Search found 25 matches

by Sabatini
Tue Mar 09, 2010 11:44 am UTC
Forum: Science
Topic: public misconceptions
Replies: 1073
Views: 151589

Re: public misconceptions

Maybe so. He keeps switching in and out of subjunctive, so it's hard to tell whether he's suggesting possibilities or positing certainties.
by Sabatini
Tue Mar 09, 2010 10:52 am UTC
Forum: Science
Topic: public misconceptions
Replies: 1073
Views: 151589

Re: public misconceptions

That's a bit of an ad hominem slant Monbiot is taking there, the good old debate tactic of labeling your unconvinceable opponent dogmatically so. Maybe the fact that that is the main message I drew from that article is biased by the fact that I despise statements of the sort, "no member of grou...
by Sabatini
Tue Mar 09, 2010 1:28 am UTC
Forum: The Help Desk
Topic: Coding This Idea: What Language?
Replies: 3
Views: 725

Re: Coding This Idea: What Language?

Many thanks!
by Sabatini
Tue Mar 09, 2010 12:50 am UTC
Forum: The Help Desk
Topic: Coding This Idea: What Language?
Replies: 3
Views: 725

Coding This Idea: What Language?

I'd like to write a program that would work as follows: when I enter a URL as an input, it would look at the source of the associated website, and if certain text strings appeared therein, it would increment the value of a certain cell in a preexisting spreadsheet by 1. (Why? I'm doing some recreati...
by Sabatini
Sat Mar 06, 2010 1:39 am UTC
Forum: Science
Topic: public misconceptions
Replies: 1073
Views: 151589

Re: public misconceptions

That no experiment has ever been conducted to observe near-lightspeed motion. I hear this one too often. "Relativity is just a theory; it's not like anyone actually knows what happens when something goes that fast!" That relativity is the theory of what happens when you (or rocket ships!) ...
by Sabatini
Tue Feb 02, 2010 12:14 pm UTC
Forum: Science
Topic: public misconceptions
Replies: 1073
Views: 151589

Re: public misconceptions

That science (here I mean "science" as far as it relates to (possible) experiment) makes statements about the way things are. Observation determines how things behave, and so experimental science makes statements about how things behave. Some people object to quantum mechanics for reasons ...
by Sabatini
Mon Dec 07, 2009 8:28 am UTC
Forum: Mathematics
Topic: Tangent lines passing through points.
Replies: 5
Views: 1306

Re: Tangent lines passing through points.

If you want a few hints, try these. (1) You know how to find the slope of a tangent line at x, right? You learned that fairly early on in calculus. (2) Think back to algebra classes. Remember something called the "point-slope" equation of a line? Back then, you were given a slope and a poi...
by Sabatini
Fri Dec 04, 2009 3:34 am UTC
Forum: Mathematics
Topic: Norm of a dot product
Replies: 25
Views: 4651

Re: Norm of a dot product

mike-l wrote:I think you are confusing norm with dot product.


Yes, yes. Silly me. :oops:
by Sabatini
Sun Nov 29, 2009 12:38 am UTC
Forum: Mathematics
Topic: Norm of a dot product
Replies: 25
Views: 4651

Re: Norm of a dot product

Dot products cannot, strictly speaking, be considered one-dimensional vectors, since any vector space or subspace must have additive inverses, and dot products are all nonnegative. It doesn't make much sense to talk about a norm for a vector outside of a vector space.
by Sabatini
Tue Nov 03, 2009 4:36 pm UTC
Forum: Science
Topic: I want to learn particle and quantum physics.
Replies: 30
Views: 4715

Re: I want to learn particle and quantum physics.

Avoid McQuarrie and Simon. It's a very readable book, but it lacks mathematical rigor. I've read a bit of Zettili's Quantum Mechanics, which so far appears to be mathematically sound. It is meant to function as the textbook for a series of introductory courses.
by Sabatini
Fri Apr 10, 2009 4:32 am UTC
Forum: Mathematics
Topic: How would you find the limit of this function?
Replies: 13
Views: 1500

Re: How would you find the limit of this function?

But from the perspective of wanting to work everything out from first principles, what guarantee do you have that \lim_{x \to 0} \frac{\sin x}{x} = 1 if you don't know anything about power series but only know geometry? A geometric guarantee. The geometric and algebraic proof that the ratio of sin(...
by Sabatini
Sun Nov 23, 2008 9:45 pm UTC
Forum: Mathematics
Topic: Integral Homework help please
Replies: 5
Views: 941

Re: Integral Homework help please

You're welcome.
by Sabatini
Sun Nov 23, 2008 8:51 pm UTC
Forum: Mathematics
Topic: Integral Homework help please
Replies: 5
Views: 941

Re: Integral Homework help please

The differential of sec(x) is sec(x)tan(x)dx . Let's see...what happens if we rewrite sec^5(x)tan(x)dx as sec^4(x) sec(x)tan(x)dx . Wow, there's a perfect differential in there! We should do a substitution. In general, trigonom...
by Sabatini
Mon Nov 17, 2008 2:26 am UTC
Forum: Mathematics
Topic: Bernoulli numbers?
Replies: 6
Views: 1547

Re: Bernoulli numbers?

