Uncovering the Secrets of Calculus 2 and Physics: Strategies for Success

[noslen]

hey everyone

Im currently looking at my white board. I can see ghosts of Riemann sums not fully erased. I call them ghost because they scared me yesterday when I almost forgot how to work one! Wait I think I see something emerging from the dark depths of my book shelf...oh my godsh its my calculus book

now that i have your attention

Im worried about the load of homework I will have next semester with calc 2, and physics

can anyone recommend any good study styles or strategies that work well, and how many hours a day could one expect studying for these classes??

by the way Mathwonk, Matt grime, HallsofIvy, Hurkly, and all the other ridicoulsly smart people here I demand to know your study strategies and don't say "practice"

thanks :shy:

 

[Maxos]

More or less 0.3 hours a day.

In fact, I'll have to increase my rate.

I suggest studying until you master the subject.

 

[Brad Barker]

hey everyone

Im currently looking at my white board. I can see ghosts of Riemann sums not fully erased. I call them ghost because they scared me yesterday when I almost forgot how to work one! Wait I think I see something emerging from the dark depths of my book shelf...oh my godsh its my calculus book

now that i have your attention

Im worried about the load of homework I will have next semester with calc 2, and physics

can anyone recommend any good study styles or strategies that work well, and how many hours a day could one expect studying for these classes??

by the way Mathwonk, Matt grime, HallsofIvy, Hurkly, and all the other ridicoulsly smart people here I demand to know your study strategies and don't say "practice"

thanks :shy:

for phys II, the prof made us read the chapter the next day's lecture was going to be about. VERY effective. you get the material first in the reading, then you get it reinforced by the lecture, plus you have an idea of what questions you'll need to be asking and what problems you'll have to solve.

i suggest reading as much as you can of the material before each lecture. with math classes this is a bit difficult (for people who aren't comfortable reading math texts, that is). in this case, the reverse may help--go to lectures, then read over the same material. and, of course, doing AT LEAST every assigned problem--as many as you need to get the concept down.

solutions manuals are recommended...

try these and mix and max styles until you get what suits you best.

 

[leright]

Just make sure you USE the textbook for reading material, and NOT for just pracice problems! Lots of ugrads do not use their textbook for reading and just rely on lecture notes and practice problems.

Also, I'd say study for maybe 1 hour for each of subject per day, and you should be good. What's really important is that you come up with a definitive study schedule and stick to it, to discourage procrastination. Procrastination is the biggest killer fo undergrads.

 

[gravenewworld]

to tell you the brutal truth, i never did the readings in the text for any class. it just put me to sleep. i just pull all nighters before the test and cram. it always seems to work (although profs. don't want to admit it does).

 

[noslen]

Thanks

I think I am going to start reading my physics book right now!

 

[leright]

to tell you the brutal truth, i never did the readings in the text for any class. it just put me to sleep. i just pull all nighters before the test and cram. it always seems to work (although profs. don't want to admit it does).

It works but you don't walk away knowing much, no matter how much you tell yourself and others otherwise...

this is also why your profs don't want you to know it works...

Don't forget that one of the main reasons you're in college is to learn.

Not to sound insulting, but I don't think this is good advice to give an undergrad, if you meant it to be advice at all...

 

[Eratosthenes]

Im worried about the load of homework I will have next semester with calc 2, and physics

can anyone recommend any good study styles or strategies that work well, and how many hours a day could one expect studying for these classes??

It is definitely doable. I took those same 2 courses over the summer. One was a 6 week course the other was a 10 week course. In the physics class we covered 3 chapters a week, so we had 1 test a week, for a total of 18 chapters. I studied every single day though. Most of my day was spent in class/driving to class though, so that made it harder. I didn't read the entire book of course, I just didn't have time, but I worked through enough examples to make sure I understood all the concepts.

Since you are taking it during a regular semester, I am sure you will do excellent! Just keep up with the work and you should do great. Go in with a positive attitude and try to understand everything. If you work on both classes every single day, you should do really well, probably a high A in both courses. Of course very few people have that much desire. Goodluck!

 

[Maxos]

you get the material first in the reading, then you get it reinforced by the lecture, plus you have an idea of what questions you'll need to be asking and what problems you'll have to solve.

I must quote you, these are really golden words!

Anyway it is my opinion that studying at home is much less productive
than having lectures (of course both are necessary).

Try to exploit it completely.

 

[Artermis]

Although I respect gravenewworld because he is a smart guy, I have to disagree with ihs advice here. I concede that the super-cram method might work for some people, but I assure you that you don't want to put yourself through that. As it has been pointed out as well, the point of undergrad is to learn, not to cram to do well on an exam; you won't learn anything from the cramming because it's cramming - not learning. Learning steadily and cumulatively is the best way, I think, rather than having a fragile hold on everything at once, it's better to have a firm hold on some of the topics.

