Notes

Notes

Attributes

Name	Value
splmm_dirmon_path	/colliand/notes/pdf
splmm_dirmon_auto	1
splmm_dirmon_subdirs	1

2000_MAT279_Nonlinear_Waves.pdf

2003_APM426_GR.pdf

Title Page

I. Force Free Particle Dynamics

Variational Characterization of Dyanmics; Hamiltonain Dynamics

Classical Free Particle

Geodesic Equation

Relativistic Free Particle

Special Relativity

Relativistic Charged Particle

2. Manifolds, Tensors

Manifolds

Vectors

Dual Vectors; Covectors

Tensors

Maxwell's Equations

Exterior Derivative

Lie Derivative

3. Curvature

Covariant Derivative

Parallel Transport

Curvature

Geodesics

4. Classical Field Theory

5. Exact Solutions

2005_APM436_Fluid_Dynamics.pdf

2007_Colliander_PDE2_Notes.pdf

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2008_APM421_Quantum_Mechanics.pdf

2008_09_08_APM421_Lecture1_Intro_Spectral_Theorem

Page 1

Titles

l.i

[fo..,.rc r \

[ltfi" J F~]

W".- L:c.,~"h: 'f'N,."y.? cr.s~,"1 t,(~,

Page 2

Titles

1.2-

.....

~ fEll

=

•

•

-

~ ... ,ll·.

II -):.

.-

~ .( v,, w') ).; 'Vi

" k ~,..J "" :1. u, .... .,/.,. ...J. 0" .. ",,1-<,:

•

ltj

r",s4-:~

Tables

Table 1

Table 2

Table 3

Page 3

Titles

•

C / I c.) ~ 1(.);

p.

'SltC.+ ",I .f-; 1)-

Page 4

Tables

Table 1

2008_09_15_APM421_Lecture2_Motivation_Schrodinger_Equation

Page 1

Titles

r ~ 1; t<

,_'ft.l 0( - 1' •• f., J: 'Ii!

-

lIw" "' .... '''I''f.w • ..,., .. J.J 4 1>- ~

~ -n.wr "L -hJA ~ J. 1,,1,'( 1..,_( ..

~ ,,'.fi.,~4t< 1,"~1 "...... '}Au. -" 1:..... .,... u.R 1/-V<cI .. (~,.)= II<.

Page 2

Titles

-u. -t A.. ..,..,,;. .. '!'f '1<1,," .,.; -r'f"

..,.,,~.

Page 3

Titles

, -

I~L~~-~-~

1 ?

,., 't~ I ~ ) t ".., C- Go{. d

f~ ..... ~ r:·"",Uio LeJi

I( +_ tt •• #I' -I1.f -+ "'I'£/,.,? A~"J .P r".~r.. 'b "I. .... , I w,

Page 4

Titles

,~ ... = ._ \, (. ,'v.. 'S) .

•

!J,.... (I""';) W~

_ _---r-· .......

2008_09_22_APM421_Lecture3_Functional_Analysis_Basics

Page 1

Titles

s.1

Jai"u/ ", {I" II == ~ v, v> Y.. It, Co _ ... .IIM --' III .

-p... //.1/rt,J "'" JI ~ ....,I,/e .' f,.11 .,,~,

.,t..4 h-/r,P .. , (I) (~, w" + ~.) = r<'< V;"'> r ~~, to> I (&J ( .. , r > ,: <~. oJ'S I

Ctm < Y, v '> >" 1/ V..· ... ,( 'V V,", ~ .. II{, r<, " C,

Page 2

Titles

s.2-

" S + I,., I sell'" I'IM

t!=.,.;-t.. 5fcc;.f.t.... 11..&..,;]

'tI 1\, It f 4: V +, ~ f 1(. III,_W '*,"""'1.-.. JAt-,

~l A i, ... _1- _......... .kf,.... A -'" ~(,r' ) = R (A I .

A- -r -t ~ ~ ~ ,.(r '" ..4 f . A,) 1o._J.H, :t,4" .(Jo.,o/r -.I- :.. L-.I.7.

Tables

Table 1

Page 3

Titles

.

<1,4;#)= <"',+)

,

! ;f {; 4 I I r .II = J '4l, ...

r ;: ~ 4, = f.' (f J~ = (f;) /' -

.... c .f.,..... of E I> (Aj) :t ~ .. ,·1,. :(

11

- ,

", f JI.

~ ~ {+': ~ ~ b (A,' 1:: f~ Eo w: L' t dl' == ~ ( (~Sf)

J. 11"+ - ~) ~ AI' :::1) "I ~ If/ ,I. , '?b) 6, :.0.

Tables

Table 1

Page 4

Titles

~ ; ~ l' ~ 1 + ~~/. 7L­

A, ; A,

P 'I .. f" Jt c1J~ ,/" • .f,- ,/ P"';: pt V ;f e ". A.... .. fw.s ... ! r.i.'&" 'I'" I-

,., .&_ • ".,...1-1• ,,'J'''''' _, ... 1-, f:s p_J..'. - (ti.Jlr-·1 ?) N("

.J.. KiP) /-tr Jf) <" . f ~ I pI = " .,.L (p-f: ...jo e 1/1',

J'/If 11A. - ..#-11 = t:J.

