Tuesday, July 26, 2011

I Lived To Die Another Day!

I'm thinking of blogging something  of importance. I was thinking of doing a post on, say, infinities and whether or not they exist in the physical universe.  Particularly in light of William Lame Craig and his horseshit, but also in regards Hamza Tzortis' bullshit. But I'm open to ideas that you lovely people might have. So, if you have a topic in mathematics you'd like addressed, drop a load suggestion in the comments section.  Depending on the topics suggested, it might take a while to get one done up (if I'm even competent to address the field). I don't know at what level I might address a given topic either.

My harebrained idea is to make it available for the maximum number of people to read and understand, but I'm open to deviating from that within certain bounds.

Of course, this could be the morphine talking here, but we'll see what kind of feedback, if any at all, this gets.


Phil Giordana said...

Fuck maths! Welcome back!

Justicar said...

I'm afraid I couldn't right now. I'm only a potential math fucker - the morphine is keeping my sticker from pecking up!

Thanks. =^_^=

Spence said...

Welcome back Justicar, good to see you're in one piece!

My maths questions are always dull. I can prove that with a crap statistical joke.

Did you know most people have more than the average number of legs?

Sorry. I'll get my coat.

Phil Giordana said...


Would that do for a sad cat?

Justicar said...

Thanks, all!

I think I'm heading to bed. I'm groggy as all get out.

TheStephenation said...

I'm going to have to deal with Taylor series later this quarter and they seem pretty terrifying...

Justicar said...

How are you with your derivatives, TS (elliot)?

Make sure you're pretty sharp on your differentiation skills, trig and logarithmic ones in particular. Also, pay attention when you're being shown how to use maple (or whatever, or get in a class that has some instruction on whatever computer algebra software you use.

Phil Giordana said...

Oï you! Yes, you, The Latest(tm): Stop abusing drugs and get over to Abbie's!

It's been dead (hahaha) slow today!

Also, have a good recovery.

TheStephenation said...

I'm usually alright with differentiation, although I'll have to brush up on logarithmic differentiation. It's integration that keeps killing me. They haven't been doing any software stuff with us in this class: it's just been assignments on Webassign and and some worksheets (and exams).

I don't think I've ever actually read anything by T.S. Eliot...

Justicar said...

The Stephanation:
you need to realize that differential and integral calculus don't go away in higher level mathematics. You've simply got to make sure that your differentiation and integration skills remain honed or else you're going to find many math classes difficult to successfully negotiate.

It's perfectly fine not to know a single proof of these, or perhaps even why they're necessary at this point. But you have to be fully comfortable with the moderate and large concepts or things will be difficult.

With respect to sequences and series, you'll be doing a fair amount of integration and differentiation along the way. With the Taylor Series, derivatives factor in heavily. Indeed, you can't use Taylor Series without derivatives.

If you have to take differential equations (despite its name), you'll fail without being comfortable recognizing the difference between a function and its integral, and how to use integrals to re-write functions to work with them.

Remember at all times that if you have a derivative (which you will have whenever you're dealing with a function - all functions are the derivative of some other function, even if only with clever restrictions needing to be set up), you have an antiderivative at play somewhere. Even if you can't find the antiderivative, it's still there. DiffEQ is heavily about integration, which is why we normally teach a module on it in any comprehensive integral calculus class.

So, if you're shoddy on your derivatives, start practicing them now.

I have some math videos on my youtube channel (though I think I've failed to address any series and sequences there - no questions on those has come up such that I recall) in which I work out a very, very, very basic (it's one of the two simplest classes of differential equations to be frank) differential equation. If you're not comfortable with the Fundamental Theorem of Calculus (and all that it implies), the problem type will be impossible for you to figure out.
Also included there are trigonometric derivatives, the likes of which you'll directly need in any standard class of this type.

The first one "proves" the derivative of the tangent function is the squared secant function. The second demonstrates the second the derivative of the tangent function (or the first derivative of the square secant function). It won't do to know just that f' of tangent is sec^2, and that f'' of tangent is secant tangent. You'll need to be able to follow all of the rules that crop up to get secant tangent out of f'' of tangent.

For the Taylor Series, you'll have to use some arbitrary number of derivatives of a function.

The same is true of the Taylor Series (and its special case called the Maclauren Series (that's where the magnitude between x and the a under consideration us a difference of 0). You simply will fail to be able to work the problem.

So, seriously and quickly, get back to your differential calculus roots and start practicing higher order derivatives or you're fucked.

Anonymous said...

Infinities... Bring it on.