 

[gravenewworld]

OH CONTRAIRE! I remember having fun last semester learning all of glycolysis, the TCA cycle, and oxidative phosophorylation in 1 sitting. Needlesss to say I :zzz: :zzz: :zzz: :zzz: for 16 hours the next night.

 

[Maxos]

Au contraire

 

[Brad Barker]

Although I respect gravenewworld because he is a smart guy, I have to disagree with ihs advice here. I concede that the super-cram method might work for some people, but I assure you that you don't want to put yourself through that. As it has been pointed out as well, the point of undergrad is to learn, not to cram to do well on an exam; you won't learn anything from the cramming because it's cramming - not learning. Learning steadily and cumulatively is the best way, I think, rather than having a fragile hold on everything at once, it's better to have a firm hold on some of the topics.

agreed. slow and steady wins the race, as it were... if by "race" we mean "long term retention of the material."



and taking calc II and physics I (i presume?) is TOTALLY able to be done, and done well, at that!

in addition to the other non-cramming advice in this thread, make sure to use office hours! during my first semester i didn't use them very much, since my phys professor answered questions via email (another resource you should use, if the professor allows for this!). but during the second semester, i'd go to office hours a few times a semester for phys II, diff eq, and biology whenever there was a homework problem i was stuck on, a concept i forgot to ask about/didn't realize i had a problem with until after lecture, wanted to talk about academic things.

after all, the profs hold office hours for a reason! they want students to use'em.

 

[Brad Barker]

Au contraire

i guess he didn't get around to crammin' for french...

 

[Maxos]

First: precision.

 

[bomba923]

Hmm--my study method is just read/ponder until you intuitively+mathematically (intuimatically) understand the concept/procedure.

*Assuming time is not significantly restricted on your tests, just focus on the understanding.
*Assuming time IS significantly restricted on your tests, focus on the PRACTICE as well.
Personally, I never really focus on the practice (I'm a Study guy, not a homework guy! Thus my HS teachers hate me!) unless I'm studying challenging material, in which case I need not only to understand the material, but also do the problems extremely quickly.
*Noslen, do not worry about the homework load...well, that is, only if your teacher doesn't consider homework as part of your class grade. Rather, focus on mathematical-intuitive understanding, and your skills. If you need like 1/2/3 problems for practice, go ahead and do those problems; seriously, Don't waste your time on tedious work if you understand the subject and are skilled with it.
However...if you really do need several hours of practice just to understand the subject/concept, well, just do the work i guess.

 

[leright]

Hmm--my study method is just read/ponder until you intuitively+mathematically (intuimatically) understand the concept/procedure.

*Assuming time is not significantly restricted on your tests, just focus on the understanding.
*Assuming time IS significantly restricted on your tests, focus on the PRACTICE as well.
Personally, I never really focus on the practice (I'm a Study guy, not a homework guy! Thus my HS teachers hate me!) unless I'm studying challenging material, in which case I need not only to understand the material, but also do the problems extremely quickly.
*Noslen, do not worry about the homework load...well, that is, only if your teacher doesn't consider homework as part of your class grade. Rather, focus on mathematical-intuitive understanding, and your skills. If you need like 1/2/3 problems for practice, go ahead and do those problems; seriously, Don't waste your time on tedious work if you understand the subject and are skilled with it.
However...if you really do need several hours of practice just to understand the subject/concept, well, just do the work i guess.

This is very similar to my strategy. Good advice! :tongue:

 

[Brad Barker]

If you need like 1/2/3 problems for practice, go ahead and do those problems; seriously, Don't waste your time on tedious work if you understand the subject and are skilled with it.
However...if you really do need several hours of practice just to understand the subject/concept, well, just do the work i guess.

oh, right, this reminds me of my calc III class.

it was--supposedly--an honors course. *eye roll*

anyway, the professor was really unorganized with his homework assignments. I'm not exaggerating, one of his assignments was problems 1-62 for a particular section.

*double eye roll*

so what i did was i picked and chose problems to tailor more to my needs. if i saw a problem and identified it as just a simple plug and chug one, or one that i could solve in a line, i'd just do one or two (either on paper or in my head!). then i'd get to the harder problems and do as many as i felt necessary.


in other words, unless your homework is collected and graded for completeness (like my complex variables class was!), you can "customize" the homework. takes a bit of practice and knowledge of what you can and can't do, or rather need practice or don't need practice with.

yeah, in my calc II class, i started to trim the assignments down once i wised up, if i remember correctly.

but again, it's MUCH safer to do more problems than you need than doing fewer!


