18.02/18.03

Quote Book

Fall 1999

*I could call that *r*, but I'm afraid to, so I
won't.*—APM

*Let's imagine the circle instead of trying to draw it.*—APM

*The gradient...what? I just said the gradient!*—APM

*Proceed by the seat of your pants...or whatever you're
wearing!*—APM

*In just shutting your eyes and following fundamental
theorem of calculus, we are led into a grievous error.*—APM

*Write it in terms of differentials, so that chemists and
other such people can understand you.*—APM

*The integral of wah blah wah wah blah...*—APM

*If it makes you more comfortable to write *λ=t,
y=1−t^{2}*, well, get over it!*—APM

*So the answer*—*what?!*—APM

*I'll have enough time before −3 minutes at the end of the lecture.*—APM

*If I wish to be extremely pompous, and of course I do...*—APM

*Put this in your notes. I don't want to write it on the
board*—*I got no room!*—APM

*Whoops! We have a collision of equations here!*—APM

*By the 18.02 chain rule, not by the piddley one you
learned in 18.01.*—APM

*If you give it to a particular chemist, and by chemist I
mean a particular branch of **MIT, probably all of MIT except the math
department, they'd say, "What?* *There's no proof there!"*—APM

*The process by which you got from here to here is highly
shady.*—APM

*And the answer is...no...but for all intents and
purposes, yes.*—APM

*And the answer is...it's already on the board.*—APM

*It's TRIVIAL.*—APM

*THIS is a formula.*—APM

*Given an infinity of paths to choose from...there's a
tendency to sit down and despair: "Which path am I supposed to
choose?!"*—APM

*Get over it now!*—APM

*Mathematicians have one, but it's of no use to the rest
of the world.*—APM

*It's good enough for awhile, till it's not good enough
anymore.*—APM

*I now know the magic value of *a*.*—APM

*While the ant is walking around I'm on the inside
changing *P* and *Q* like mad...there I am changing *P*
and *Q*, and the ant thinks nothing has happened.*—APM

*If you've got a hairy line integral around a simple
curve, magic things happen.*—APM

*You know you know, but you're not gonna say because
you're afraid the other guys are gonna get you after school...*—APM

*Of course you get the answer if you're lucky.*—APM

*I could have made it even hairier, but after a while I
decided enough was enough.*—APM

*Ok...that's unfortunate...no! Because we have Green's
theorem to save us!*—APM

*Put that down in your notes...I don't want to write it
down.*—APM

*I'm in trouble, not deep trouble, just puzzled...which I
just experienced.*—APM

*No one would believe it was true unless it was proved.
Unless you accept authority, which you shouldn't.*—APM

*There's no way of learning that except by brute force.*—APM

*Of course I should try to confuse you just so you'll get
unconfused. No, lets not do that.*—APM

*I'll do it rapidly and you'll be just as satisfied if
not more satisfied.*—APM

*It's easy to say plus or minus.*—APM

*After a while it's not so tiny anymore and all bets are
off.*—APM

*Nor has anyone ever proposed to me...*—APM

*Green's theorem*—*the one we know and love.*—APM

*It's an...it's an...it's an abstraction.*—APM

*Per per per per unit length per second.*—APM

*What goes in must come out, if the fluid's reasonable
like *H_{2}O*.*—APM

M* had a name change*—APM

*Something unknown to all these little ants floating on
their little boats is, it's raining.*—APM

*The *RHS* represents what God sees from above.*—APM

*Green's theorem is true. It's us that are false.*—APM

*Of course it does...erra erra.*—APM

*I can't position an any at the origin. That'd be the
black hole, or the anti-black hole.*—APM

*In physics they can't calculate any line integrals and
wouldn't know how even if they wanted to.*—APM

*It's exactly what gives the secret guy from above the
ability to be pumping in (with a thin, hyperdermic needle).*—APM

*I don't think that's *z=y*. It is, because I
declared it to be *z=y*!*—APM

*An equation like nothing I've ever seen before,
but...courage!*—APM

*The evil song and dance of limits.*—APM

*That's not a bad integral. That's a good integral.*—APM

*Which piece of cantaloupe would you rather have? This
one! Unless you don't like cantaloupe...*—APM

