, but in either case it is irrelevant to the problem at hand. I didn't even know what divergence was when I took the test. Would you at least explain to me why I got it wrong then?

I have never seen such a scenario. A succession of oppositely charged plates might approximate it to some degree if placed just right...

 

[CosmicKitten]

I completely agree with Aleph. This isn't test anxiety. First off, the field of an infinite sheet of charge is uniform and in real life this is a brilliant approximation to actual charge sheets. Secondly, just because the divergence of an E field is zero doesn't mean it is unphysical. In electrostatics if your charge density is compactly supported then the E field has vanishing divergence outside of the compact support. There is nothing crazy about this, it comes right out of the formulas even. There is no shame in not teaching the differential form of Maxwell's equations in a first course in EM and clearly they only confused you MORE for this exam. Just because it "seems" more complicated doesn't mean it makes things any clearer and makes you any more capable of acing an exam just because you know what it looked like.

Don't over think things and don't belittle your classes for being too "simple" because if you don't have a handle on the "simple" things then you shouldn't be jumping ahead to the more complicated things. You can even memorize the form of maxwell's equations in my signature below but that won't help you at all for your EM exams. Many times, the simpler math allows for much more physical understanding.

You do realize the scenario I am talking about, to make a gravitational analogy, is like if you were to fly a rocket away from the earth, the gravitational force would remain the same no matter how far the rocket is away from the Earth (which does not happen because force shrinks inversely to the square of the distance); when you explain a sheet, I am imagining a plane with point charges distributed so uniformly that we can pretend that (given a fixed distance) the field over the sheet is the same everywhere, and ignore that it is in fact weaker at points whose distance perpendicular to the sheet does not align with a point of charge on the sheet. Please correct me if this is not the kind of sheet you are describing... wait, I am considering infinity now... if you add up the tiny tiny contributions from the charges on the sheet that are at a very very great distance away... the contribution would be slightly greater at a greater distance, so I guess I can see how that approximates a uniform field. Remember I am thinking of field vectors from point charges at greater and greater distances away, if one would sum up the contributions (which would run to zero as the distance away on the sheet approaches infinity) they would converge to close to the same value regardless of how far away the point where the field is measured at is - do you have a source that shows how this was originally derived?

Oh yes, I believe I heard about the case where the Gauss integral can be done where the infinitesimal space that the point containing the charge is enclosed inside is left out. Is that what you mean by 'compactly supported'? I didn't quite finish that book; I took it back to the library so I wouldn't lose it or rack up another library fine while studying another book, but I have full intentions of returning to it.

And no, they did not teach that in this class, nor had I studied it on my own at the time. I was too busy worrying about transferring and starting a physics club and a math competition and just walking back and forth from and not missing class (believe me it takes a day's worth of concentration not to miss one class) so I just didn't have time to study. Not even the easy stuff. That's why I believe I would have had an easier time if I did not have to worry about attending class. I cannot lose myself in a physics book if I have that little voice nagging at the back of my mind telling me, "you have class at six you have class at six you have class at six" and I have to completely lose all sense of time and space to study anything, especially math, which for me requires a lot of visualization to try and figure out why these rules work, and even then my mind wanders off, is too distracted by itself.

But studying harder material only helps. See, I understand things so quickly that I don't work on them long enough to remember simple things. In fact my mind unconsciously discards things it does not see the value of. And so in order to be studying it for long enough to have a firm enough understanding to remember it, I need to study it at a higher level. Studies have shown that ADHD people will score higher on tests that require a little more challenge, that channel more parts of the brain so that the thoughts don't wind up slipping into some other territory and being drawn fully away from the conscious focus.

I did not even realize what was wrong with these problems until after I read that harder E&M book.

Wait... so you think I just like to know what the equations LOOK like. Well today I learned what determinants in matrices look like:

A matrix can be three rows, each a separate vector, the columns representing the x, y, and z components of those vectors A, B, and C, respectively. The determinant is a measure of the volume of the paralleliped formed by those vectors. As for how the rules about matrices work:
-You can add a scalar multiple of one row to another row and it will still have the same determinant. I picture, say, vector A being transformed into the sum of vectors A + B and so that will squish and stretch the paralleliped but it will still have the same volume. You cannot add a multiple of vector A to vector A though because that definitely increase the volume and therefore the determinant of the paralleliped.
-if one row or column is zero, then the determinant is zero, and the converse is also true. That is, if one of the vectors is zero, then you don't have a three dimensional paralleliped you have a flat parallelogram. Same goes if vectors A, B, and C are all completely missing components from either the x, y, or z axis (now if they are missing components from two of those, then what you have is a line segment).

Knowing this I think would make a linear algebra class make more sense to me, I mean I would know what I'm doing with Gaussian elimination. If I ever get confused I could imagine what I would be doing to that paralleliped (which is only one example of what matrices can be used to represent of course) and if that makes sense, then I can do it. But they don't teach that in a basic linear algebra class do they?