(and i have to disagree with the above posters. knowing the concepts is absolutely essential and your primary task--however, you need to prove to yourself that you would be able to solve problems related to those concepts well-before test day, when it will actually count. or if you see a problem in REAL life, when it will REALLY count! )

 

[SamuelGreen800]

For both, read the texts before class, and review the day after class (or sooner, whatever works for you).

For Math, do every practice problem your instructor assigns you. There is simply nothing better than repetition for nailing the mechanical part of it. And read the actual text, and work over any broken-down problems it gives in the text.

For Physics, work on really grasping the concepts before hitting the problems too hard. It's nothing but wasted time if you try to Math your way through the work before you really "get" the Physics. Thinking about applications of the Physics to everyday objects can really help with the memorisation of concepts, especially if you assign a different, distinct object to every concept.

 

[Stephan Hoyer]

Studying the concepts is nice, but the really essential thing is that you can do the problems. Problems can be unintuitive sometimes (or have multiple ways to solve) and the only way to figure out that stuff is through practice. Just because you know F=ma doesn't give you all of mechanics, for instance. Those shortcuts and best procedures are a matter of practice and there really isn't any way to just pick that stuff up by looking at the book. Examples help, but they really are no substitute for doing it yourself -- and just as importantly, knowing you can do it yourself.

 

[Brad Barker]

For Physics, work on really grasping the concepts before hitting the problems too hard. It's nothing but wasted time if you try to Math your way through the work before you really "get" the Physics. Thinking about applications of the Physics to everyday objects can really help with the memorisation of concepts, especially if you assign a different, distinct object to every concept.

yes! this is great advice.

 

[iggybaseball]

hey everyone

Im currently looking at my white board. I can see ghosts of Riemann sums not fully erased. I call them ghost because they scared me yesterday when I almost forgot how to work one! Wait I think I see something emerging from the dark depths of my book shelf...oh my godsh its my calculus book

now that i have your attention

Im worried about the load of homework I will have next semester with calc 2, and physics

can anyone recommend any good study styles or strategies that work well, and how many hours a day could one expect studying for these classes??

by the way Mathwonk, Matt grime, HallsofIvy, Hurkly, and all the other ridicoulsly smart people here I demand to know your study strategies and don't say "practice"

thanks :shy:

I took physics one this summer and I am finishing Calc 2 as we speak. The schedule is challenging since so much material must be covered in a much shorter time frame as explained by Eratosthenes. I would advise that you read ahead. I believe it was my Biology professor that told me on average a person retains about 40% the first time they see knew material and like 60% after the second or third time. She always advised reading the material so that we could come to class and absorb much more. I found out that if you really pay attention in class and if you have an extrememly good professor, you can cut down on some of your studying time. However it's hard to tell exactly how much time you will need to devote before you actually get in the class and start working. Just stay positive and willing to work until you succeed.

 

[bomba923]

(and i have to disagree with the above posters. knowing the concepts is absolutely essential and your primary task--however, you need to prove to yourself that you would be able to solve problems related to those concepts well-before test day, when it will actually count. or if you see a problem in REAL life, when it will REALLY count!

I don't know if you're referring to me in particular, but I said

*Noslen, do not worry about the homework load...well, that is, only if your teacher doesn't consider homework as part of your class grade. Rather, focus on mathematical-intuitive understanding, and your skills. If you need like 1/2/3 problems for practice, go ahead and do those problems; seriously, Don't waste your time on tedious work if you understand the subject and are skilled with it.

Without the mathematical+intuitive understanding, the homework is just memorization of some procedures/systems, requiring little or no thought; also, some might get upset/bored and wonder why they need the material anyway.
*But anyway, I mentioned "if you understand the subject and are skilled with it"-->and by "skilled with it" I meant able to solve problems quickly-->or as quickly as demanded by the exam.

Studying the concepts is nice, but the really essential thing is that you can do the problems. Problems can be unintuitive sometimes (or have multiple ways to solve) and the only way to figure out that stuff is through practice. Just because you know F=ma doesn't give you all of mechanics, for instance.