*I keep integrating until I get to this magic moment!*—APM

*Which θs do I want? Which ψs do I want?*—APM

*Life can only get better after this.*—APM

*All theorems have three names. A French name, a German
name, and a Russian name*—*each nationality having claimed to
discover it first. Once in a while there's an English name, too, but it's
always Newton.*—APM

*If an any could visit every part and never find anything
peculiar...*—APM

*None of these are any good. All of your suggestions are
terrible.*—APM

*It's one, masquerading as *δz/δz*!*—APM

*If an ant would fall off, then it's not a closed
surface.*—APM

*Someday you have to grow up and use the same variable
for something, well...today is that day.*—APM

*You didn't tell me. That's your answer to me, not my
answer.*—APM

*Nonetheless, it's useful despite being your favorite
topic.*—APM [Regarding the independent chain rule]

*That long song and dance about Jacobians.*—APM

*It's better to keep it out and hope for good things.*—APM

*Half the time it must be pointing up, half the time it
must be pointing down. Except when it's sideways.*—APM

*I know you would fall off a cube but the ant wouldn't
fall off the cube and the question is whether the any would fall off the
cube.*—APM

N. N* is an integer.*—APM

*I checked a few engineering books and they're full of
it!*—APM

*What you can say is, I've done an experiment which
disproves (the fact that heat flows from hot to cold). But everyone will
think you're a crack pot.*—APM

*On the other hand, the more I say, the less you'll
understand.*—APM

*If you're upset just pretend you're in some foreign
country where they write zs as xs.*—APM

*Stuff is the same as thing.*—APM

*One only understands things the 2nd time around, which
is why you have to keep taking mathematics, so you understand what you did
before.*—APM

*So never stop taking mathematics.*—APM

*All I have to do is change the E to F which just
involves erasing the bottom line.*—APM

*That's not right. Well, it is right except it isn't
quite...*—APM

*Now we're up to today.*—APM

*Ugliness supersedes all rules of grammar.*—APM

*I stood on my head telling you to never substitute into
that formula.*—APM

*If you want to be babyish you can put it in the notes
but I'm not gonna write it and subject myself to shame.*—APM

*My apologies, so let me ruin your notes.*—APM

*I propose to do things entirely in your heads.**—APM*

*If you want to look smart in recitation with a vein of
hope of boosting your grade a point or two...*—APM

*There being no such thing, I can make it anything I
like.*—APM

*Come on! It's my only visual aid all term! It's gotta
work!*—APM

*Maybe little babies on the Internet do this.*—APM

*The reason it is not zero is because it makes no
sense.*—APM

*You'll see this term in your book, if you've read the
book. Don't comment.*—APM

*When you write a book you're not allowed to wave hands
too much, but you don't even have hands to wave*—*you have to
wave pages.*—APM

*It's clear, well...it's not that clear but it's clear
to me.*—APM

*You could put those together as one superconstant but
there'd be no advantage.*—APM

*Your professor is pleased!*—APM

-ix* is a general suffix,
as in suffix.*—APM

*Lets be pompous and put a proof.*—APM

*The computer method is grossly inefficient.*—APM

*...boats that are smuggling drugs.*—APM

*However, for the enrichment of your vocabulary...*—APM

*Every differential equation has an uncountable amount
of integrating factors. It's usually impossible to find any of them.*—APM

*They make the fatal fatal error of differentiating
this equation the way it stands.*—APM

*If you don't know anything, that's good.*—APM

*Grown-up terminology: mvah, bah!*—APM

*Your powers of generalization will get you as far as
you want.*—APM

*It's the wrong answer anyway. What's the point of
having three decimal places?*—APM

* Achoo!&mdash*Audience member

*Excuse me...uh, excuse you!*—APM

*A slope is supposed to be a number so when it approaches
infinity it gets upset.*—APM

*Numerical calculations of an **ODE was a job
that took all summer.*—APM

*#1, #2, #3, #4, #5 in that order.*—APM

*You are under fake moral obligation to solve.*—APM

*We don't bother with details from everyday life in here.*—APM

*That is the one solution that separated the upward-going
sheep from the downward-going goats.*—APM

*Mathematics is the art of accurate reasoning on
inaccurately-drawn figures...let that be our motto.*—APM

*This is a box. They always call it a...you know, a box!*—APM

*A good spring*—*not the bad kind.*—APM

*You can solve pairs of simultaneous linear equations,
except when you can't.*—APM