 

[Jorriss]

And then there are problems I'm not sure whether I got right or wrong because the cat went potty and blurred out the red x or check,

What.

 

[CosmicKitten]

I'm sorry, but that doesn't suggest "test anxiety" to me. It just shows woeful lack of understanding of the basics.

There is nothing unphysical about this field, and (if as you claim later in the post) you "undestand" capacitors, you would know a physical situation that would produce it - at least, to a good approximation.

A capacitor of a given capacitance always has that capacitance, that is always the same ratio of charge to voltage. Add more voltage to it, then the charge on the plates will increase.

As for the other equation involving the area... the greater the area, the greater the charge for the given voltage. The greater the distance, the smaller the voltage for a given charge, and therefore the greater capacitance.

But seriously you don't even need to understand such things for a simple E/M class... I still had questions about capacitance. Is the charge supposed to reach a point that it discharges through the capacitor? But that's not what happens; it's the voltage of the battery that keeps the voltage steady between the plates right? And when the voltage is turned off it discharges at a rate that involves e to the power of something I can't quite memorize, but it can be used sort of as a battery itself, but suppose after disconnecting the battery there is just empty space there? Then you have a two capacitor system? How would that work? But there would be a switch you could turn on to discharge it through where you want it to be discharged? What would be the practical purpose of that anyway?

Even more interesting is when inductors are introduced. Capacitors and inductors are both a form of resistance but capacitors follow the reverse of the laws for determining the voltage and current through resistors in series and parallel. But if you put one over the capacitor and package it in a form called impedance that you can add with inductors and resistors, that is far simpler than worrying about all those laws now isn't it? And if the inductor and capacitor are in sync with the AC voltage?? I need to get that book back... oh and I studied some on MIT's open course ware, their E/M class is so superior to the one I had... I was only in it for half a semester, but I doubt they cover impedance at any degree of depth...

Anyway, for me, the more things to remember, the more I will remember! Long term memories are easier for me to focus on than short term memories or anything in the world outside my head for that matter, so there is something to be said about trying to commit much to memory.

 

[CosmicKitten]

What.

The teacher marks either an x if it's wrong or a check if it's right. I had the binder with my test in it inside this box that my cat had a bad habit of mistaking for a litter box, so the red ink got blurred out...

 

[Jorriss]

This thread has gotten a bit out of hand.

You state you want self study help, but the best advice I think I can give is that you should not be studying ahead - not yet.

You are filling yourself with many incorrect concepts.

Go back to community college. Take classes and try and learn what is in those classes only. And go to your professors office hours often.

 

[micromass]

This thread has gotten a bit out of hand.

You state you want self study help, but the best advice I think I can give is that you should not be studying ahead - not yet.

You are filling yourself with many incorrect concepts.

Go back to community college. Take classes and try and learn what is in those classes only. And go to your professors office hours often.

Very true. To learn mathematics and physics, you need to do things mostly in the order that the course does things. If you're going to study ahead, then you're going to be confused. Or you're going to make things more difficult than they really are. There's a reason that they teach classical mechanics and then QM. Even though it's possible to do QM and then derive classical mechanics as a limiting case.

 

[WannabeNewton]

Ok this thread is veering off very fast and doesn't really have anything left to do with the OP anymore but I will try to indulge you and tie things into your studies.

You do realize the scenario I am talking about, to make a gravitational analogy, is like if you were to fly a rocket away from the earth, the gravitational force would remain the same no matter how far the rocket is away from the Earth (which does not happen because force shrinks inversely to the square of the distance)

This is but a specific example. In physics giving one example of something non - uniform does not rule out the possibility of uniform fields.

do you have a source that shows how this was originally derived?

You can derive it yourself using Gauss's law, it is a trivial derivation.

Is that what you mean by 'compactly supported'?

A compact support has a simple technical definition but it requires knowledge of topology and I don't think you are at that stage as of yet. For now just think of it as a closed and bounded region of space (this is actually perfectly valid in euclidean space because of Heine - Borel).

I cannot lose myself in a physics book if I have that little voice nagging at the back of my mind telling me, "you have class at six you have class at six you have class at six" and I have to completely lose all sense of time and space to study anything, especially math, which for me requires a lot of visualization to try and figure out why these rules work, and even then my mind wanders off, is too distracted by itself.

I understand, it happens to me as well - school is stressful.

But studying harder material only helps. See, I understand things so quickly that I don't work on them long enough to remember simple things.

This doesn't make any sense. Just stick to the basics until you fully understand those. This is just as true in physics as it is in math. You can't immediately jump into a book on Lebesgue integrals and measure spaces without having first learned analysis because trying to pick up the basic things along the way will only confuse you more, take away from you actually understanding the important basics first, and screw you over on exams. Physics is no different: you don't jump into a book on advanced electromagnetism before first understanding the fundamentals. First understand basic classical mechanics and EM before moving on. Not everyone picks up things in a matter of seconds effectively and that's ok, just don't rush things.

