differential equations
« on: January 18, 2007, 09:32:42 PM »
Damn this is a hard class.... :shock:


Kit

differential equations
« Reply #1 on: January 19, 2007, 04:16:21 AM »
Hmmm.....lets see.

+5-5=nothing
"Relaxing on the axis of the wheel of life."

bcarso

differential equations
« Reply #2 on: January 19, 2007, 08:14:20 AM »
Braun's book is really good for motivation, justifiably popular and in its fourth edition now.  ISBN is 0387978941.

For a more mathematical approach V. I. Arnold has written much and magisterially on the subject, including some fairly introductory things.  One advanced text on nonlinear dynamical systems essentially summarizes all of linear DE stuff in one breathtaking* page of matrix equations.  I practically laughed out loud when I read it, it was so terse---sort of the mathematician's equivalent of the physicist writing down the Schrödinger equation and claiming that it summarizes all of chemistry.


*well, I don't get out much...

Greg

differential equations
« Reply #3 on: January 19, 2007, 10:23:33 AM »
I had a great Diff EQ teacher in college. He was a British physics guy who someone got wrapped up in teaching a Math class. I definitely preferred his approach because he stressed how Diff EQ can be used to model real world situations... assuming ideal conditions of course. However his Math was rigorous and very complete theoretically.

In some sense, Math doesn't make sense until you take Calculus... then Math really makes sense when you take Diff EQ. Or at least the "why" question gets answered.
Greg Stein
New Orleans, LA

SonsOfThunder

differential equations
« Reply #4 on: January 21, 2007, 09:03:36 AM »
And in about 90% of the jobs out there, you'll have VERY little use for this.  I have been working as an EE for 12 yrs now.  Most of what I learned in school was just for background...to help me have an intuitive feel for what's going on inside the box/transistor and to help me understand the mechanisms of the problem.

Maybe this is just my experience.  Hang in there!  If I can make it through, certainly you can.  The main thing I learned in school is that if you can stick it out, you can make it through almost anything!

HTH!
Charlie
"The sow would rather have her ear than a purse." - PRR

bcarso

differential equations
« Reply #5 on: January 21, 2007, 12:57:36 PM »
Quote from: "SonsOfThunder"
 The main thing I learned in school is that if you can stick it out, you can make it through almost anything!

HTH!
Charlie


Agree.  It's mostly an endurance test, especially if you have been doing essentially nothing but school for all of the time.

A friend remarked that if one is still interested in the subject by the time you get an advanced degree, especially a doctorate, then you are really beating the odds.  Then, unless you have either played academic politics superbly well, or are just indisputably fookin' brilliant, you can go and get a programming job  :razz:, or if you are a tireless self-promoter and even better of some intriguing ethnicity, dazzle venture capitalists and nouveau-illionaires and start a company, and see how much of other-people's-money you can squander.

Once you are out and get some real-world experience though, you may well come to appreciate some of the stuff you took courses in and remembered just long enough to pass.  Then it may be time to go back to school with renewed motivation.  Your focus will be better---hormones will have subsided somewhat, and now you know what the material is for.  OTOH more than likely you've settled down and have a family and all of the attendant responsibilities, and will talk yourself out of the program as you come home at night and sink into the chair.

Education, like sex, is usually wasted on the young.

differential equations
« Reply #6 on: February 01, 2007, 10:31:15 PM »
Quote from: "SonsOfThunder"
And in about 90% of the jobs out there, you'll have VERY little use for this.  I have been working as an EE for 12 yrs now.  Most of what I learned in school was just for background...to help me have an intuitive feel for what's going on inside the box/transistor and to help me understand the mechanisms of the problem.

Maybe this is just my experience.  Hang in there!  If I can make it through, certainly you can.  The main thing I learned in school is that if you can stick it out, you can make it through almost anything!

HTH!
Charlie


Diff Equations are of little use in real life because computers solve them for you using numeric calculus!!!!

The great thing about them is they are so universal. ie the vibration of any membrane has the same diff eq.  Only conditions of contour ( I never study maths in english so I dont the exact term ) change the problem.
Wonderland Audio Spain
www.wonderlandaudio.com

differential equations
« Reply #7 on: February 01, 2007, 10:52:13 PM »
Quote from: "Wonderlandaudio"

Diff Equations are of little use in real life because computers solve them for you using numeric calculus!!!!


