Actually, I think I've resolved my confusion on the matter by searching around on the internet about differentials. The following link helped clear the issue up a bit: http://mathforum.org/library/drmath/view/65462.html
I understand why a definite integral of the form ^{b}_{a}∫ƒ(x)dx has the differential dx in it. What I don't understand, and what my teacher hasn't explained is why an indefinite integral (i.e. an antiderivative) requires the differential. Why does ∫ƒ(x)dx require that dx to mean...
Although I admit that my wording in the title was poor (I even said that I "didn't articulate my confusion very well" in my original post), I used the word "unrelated" to show that Event 1 doesn't actually have any bearing on Event 2 (winning the lottery doesn't actually cause someone to be more...
That makes sense. However, it just seems to me that probabilities have no physical roots in reality (they are just quantities invented by humans to make predictions with imperfect knowledge) and therefore problems like the gambler's fallacy are more philosophical than physical.
For a long time now I've been thinking about something I find odd about probabilities. For example, let's say that I win the lottery, something that is extremely unlikely. What is the probability that I will be struck by lightning? The odds of someone winning the lottery and getting struck by...
I understand the derivation that on an inclined plane of angle θ, the acceleration of the object on the plane, parallel to the plane, is a=g*sinθ. However, I was just thinking about it, and should it not be a=g/sinθ ?
I got this because sinθ = g/a. θ is the angle between the ramp and the...
As a high school student, I enjoy studying mathematics on my spare time. Having recently worked through a textbook on vector calculus, I am in need of a textbook that will give me a solid introduction to differential equations.
Any suggestions will help my search; however, I would prefer a...
I get what your saying, but unfortunately I wasn't there for the "information superhighway" hype; I was born in the late 90s.
I don't really have a concrete example. One just reads things when one travels through the wonderful world of the internet. Although I do remember reading somewhere that...
So lately (meaning the past few years) I've been hearing a lot about graphene and how it's amazing. It's apparently super strong, has a high conductivity and many other amazing properties. It was the subject for which a nobel prize was won, and it supposedly will change the future. I can't...
As a soon to be physics major I am about to purchase a laptop. However, I can't decide what I want. Should I go for a laptop with a dual core processor with a higher clock rate or a quad core processor with a slower clock rate. The laptop with the quad core is a bit out of my price range but I...
Actually they do sell what they offer...remember the programs are not the products, we, as viewers, are the products they are selling to other companies with ads. I doubt that this kind of programming is harmful. It definitely isn't helping get rid of misconceptions but I don't think it is...
I don't know what you people expect from these television channels. Everyone knows that these are businesses trying to get your attention, and if that means selling entertaining nonsense then that is what they'll do. People really need to roll with disillusionment better instead of getting irate.
I must say I was quite disappointed with the Hobbit. I am a huge fan of Lotr; books and movies. The best thing about the Lotr movies was that it kept very much to the Tolkien spirit. However, the Hobbit was way to cartoony and over the top, something Tolkien never was. That is what made Lotr...