Ahh yes...my many classmates (I'm a HS junior) who got A's/B's in Physics B simply by memorizing formulas and relying on the full page of notes the teacher allows on midterms and finals (yes, the teacher was lazy, and passed some students b/c of "hard work" and "neat notebooks" regardless of how much they didn't learn/understand. She sort of disliked me b/c I got A's on tests but barely did any work). I can only imagine..confident with such grades, they're (like 60% of the class!) moving into AP Physics-which is Physics C for my HS--with their latest math class being 'trig' or "advanced algebra", which for my school is just prep for trig. You're right: F=ma does NOT give you all of mechanics

Now Stephan hoyer, I'm sorry--I know this was NOT what you were talking about. But I see what you mean--->in my CalcII class, I "intuitively" understood integrals and the procedures to solve them, but it was PRACTICE that allowed me to solve integrals in a minute or less. Yes, harder integrals may take more seconds...but I see what you mean. That, you see, is why I said:

*Assuming time is not significantly restricted on your tests. .. ..

(Sorry--well I'm sorry about sounding prudish. Really, I'm only in HS I know that you guys have much more experience than me (and different as well-->college $\ne$ high school! ))

 

[leright]

I do believe that having an intuitive and mathematically rigorous understanding of physical concepts is the most important aspect of your education, but being able to work physics problems quickly and efficiently is nearly as important. However, sometimes I focus too much on the concepts and the derivations in the textbook and too little on HOW to work various problems and I do too little practice problems at times. this means I have to spend a lot of time on exams THINKING about how to work the problems since I don't immediately know how to do it when I see it, and this is not good at all. Sometimes this causes me to get "B"s in certain classes, which is not good for someone aspiring to attend graduate school in physics.

From now on I am going to try and work more practice problems! However, developing a conceptual understanding is still the most important thing!

 

[noslen]

Im already planning a strategy for next semester. I think I am going to spend more time reading the books and thinking about the laws and theorems; Rather than working problem after problem like last semester.

Great feedback! :tongue2:

 

[Maxos]

I think you can spend precious time reading and trying to understand during the period of lectures, whereas problem practice should be taken just before written papers.
That's the best compromise

 

[Brad Barker]

I do believe that having an intuitive and mathematically rigorous understanding of physical concepts is the most important aspect of your education, but being able to work physics problems quickly and efficiently is nearly as important. However, sometimes I focus too much on the concepts and the derivations in the textbook and too little on HOW to work various problems and I do too little practice problems at times. this means I have to spend a lot of time on exams THINKING about how to work the problems since I don't immediately know how to do it when I see it, and this is not good at all. Sometimes this causes me to get "B"s in certain classes, which is not good for someone aspiring to attend graduate school in physics.

From now on I am going to try and work more practice problems! However, developing a conceptual understanding is still the most important thing!

yes!

for example, it's one thing knowing and understanding kirchhoffs laws and how to apply them.

but it's another thing when you see a ridiculous DC circuit on an exam--especially if you haven't gotten much practice!

concepts are paramount, but practice makes perfect, as it were.

 

[leon1127]

I have always studied 1 year head than what i am learning right now. (i studied 10 hours a day)
And try to relate different subject together to think deeply, always think about the sense behind the text.
Life is often easier if you are able to look from higher aspect.

 

[bomba923]

Life is often easier if you are able to look from higher aspect.

And more reasonable as well!

 

[derekmohammed]

One thing that I notice is not noted on here is group studying. It is a great way to learn, I found it really helpful in Physics 2 (electrodymamics) and calc 2. We would get together (probably 5or 6 of us), pick some of the more difficult questions disscuss them then solve them. It is fun and informative since you are learning together. Sometimes we would spend hours working on prblems from our textbooks.

For calc 2 we would choose ten problems and do them, when everyone was finsihed we would compare anwsers to see if our anwsers were correct. Again a great way to study since you get to find other peoples mistakes and your own.

I recommend group studying for everyone.

Derek

 

[Brad Barker]

I have always studied 1 year head than what i am learning right now. (i studied 10 hours a day)
And try to relate different subject together to think deeply, always think about the sense behind the text.
Life is often easier if you are able to look from higher aspect.

yeah, i do that, too.

but not for 10 hours a day. yeesh.

 

[mathwonk]

Here is some advice I once gave a class of the best students in one of the best private high schools in my state, after completing a Spivak style precalculus course with me. One of them has phD in physics now and another is full professor of math at an Ivy league school.

Comments:

I've enjoyed this class a great deal, and I've learned a lot about the attitude of high school kids (i.e. young adults) towards math. and towards school, and a bit about the people who have been in my class. One of the things that came as a bit of a surprise to me, oddly enough, was that math apparently does not mean nearly as much to the students as it does to me. In a way some of the students seem to have expected me to be a salesman of mathematics and to be prepared to sell them on it. I had rather expected to find people as prepared to "buy" as if I were selling water to people lost in the desert. I remember the shock I felt the day one student responded indignantly to my suggestion that one way to scavenge time to do math was to skip lunch. Other students apparently thought nothing of missing the state math meet for various other commitments. It became clear that students in high school have so many activities to participate in that they cannot easily find time for a really intensive involvement in perhaps any of them.