Hmm... Analyzing complex things with several feedbacks is much more interesting with pencil in hands than on computer screen, at least you feel better how it depends on parameters.  :cool:













 :green:

differential equations
« Reply #8 on: February 01, 2007, 11:03:12 PM »
Totally agree... The problem is most of the time the solution to a diff eq can only be an aproximation. Only a few very simple ones have a solution you can write as a real function, like the Simple Harmonic Movement, or even the Simple Attenuated Harmonic Movement ( only if attenuation is proportional to speed!!! ). Not far beyond that you get into the black hole....
Wonderland Audio Spain
www.wonderlandaudio.com

bcarso

differential equations
« Reply #9 on: February 02, 2007, 03:57:54 AM »
To some extent as a consequence of not having powerful computers, Soviet mathematicians achieved tremendous results in dynamical systems.


CJ

differential equations
« Reply #10 on: February 02, 2007, 04:36:29 AM »
Math is supposed to teach you to think clearly and honestly.
So you learn a skill, not a formula.
Nobody remembers formulas, unless your really weird, but the logical thinking part will stay with you.

If a rice krispie falls out of your cereal bowl, you have a dfferential of one rice krispie.
The is the whole course, pretty much.

Mathematica has gone the way like  most programs where the author hangs around too long, cluttered to the point to where it IS faster to use the slide rule, so what the heck.
If I can't fix it, I can fix it so nobody else can!
Frank's Tube Page: www.mif.pg.gda.pl/homepages/frank/vs.html
Guitar Amps: http://bmamps.com/Tech_sch.html

differential equations
« Reply #11 on: February 02, 2007, 07:47:55 AM »
Quote from: "bcarso"
To some extent as a consequence of not having powerful computers, Soviet mathematicians achieved tremendous results in dynamical systems.


Come on...

mikep

differential equations
« Reply #12 on: February 02, 2007, 09:44:36 AM »
Quote from: "Greg"
I had a great Diff EQ teacher in college. He was a British physics guy who someone got wrapped up in teaching a Math class.


I had a similar experience, at my university for some reason the Aerospace engineering department had their own diff.eq. course. (Im an ME by the way)  The professor was a jamaican engineer, and was far more stimulating then the weirdo teaching the math department's version ( I spent a few weeks in there first).

I think anyone who says things like "you'll never use this stuff" either didn't understand it or didn't go far enough past that point to appriciate it.  I dont want to sound cheesy, but in my opinion, understanding Calculus changes your outlook on life.  the concept of derrivatives, integrals, rate of change, area under a curve.. it is pretty universal.  Computational fluid mechanics, now THERE is something I'm never going to use.


mike

bcarso

differential equations
« Reply #13 on: February 02, 2007, 01:03:13 PM »
We each have our particular thresholds for considering some branch of maths unlikely to be ever applicable to anything we are interested in.  And then there's the often-avowed attitude of professional mathematicians themselves, who will even boast that their work is certain to never have "practical" application.  

But it (almost?) always does, eventually.  Perhaps the most famous example was G. H. Hardy declaring that his work in number theory was completely without applications.  Anyone working in coding theory and cryptography now finds that assertion quite hilariously false.  There are many other examples.

I tend to stretch the envelope a bit in my ambitions in re maths, particularly in how abstract something may be that I half-heartedly study being potentially applicable, but at the end of the day often am as lazy and expedience-driven as the next sod and turn to tools at hand rather than lengthy pondering and pencil and paper.  Computers are a mixed blessing. But I am quite serious about the Rooskies---maybe not so much now, but for a long time (and it's not just my opinion, but one widely shared) they did advance differential equations theory (in the dynamical systems case, especially the much-more-difficult nonlinear varieties) disproportionately to their numbers.

There's another effect at work sometimes as well, a counterintuitive one:  make it difficult to pursue something (music for example), and those who end up managing to do it will produce something of significance.  I forget who it was (Vidal perhaps?) who said that he would strongly discourage anyone in such pursuits, and would be particularly opposed to any state support for the arts (since he tends to be left-liberal that sounds implasuible, but he's also famously sarcastic-ironic).  Sounds quite perverse and with highly suspect motivations, but I can sort of see it.