*Since you did me the honor of coming here after what I'm
sure was a grueling 8.02 exam, let me return the favor.*—APM

*That's the way they look*—*start out bravely
and then die away.*—APM

*I could gloss over this point but I wouldn't be able to
sleep at night if I did.*—APM

*A little overkill doesn't hurt much.*—APM

*Now we have a genuine, good, bonafide equation.*—APM

*It's like one of those annoying crossword puzzles.*—APM

*Now where am I? Damn! I haven't made any progress!*—APM

*Who would have thought it? I did! I knew it all along!
Ha!*—APM

dx dx dx—APM

*My galloping senility*—APM

*ii...it's the most perfectly imaginary number you can
imagine.*—APM

*Put that in your notes! It's privileged information
since you came to lecture.*—APM

*I'm wondering why I didn't ask you to do it for
homework, but I'm getting soft.*—APM

*Solutions die as time goes on as opposed to living
things which thrive and multiply and are fruitful and all that...*—APM

*On matlab, you'll believe it when you see it. Or no, you
won't, but it's the best I can do.*—APM

*In the end, the dying exponential takes over and flops
down listlessly to zero.*—APM

*Complete in 29 words or less, and send in with two box
tops or a reasonable facsimile.*—APM

*Your exam will be reasonable, but I've said that before
and turned out to be lying.*—APM

[after reading Hale Bradt's 8.02 notes on the board from the
previous lecture] *Gotta stay one step ahead of you-know-who!*—APM

*This isn't gonna be a long song and dance...it's only
gonna be about five minutes worth of song and dance, but I'm still gonna
call it theory.*—APM

*They form a magic little charm circle that you can never
get out of no matter how much you differentiate.*—APM

*Bad means not special.*—APM

*Some function of...er...daah!*—APM

*Again, the grammar defeats me entirely.*—APM

*You differentiate tan and get sin again, with a sign in
front, or a funny little negative thing...*—APM

*It's important to learn to do calculations in a
systematic way. I don't know. I can't finish the sentence!*—APM

*Armed with these two formulas you can do any problem!*—APM

*I now have to decomplexify...ugh! That's not a
word...except within these hallowed walls!*—APM

*I'm doing it so that you'll learn them. So when you
don't learn them at least you'll know that you're doing something wrong.*—APM

*That's gonna be a two cup of coffee problem.*—APM

*I'll complexify it this way...heh heh! And make it
simpler.*—APM

*This is the second magic formula that will enable us to
do anything.*—APM

*I have to prove it because nobody would believe a
formula like that.*—APM

*Argh! This is absurd! Two mistakes in two inches!*—APM

*My mathematical conscience, since I've spent so much
time writing pseudo-physics on the board, won't let me just write the
formula.*—APM

*The Germans 100 years ago wrote the best text
books...They were experts of pedagogy.*—APM

*I don't make a fetish of induction. I'm not knocking it.*—APM

*Motivation in the middle of the period!!*—APM

*You write in the word equation. I want to use as little
chalk as possible.*—APM

*When I was a fraternity boy I had to memorize the Greek
alphabet forwards and backwards. I reject that part of my existence.*—APM

*Of course, you have to apply the operator to both sides
to preserve the peace and quiet.*—APM

*They're annihilated by the derivative operator!*—APM

*There is a theorem now which has to be invoked...I now
invoke the theorem.*—APM

*Put this in your notes! And the second reason is...even
if it weren't it would still be okay because...okay. There is no second
reason.*—APM

*I'll be able to get it all in if I talk twice as fast as
I am now.*—APM

*This is where the book and I part company.*—APM

*We're now going to calculate the 2nd *log*
polynomial...grr! Remember, you saw it here first!*—APM

*To give the devil his due, he was a nice man, actually.*—APM

*There is no advantage, okay, stop me from saying this,
but there is no advantage in copying, copying, copying.*—APM

*Times doddle-*y*. Or was that diddle-*y*?*—APM

*I'll let you out early...you know, as soon as you stop
liking culture.*—APM

*This is my way, and it's going to be your way also.*—APM

*Why? Because if you don't, you'd better!*—APM

*Computers get the wrong answer, only people can get the
right answer. That is why you are. Computers will always get the wrong
answer to that.*—APM