In spite of the original intent, it was not feasible to give the class in the way it would be given at a state University. University students, even ones with much less ability than those in this class, are motivated to work much harder than did this class and thus to cover much more ground. I understand that it is difficult for a middle aged, settled, professional with only one academic focus in his life to recall the point of view of a young person, with all the world of options open before him, and with greater personal concerns confronting his mind than mulling some mathematical problem. Still I would have expected somehow in all a school like this to find a few who were as much in love with mathematics as I seem to recall having been even as a young student.

I remember regularly staying after school to practice for the math team, spending study halls doing math, and going to university libraries to read math books that contained what seemed like rare and beautiful information not available in our textbooks. (I also found time to play on the basketball team and the track team, sing in the madrigals and chorus and play in the band and the orchestra). I think this is a wonderful school, but in a way there may have occurred here some loss of innocence as to learning and discovery and its intrinsic joy and value, from the scramble to prepare ones vita for college admission, and possibly even to live up to someone else's values. There are also wonderful things going on, provoked by teachers who know better than I how to reach and hold the imagination of teens.

Well anyway, I appreciate the kids for sticking with me, especially in my most aridly humorless moments. The class finally evolved to where I was not really trying to cover any particular quantity of material, but simply to regularly expose the class to some beautiful and deep ideas. Also I did not have the time to grade a lot of homework, which probably means they did not do a lot of it. Consequently I do not really think this class should substitute for a similar class at the university level, and I would recommend that the same material be studied again in an atmosphere in which the students are really expected to master it. Of course one can conceive of schools or courses where time spent restudying this material would be wasted, so I am recommending a high level, well taught, honors course at a good school.

Ideally one should follow this course by a Spivak calculus class modeled on the old math 11 at Harvard, which is no longer offered there because Harvard faculty believe there is no longer a population of bright potential math majors there who are also so unsophisticated as to need a first year calculus course. A second option would be to take a more advanced course like differential geometry or differential topology or even beginning analysis. The advantage, or disappointment depending on your view, of taking an especially sophisticated early course is that later courses usually don't really expect you to know that stuff. This means you will have the prerecquisites for more courses than you think you do, but that a lot of courses will seem tiresomely condescending.

A student from this course who finds himself at Harvard might do well to take math 21, if they still have that. The much more difficult math 55 still remains from the old math11-55 sequence but 55 would be quite a challenge in my opinion. Of course if a student feels the way the students at Harvard did in the old days it would probably be impossible to discourage him from taking the most difficult course available. Students in the 60's seemed to fight for space in those courses, even if not always wisely so. We thought it was a badge of honor to be admitted to the most ridiculously hard courses, and took the most well meaning contrary advice as a sad underevaluation of our abilities, sometimes rightly, sometimes with painful results.

My advice is to never underestimate yourself, but neither should you underestimate how hard you are going to have work to realize your true potential. Getting into the right course in college is important and deserves some study. Always interview the professor, look at the book and interview students who have taken the course. But if you are an ambitious hard working math lover, don't listen to the negative comments of some lazy friend or math hater about how hard so and so is. The advice probably won't apply to you. Also attend the first meeting of a course you are interested in taking to see if you like it, or audit it the year before if it is particularly difficult and important. I sat in on and studied an entire semester analysis course in addition to my regular load just because what I learned helped me in my own courses. Afterwards I didn't bother to take the audited course, but I learned more from it than many I did take.

A rule I always followed, which has exceptions, was to take courses from full professors and avoid courses from graduate students. Grad students may be wonderful teachers but they usually are not, and they don't know nearly as much as professors. People who brag on how good some grad student is as a teacher of some lower level course may really mean that he teaches an easy course. Of course there are schools where people get to be full professors just by being the oldest person around, and where the younger professors are the best. In general the better you think you are, or want to be, the more highly qualified teachers you should seek out.

 

[Eratosthenes]

My advice is to never underestimate yourself, but neither should you underestimate how hard you are going to have work to realize your true potential.

I read your whole post but that is just excellent, I could not agree more.

 

[mathwonk]

and by the way, unless his thesis is already approved, matt is obviously a shining counterexample to my old advice to avoid grad student teachers vis a vis professors.

But technically I believe he is both a professor and a grad student at the moment, or as one of my late coworkers at the meat market put it: "a card sharp and a professor too!"

 

[Manchot]

Mathwonk, just out of curiosity, why is your avatar a Pikachu? I've always wondered that.