Eric Best

differential equations
« Reply #14 on: February 02, 2007, 01:54:59 PM »
I rarely chime in, but here I will.  I was a math major (and teacher).  Everything completely cleared up when I took a theoretical calculus class.   This was my final math class to graduate. All we did was prove everything I had learned in all of my previous calculus classes.  It lifted the great veil on everything.  

This might be a good class for the engineers to take too, but it was a lot of work and they have to get a lot of other classes in.
If you are too open minded, your brains will fall out.

differential equations
« Reply #15 on: February 02, 2007, 02:23:18 PM »
Quote from: "Eric Best"
I rarely chime in, but here I will.  I was a math major (and teacher).  Everything completely cleared up when I took a theoretical calculus class.   This was my final math class to graduate. All we did was prove everything I had learned in all of my previous calculus classes.  It lifted the great veil on everything.  

This might be a good class for the engineers to take too, but it was a lot of work and they have to get a lot of other classes in.


In Soviet universities it was from the beginning, to prove everything you learn. Nothing was given like, "Study and remember, it is the truth". I think, it is the main reason of advance of Soviet mathematicians, not that funny rumor about absence of fast computers that forced them to learn mathematics well.

...speaking of differential equations, I was impressed by analog computer when I got a first access to it. I played with it trying to imagine possible and impossible combinations of feedbacks and see what happens with the system when some parameters are changed... Playing with it, I was thinking also about human beings, that are self-regulated systems, inside of a bigger system... And dreamed about differential equations that reflect processes in human body and mind, in society, particularly on stock markets that are parts of the whole system...  :cool:

AnalogPackrat

differential equations
« Reply #16 on: February 02, 2007, 03:32:22 PM »
At this point in my life (40 years old) I really wish I could go back and take a few courses over again.  Calc and DiffEq would be on the list.  As an engineering undergrad I had to take 3 semesters of calc and one of diff eq.  I had the misfortune of having a really nice old, grandfatherly (Gandalf-like, in fact), prof for the first semester (intro to derivatives, etc.).  Class was at 8am four days a week.  Ugh.  Anyway, the prof was way past his prime and I later learned that his wife was ill (I believe she died sometime the next year).  Classes were not productive and I was immediately behind in understanding calc.  

Second semester (integral calc) I had this energetic little middle-aged woman prof who was big on memorization.  It sucked.  Third semester was multi-variate calc and I had a really great post doc for lecture.  He was very energetic, entertaining, and descriptive in his teaching.  I made up a lot of lost ground there.  I'll always remember the way he explained the equation for a cycloid.  He grabbed the trashcan and emptied it on the floor in the corner, put its open face flat against the chalkboard with the rim resting on the chalk tray, then he held a piece of chalk firmly against the seam of the can (touching the board) while rolling the can down the chalk tray.  Not only was this fun to watch, it actually clarified the whole thing in my head nearly instantly.  He was also into jazz and fusion.  When Shadowfax played on campus that semester he was on the front row and clearly having a blast despite his leg cast (rock climbing accident a few weeks earlier).

Diff eq was taught by an ex-Navy lecturer.  Very rigid, very dry, like something out of the 40s or 50s...which he was.  His one quirk was throwing in a little numerical solutions stuff.  You had to have one of those $$ old cruddy first gen BASIC calculators to take the exams because he always had one numerical problem on them.

So, what's my point?  The teacher and the method of teaching makes at least as much difference (sorry...) as the student with respect to information transfer.

A P

p.s.  Wavebourn--in grad school I took a graph theory class that was taught in the "prove everything from first principles" style.  It really worked for me--that was, by far, my favorite math class of all time.  Got to meet Paul Erdos hat semester--he was gone five years later.

p.p.s. I've forgotten how to do special chars--umlauts and such...
If it is to be, it is up to me.

differential equations
« Reply #17 on: February 02, 2007, 03:50:08 PM »
Quote from: "AnalogPackrat"

p.s.  Wavebourn--in grad school I took a graph theory class that was taught in the "prove everything from first principles" style.  It really worked for me--that was, by far, my favorite math class of all time.  Got to meet Paul Erdos hat semester--he was gone five years later.


Sorry, I hated graph theory... I thought it was kinda useless for electrical engineering.  :cool:


 

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