*Zero is always less than one!*—APM

*If I just inspired two of you to learn it, that would be
double the number that would normally know it.*—APM

*We've been away from differential equations too long. My
God! Half an hour and I'm getting withdrawal symptoms!*—APM

*6/20? Crazy number!*—APM

*Fair answer, but the wrong one.*—APM

*In practice, there's no difficulty with that except
sometimes when there is difficulty.*—APM

*The other terms are negligible compared to them, no
matter how big they think they are!*—APM

*By abusive language, as the French say, infinity!*—APM

*You must always skip a step.*—APM

*I apologize for you that are theoreticians and know
everything.*—APM

*If it converges when *x=0*, that is NOT
considered exciting.*—APM

*Since I'm lecturing, I can get away with anything!*—APM

*You're at MIT...by definition, you can do that yourself.*—APM

*I can either be a good boy or a bad boy with this
calculation.*—APM

*It's the variable lurking in the wings, waiting to come
out and be the answer.*—APM

*Calculagate...calculate...*—APM

*Translation: blah blah blah blah limit limit blah blah
blah blah.*—APM

*And *n(n–1)*...ha ha, stop! Aah!*—APM

*You put it all on one line at the cost of double the
parentheses and triple the difficulty.*—APM

*Now, lets be a differential equations course.*—APM

*Watch this! It's real cute.*—APM

*Crazy, definite, improper...*—APM

*You agreed to let me be sloppy. Or I agreed that you
would agree to let me be sloppy.*—APM

*Awww...sh...I don't want to baby you...even if you don't
know what I'm doing, at least you'll feel like you're being treated like an
adult.*—APM

*I'm pulling myself up by my own bootstraps. What are
bootstraps anyhow? ...something you pull yourself up by...I don't know!*—APM

*We're on a desert island, we've got nothing to do. We
wonder what the Laplace transform is. That ought to keep us occupied for 10
years at least!*—APM

*I can't explain why I'm doing what I'm doing, but it's
really the thing to do!*—APM

*I'll write it down in little letters here that the back
row won't be able to read, just to penalize them for sitting there.*—APM

*This is pattern recognition here...make your own
pattern!*—APM

*Use any number. p you could use, if you were foolish!*—APM

*This guy doesn't go so fast that the other guy can't
kill him in the race to infinity.*—APM

(s^{2}−1)y = s + 1/(s+1) =* ...diddly
stuff.*—APM

*Weird!*—APM

*Where shall I write? Where shall I write! Don't know!*—APM

*Goddamn! I keep writing t!*—APM

*We can't take a day off in 18.03. It's a really
important subject, unlike others!*—APM

*This next line is the shakiest thing I will do all term.*—APM

*Gulp! There isn't going to be room!*—APM

*Since I forget it, when I do remember it I want to show
everyone that I do!*—APM

*If you can see purple in the back row...if not, you
shouldn't be sitting there.*—APM

*Use the desert island method! You have 20 years to
figure out what this is so lets figure out what it is.*—APM

*Calculate it, all right? Lets do it! Grrrrr...*—APM

*Mentally psychological psychological mathematics.*—APM

*It looks horrible, but it's always darkest before the
dawn...like any of you have seen dawns!*—APM

*Is the microphone on? No? Shit! ...I guess it must be
on.*—APM

*If the EE department has another
convention...bless them.*—APM

*It's not dramatic enough. Damn.*—APM

*Bah! I don't know what I'm doing!*—APM

*I was thinking of torturing you by calling it *t*. Well,
lets call it *t.—APM

*How should you have thought of the Laplace Transform all
by yourselves and covered yourselves in eternal glory?*—APM

*Ergonomically insufficient eraser!*—APM

*Almost all of the rest of the lecture has quotation
marks around it meaning that it's not exactly mathematics and I'm not
exactly responsible for it. I'm definitely not responsible for it. I'm
definitely not responsible for it but you are.*—APM

*This is good enough to be in colored chalk!*—APM

*This is our system. Solve *ME*!*—APM

*It would be grossly, totally, absolutely wrong!*—APM

*Your book then goes on to explain how to do this with
Laplace Transforms. Heh heh. I am very kind and we're skipping that, too.*—APM