Thankee.
by Sabatini
Wed Nov 12, 2008 4:41 am UTC
Forum: Mathematics
Topic: Bernoulli numbers?
Replies: 6
Views: 1547

Re: Bernoulli numbers?

I'd like it, if you please.
by Sabatini
Sat Nov 01, 2008 11:10 pm UTC
Forum: Mathematics
Topic: Vector projection.
Replies: 8
Views: 1366

Re: Vector projection.

You read my post correctly. I was wrong. Thank you for correcting me.
by Sabatini
Fri Oct 31, 2008 4:44 am UTC
Forum: Mathematics
Topic: Vector projection.
Replies: 8
Views: 1366

Re: Vector projection.

I'm not sure if this is the best way, but how I'd do it is: Make an orthogonal basis for the subspace you're projecting onto (for two vectors, you can use just a and b - proj a b). Project x onto each vector in the basis. Add all the projections together. An orthogonal basis isn't necessary, is it?
by Sabatini
Tue Oct 28, 2008 9:52 pm UTC
Forum: Mathematics
Topic: Proof of Taylor expansion of trigonometric functions
Replies: 6
Views: 2102

Re: Proof of Taylor expansion of trigonometric functions

I assume that you know how to obtain a Taylor Series. To prove that the expansion you obtain from Taylor's Theorem converges to the function in question requires showing that the remainder term of the nth Taylor polynomial goes to zero as n goes to infinity.
by Sabatini
Sun Oct 12, 2008 1:07 am UTC
Forum: Mathematics
Topic: Learning Calculus Online
Replies: 11
Views: 2034

Re: Learning Calculus Online

I highly recommend learning from a book instead. Then just take any questions you have to some place like this. It is, of course, feasible to learn calculus from any source. I learned the first year of single-variable from Ellis & Gulick, 3rd Edition. However, I would suggest getting yourself a ...
by Sabatini
Sat Oct 11, 2008 1:06 am UTC
Forum: Mathematics
Topic: Need help proving a trigometric identity
Replies: 11
Views: 2804

Re: Need help proving a trigometric identity

It can be broken down in the following way: =(((1/cosA)-(sinA/cosA))((1/cosA)+(sinA/cosA)))/((1/sinA)-(cosA/sinA))=((1-sinA)(1+sinA)(sinA))/((cos^2A)(1-cosA)) =((1-sin^2A)(sinA))/((cos^2A)(1-cosA)) =((cos^2A)(sinA))/((cos^2A)(1-cosA)) =(sinA)/(1-cosA) =((1+cosA)(sinA))/((1+cosA)(1-cosA)) =((sinA+co...
by Sabatini
Fri Oct 10, 2008 1:45 am UTC
Forum: Mathematics
Topic: Need help proving a trigometric identity
Replies: 11
Views: 2804

Re: Need help proving a trigometric identity

Maybe a conjugate or three?
by Sabatini
Thu Oct 09, 2008 10:28 pm UTC
Forum: Mathematics
Topic: Need help proving a trigometric identity
Replies: 11
Views: 2804

Re: Trigometric proving problem

Seconded. In general, transferring the problem to the world of sines and cosines is a good problem-solving approach.
by Sabatini
Thu Oct 09, 2008 2:52 am UTC
Forum: Mathematics
Topic: Where do cross product comes from?
Replies: 5
Views: 1714

Re: Where do cross product comes from?

"Why does it give the 'real' answer?" You know that the magnitude of the cross-product of a and b is absin(E), where E is the angle between the vectors, right? So the magnitude of the cross-product (which is what you usually concern yourself with in physics) is proportional to the magnitud...
by Sabatini
Tue Oct 07, 2008 11:19 pm UTC
Forum: Mathematics
Topic: Series question
Replies: 2
Views: 802

Re: Series question

Here's what I'm pretty sure they want you to do: Find a (binomial) series expansion of the derivative of arcsin(x), and then integrate that beast and find the constant of integration. Here's something else you could do: Integrate by parts an infinite number of times in succession. It's called Bernou...
by Sabatini
Tue Oct 07, 2008 12:06 am UTC
Forum: Mathematics
Topic: Seperation of variables for second-order diff. eq?
Replies: 7
Views: 1714

Re: Seperation of variables for second-order diff. eq?

Er, d-squared-x is just index notation for ddx. Inasmuch as an indefinite integral is (conventionally) an indefinite inverse of d, the integral of d-squared-x is dx+C for some constant C. Working out how the other integral works is looking to take me a bit more thought, though. You can integrate dtd...

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