Math help - eigenvalues

[Jeff7]

Originally posted by: TecHNooB
That's so wrong. Calculus is amazing! Maybe some of the procedures may seem like memorizing if you have forgetten the proofs, but the results very useful!

I guess it has to "click" or something. 2+2=4, I can see how that works. Sine of an angle versus what it does on a triangle, makes perfect sense.
Going from x² to 2x, or from ln(x) to 1/x, or whatever it is, it just seems like a procedure to memorize; it doesn't really mean anything to me though, like saying "A chicken turns into two sheep." It's just mentally like, "Well...ok then." I memorize it, but it lacks any practical meaning.
(Logarithms are kind of out there on their own, that chapter was skipped in AlgII back in 9th grade, and I never saw logarithms again until Calc II in my sophomore year of college.)

 

[dighn]

Originally posted by: Jeff7

Originally posted by: TecHNooB
That's so wrong. Calculus is amazing! Maybe some of the procedures may seem like memorizing if you have forgetten the proofs, but the results very useful!

I guess it has to "click" or something. 2+2=4, I can see how that works. Sine of an angle versus what it does on a triangle, makes perfect sense.
Going from x² to 2x, or from ln(x) to 1/x, or whatever it is, it just seems like a procedure to memorize; it doesn't really mean anything to me though, like saying "A chicken turns into two sheep." It's just mentally like, "Well...ok then." I memorize it, but it lacks any practical meaning.
(Logarithms are kind of out there on their own, that chapter was skipped in AlgII back in 9th grade, and I never saw logarithms again until Calc II in my sophomore year of college.)

i don't know what the classes you had were like, but we were taught the meanings of derivatives, and how to derive by hand some of the basic rules like the power rule. once you do that though it's easier to just memorize the rules.

 

[blinky8225]

Originally posted by: Jeff7

Originally posted by: TecHNooB
That's so wrong. Calculus is amazing! Maybe some of the procedures may seem like memorizing if you have forgetten the proofs, but the results very useful!

I guess it has to "click" or something. 2+2=4, I can see how that works. Sine of an angle versus what it does on a triangle, makes perfect sense.
Going from x² to 2x, or from ln(x) to 1/x, or whatever it is, it just seems like a procedure to memorize; it doesn't really mean anything to me though, like saying "A chicken turns into two sheep." It's just mentally like, "Well...ok then." I memorize it, but it lacks any practical meaning.
(Logarithms are kind of out there on their own, that chapter was skipped in AlgII back in 9th grade, and I never saw logarithms again until Calc II in my sophomore year of college.)

There's a proof for those procedures involving limits. Remember how you take the slope of the curve as deltaX approaches zero? Hence, the derivative gives you the rate of change. However, doing this over and over is very time consuming and repetitive. Therefore you learn to do it like that.

I think it's unfortunate that so many people think mathematics is about memorizing procedures when it really is about thinking logically and seeing patterns and relationships between entities.

 

[alphatarget1]

Originally posted by: CraKaJaX
it's actually really helpful. Diff EQ however, was not.

Almost all physical phenomenons are governed by differential equations...

 

[Jeff7]

Originally posted by: blinky8225
There's a proof for those procedures involving limits. Remember how you take the slope of the curve as deltaX approaches zero? Hence, the derivative gives you the rate of change. However, doing this over and over is very time consuming and repetitive. Therefore you learn to do it like that.

I think it's unfortunate that so many people think mathematics is about memorizing procedures when it really is about thinking logically and seeing patterns and relationships between entities.

Yes, I remember the logical thinking and patterns and all that; and I guess it worked out for me, but when I came upon calculus in 12th grade, it was a brick wall. Math was easy stuff for me, for the most part. I wasn't quick at it - that Challenge 24 game, for example, I was rarely first to see the procedure to get to 24, but I could get it eventually. The speed just wasn't there.
But calculus: Brick wall! I had it in 12th grade and barely managed to pass; I actually failed the final by 6 percentage points. Then I had it again in freshman year at the university (this was around 5 years later), and it was as then as it was in high school. 69% on the first test.

And yes, I know that math should be about logic and relationships and all that; it was just fine until calculus. Then there were no patterns visible anymore, at least to me. All I could do was memorize the steps and chug through.

Limits also made little sense to me. Such and such as whatever approaches zero, and it can be an infinitesimal quantity above zero, but if you set something equal to zero, it all goes to hell. Solving those things also made little sense. Each step was another sledgehammer to the brain, I didn't know why it was being done, and it just did more and more damage with each incremental blow.

CalcII: There was more pattern-finding there. Sequences of numbers were given, and we were to somehow see the pattern. (2n-1)/(3n²-2), stuff like that. If it was much worse than 1,3,5,7,9, it was pure trial and error. On tests, the "find the pattern" section would get skipped and left for the end, if I had time to screw around with it.

Visual patterns and aural patterns - they're no problem. I don't like store-bought white noise generators because the recording of white noise cycles about every 30 seconds or so, and it becomes distracting. I haven't had much luck with LED candles either, as I have yet to find one that is truly random. (I may have to build such a thing myself, one of these days.)

Numeric patterns though, nope.

 

[CraKaJaX]

Originally posted by: alphatarget1

Originally posted by: CraKaJaX
it's actually really helpful. Diff EQ however, was not.

Almost all physical phenomenons are governed by differential equations...

Very true, but I believe that the stuff learned in Linear Algebra (at least here) is more helpful than the Diff EQ class was. When in gods name am I ever going to use the equation for an eel?