*Nevermind what I did. Just write it down somehow.*—APM

*This must be in pink! Where's the pink? Or whatever the
color is! It's called color-coding. The ideas in this course will be
color-coded for the second half of the course. Since I have a brand-new box
of chalk!*—APM

*It's one thing to watch a point moving. Grroowwerr!*—APM

*It has a bunch of vectors like this...aah! Stop me!*—APM

*I don't know if they're the most important. They're the
only kind you can solve.*—APM

*This was the beginning of time. Namely, four weeks ago.*—APM

*The notes were written because I didn't think the book
to be sufficiently intelligible.*—APM

*Start with this and by brute force follow it through
with your nose.*—APM

*Fill in with curves near those, which are curvy.*—APM

*Now we're gonna pass the law of conservation of pink!*—APM

*The origin of which sits there forever, perfect,
contemplating its navel.*—APM

F = ma*? It's always *f = ma*. No! *ma = f*!
That's Newton's other law!*—APM

*Blah blah blah blah blah blah blah. Trust me!*—APM

*Some people need to hear my say it. Nobody likes to
read. Even faculty won't read.*—APM

*Slowly*—*like moving through Jello.*—APM

*It's not fair that *−2* should have a word but not *+2*.*—APM

*Computers have their own set of difficulties.*—APM

*So it remains, in splendid isolation!*—APM

*Mathematics is not a science.*—APM

*Unless you cheat, this is the region *D*. Ha ha.*—APM

*I'm just speaking common language, that's all.*—APM

*If I seem rather indecisive, it's because I am.*—APM

*You don't often see them. In fact, you do often see
them, I've just been careful not to let you see them.*—APM

*Trust me...well, don't trust me! Do it! Look it up!*—APM

*I'm not exactly doing your homework for you...I'm just
approximately doing your homework for you.*—APM

*The English is rather tortured, but you know what I
mean...*—APM

*Not all theorems are green worthy! I have to be careful!*—APM

*Talk faster...no no, talk a lot faster! I can't be this
slow, I mean, Hale Bradt would have finished the extended Ampere's law by
now!*—APM

*The even series is the hyperbolic *sinh*, the odd
series is the hyperbolic *cosh*...these crazy, drunk things!*—APM

*In a certain deep, but shallow sense...*—APM

*This is a danger curve! Be careful!*—APM

*Just relax and sit back and laugh!*—APM

*I can continue in this merry way...*—APM

*This'll be the only part of this lecture you'll
understand.*—APM

*You'll understand in a second*—*not a second.
Maybe five minutes.*—APM

*Now I'll have matrices and I'll lord it over my little
sister.*—APM

*You get the picture, as they say!*—APM

*Now, all of what I've said is true, but it's misleading.*—APM

[In a funny, low voice]* As is well known by us in the
field...that's to put you down so that you can't complain that you never
learned it.*—APM

*Talking is of equal importance as computing, at least if
you read books and papers and write them.*—APM

*Grahh! Grahh! Grahh! You're not supposed to erase, but
once in a while, it's okay.*—APM

*The solution..."as is well known..." that's so
you don't fight back!*—APM

*This cannot be a simplification. Of course it isn't. You
don't have to do any less work...you have to do all the old work and a
little bit of new work. It's just a change in language.*—APM

*Just to mutter for two minutes*—*oh, I can't
mutter for too long...lets mutter at the end of the period, or else I'll
mutter next time.*—APM

[In singsong voice] *You do hear...bah bah bah BUMM!!!*—APM

*I don't think you'll have any trouble following it,
it'll just seem mysterious but that's fine. That's the way mathematics is.*—APM

*For the rest of this period, t and x are the same
letter.*—APM

*"Ah ha!" he said in Latin! He covered himself
in ego and glory.*—APM

*Here's my function. I'm gonna calculate the thing
of...thing means Fourier series.*—APM

*I know in advance that I won't need it, so heh heh. *[Writes
"heh heh"]—APM

*Oops...I called that *A_{n}*. It was
supposed to be *B_{n}*...you're adaptable, right? I know
you're not adaptable, but be adaptable.*—APM

*Your middle ear is a spiral filled with fluid. A sort of
pink fluid.*—APM

[Regarding the final exam]* It won't be to pick your
favorite differential equation and explain how it changed your life.*—APM

*Aah...sigh sigh sigh...*—APM