But they don't teach that in a basic linear algebra class do they?

I don't know. I never took an applied linear algebra class which is what you are describing. I took a theoretical one. A book I can recommend to you, if you are dedicated and interested, in order to solidify your fundamentals of EM is "Electricity and Magnetism" - Edward M. Purcell (it is a freshman level textbook but be warned, it is not easy by any means)

 

[CosmicKitten]

Very true. To learn mathematics and physics, you need to do things mostly in the order that the course does things. If you're going to study ahead, then you're going to be confused. Or you're going to make things more difficult than they really are. There's a reason that they teach classical mechanics and then QM. Even though it's possible to do QM and then derive classical mechanics as a limiting case.

On the contrary, I get confused when I am given simple equations and do not know why or what they are for. The graduate level text I am reading is not confusing at all. Bear in mind I studied a lot of the 'basics' before I got to this level, I studied them on my own. I have a hard time in class because listening to a lecture - particularly from a lecturer that barely knows English, a problem that is stereotypical for big universities but just as much a problem for big city community colleges. But it really doesn't matter because if a lecturer cannot keep pace with the speed of one's thinking then there is NOT going to be any benefit from it. The talking only shuts off my brain which tells me things while I am reading it.

I got so bored in the physics 1 class I cried and was depressed all of the time. And that was at a four year college. I got probably the only A in the class and I didn't study, didn't do homework, doodled in class... I also got an easy A in a chemistry class at another community college. I literally remembered everything from high school.

I actually got tutoring and did the homework in that E/M class, and in the calc 2 class and the waves/optics/ modern physics class at this last comm. college and look where it got me.

I mean, what's wrong with teaching you a few basics and then having you apply them to a few graduate level problems as practice? That way you learn it all at once. Saves time. You see how the basics fit into the whole scheme of things.

BTW with just the barest knowledge of mechanics and differential equations I pondered the n-body problem, I decided that if you were to treat all the other masses as if they were held still and measure the motion of each over a small interval of time, and then for the next time interval use the positions attained from measuring the motion the way of the previous interval, and so on, and if you sum up the time intervals and take the limit as the number of time intervals goes to infinity (and thus the length of each goes to zero) then that approximates the motion of the n-bodies; the problem with evaluating an integral from that is that the equation for position changes with each time step as the bodies move. This is the Euler method am I correct? (To say that I discovered it on my own, while true, would be rather presumptuous given that it's quite obvious, even to me, who found limits of sums to be a struggling point, as in I can't remember the exact equation).

 

[Jorriss]

On the contrary, I get confused when I am given simple equations and do not know why or what they are for. The graduate level text I am reading is not confusing at all.

The problem is that you are confused now, but you do not know it. You aren't understanding your graduate text. Your posts here show an enormous level of misunderstanding.

You need to drop this inflated view of yourself, be a bit more humble, and learn the basics.

 

[CosmicKitten]

This thread has gotten a bit out of hand.

You state you want self study help, but the best advice I think I can give is that you should not be studying ahead - not yet.

You are filling yourself with many incorrect concepts.

Go back to community college. Take classes and try and learn what is in those classes only. And go to your professors office hours often.

Yeah, I tried that. Didn't work out.

Most graduate level textbooks have a review of undergrad level stuff at the beginning and for me that is enough to help me understand it.

Keep in mind, I have been studying on my own for a year. A YEAR. I don't work except to tutor kids in math for spare cash a couple times a week or so, so that's a lot of spare time. Anyway, by now community college is utterly pointless.

I will maybe go back to comm. college to study something else like foreign languages; meanwhile, I will raise hell at UCSD if I have to to let me take some graduate level classes, once I have the money to pay for a few of them; perhaps take the PGRE if I can spare for that too. My mom after all skipped the intro classes when she was going to UCSD. She only got a B minus GPA but at least she learned things. Never got anywhere in life though but that was her fault; she didn't know what she wanted to be, I have wanted to be a physicist since I was 17 and was sadly cut a raw deal by my foster parent but oh did my mind wander when I read the laypeople's introduction to string theory at the high school library...

And if I fail (or get a poor passing grade as is more likely) then at least I will have learned something in the process!

 

[Vanadium 50]

CosmicKitten, what you are doing now clearly isn't working for you. However, your response to suggestions has been to indicate that you want to keep doing what you have been doing. I think you have a choice to make.

 

[CosmicKitten]

The problem is that you are confused now, but you do not know it. You aren't understanding your graduate text. Your posts here show an enormous level of misunderstanding.

You need to drop this inflated view of yourself, be a bit more humble, and learn the basics.

Would you care to explain how I am misunderstanding? Mind you I have a hard time articulating what is going on in my head. I do not think in words as I imagine some people do.

Mind you I am 23, which is well into my 40s in physicists' years. I AM LOSING TIME