.4 : 1;, Ay"l!.... o4. s-"" A.... (r,. • .-..) ... f -I"'~)

Tables

Table 1

Table 2

Page 5

Titles

'CJ} t I '-n

-

Tables

Table 1

2008_09_29_APM421_Lecture4_Existence_of_Dynamics

Page 1

Titles

v '" (; j) (A )

!:- .... "'~ 5 t..w 11..1" 1>.... J,j..;!<- j A" ci,/""'. ~ ~"1 v<. ./. .........• /'-f>,~

A

~11-1~i""A ==- 5r~·---f .. ; (. + i) (A) -::: P(A' )

• 3 r,~4.'< 'l"""fVT .;1< .. ,," ....... "'/- uf/- • .I.J·,:'/-'

• If" + c. .. / '7t, _Iv:' OJ''''t.. c..... b< ' ,,·,-d t p. "" µ.I .fo i.-,& J.,.... ~ .f.

5JA.t~JlA) v °/~~

,

fi.M:~ SL..~ t,.,.1 ... 1.. ~ f,..... {..(!"w.", 1L.-/.? ........ >T-..J....X.

Page 2

Titles

~- .

~IMl)I: I];.(')JL

\I 4 ..fi! - z. ~ (c) [1'111 It-4''fIJ

""" (p. c(".l < t = o. 1Lw') t:..., (A - " {) I:' J4.,.. """ H 5, 01 - ~!l) -/

cf9

Tables

Table 1

Page 3

Titles

( I 0 (0 -/)

1= 00), H; ,.;> .

A: HI ~ tH.

Tables

Table 1

Page 4

Tables

Table 1

Page 5

Titles

c;> _ J).y ~ "V' - ,'<tt) JJ =- ~ i )J +' ( ,Yr - \'1') ~ IT =

~ r 1I..f.! ( t' -y - I I' V ) .r a d I} J

vrJ"

J 1 ,y /I -= II ~ V! 1 11

Q

,

Page 6

Titles

Ut\, -fa.,. Y {)fLM. -/-9, 5

.J...

)~ (e1A:"A eJAJ..f > ~ (,+, .p)-

>. -?> t>O I

c::::-. 'I { ( .iA-)¥ ~.A' A

'A

Tables

Table 1

Page 7

Tables

Table 1

Page 8

Titles

[,..tl 'L P r:.,';';- , -t (() "'"""" "/J< ) ~ ,'-":; (, .- i<....

1k fr-'-/-" L; (y uCt) = ,,-"HI/Ii

~"Y ~ /.r ..... / ~~i;'

?'""<;9<c ' 7L hJ e -~. If, + 11<

Page 9

Titles

9"-/ r'P/-Y ..j.;/ -rrN): V 0f, + E iii

< -I' ) v{n il(n ~) '" <: r?{f1+, WS1 f >

"'" j oJ., (e i 1M! 'f -( -,' II, 5;"',p >

'fl,.,r I 1J(f) ""0 (51 ~ 'V(.f 15" )

2008_10_06_APM421_Lecture5_Fourier_Tranform

Page 1

Titles

< -+, f- ( If I Xj 1 f > .

Tables

Table 1

Page 2

Titles

. A + ~ 11 I ~ :=. H ·P'1/ 'fH

... ,.,.-",., ""'''fIlllrWPW .N1f'kw I H ~..."Jq ~r,~?>

. '(.d )l 1) ': -j

(1)( : -"l.w~3.

-­

. fe

""

-

f"'1f SM"1$ ~NJJ"';)

Tables

Table 1

Page 3

Titles

~."

Page 4

Titles

s.'-/

- -

,...

~ l

L. f;.,,: v -fv.".,.~-I.,,-)

flC~t •• , & f'.! (A',,,'''''' ~

-

-fiJ{ • .., • ...., ~(~"ff)

-n.... I.:IIW&""''' ~ l..c ~SJ"& LtM.M.A • )

"

# ,s (4,,-#.''''''.'''' ~,1

(H.',,", I 'fl.,') Q c4/tl

6J,. f.tJ,v /LA. "'-It,~" ,

Tables

Table 1

Page 5

Titles

S.S

p,_ /I... .('., ... 1. .(J, ~.

:u

).,'AI.., ~r -!vl-

tk ~"f.N"

Page 6

Titles

.

'V.. -j...... cfµ'-" ,1 +..... ~., ,.,_ ...

Page 7

Titles

s. t-

fJ •

J ~ ~ 0 W<. q/",(, r Iv-t ell W\"""

~) I ",I,..' -t.. n... -t...e{.;. .(J. ~ 1...2.. !

,.,..,.,

..

"

~.,I •• ", .. by _ : ... ~ ok f,...·ftJ.. .1- ; ) .

f- = (p)V

Tables

Table 1

Table 2

Page 8

Titles

111" tl ~ C 1/111

(".... ...1 y t..IJ .f.... .. /wIi..A", ~t.. .. c< .I $ ~"1

1r< f'

Tables

Table 1

Table 2

Page 9

Titles

~t I.,. 1. -:: 1 -I- 1

r r ,.

Tables

Table 1

2008_10_14_APM421_Lecture6_Convolution

Page 1

Titles

k pae .. Q.'4

Tables

Table 1

Page 2

Titles

.101- J. r"!"::;2.

-

c

1/ I "

;V"k h .. f (1- -'-) + it _.L) • (,- L) :::. 1-

pi f /"

J.

r r I

_ +- _ _ I J. - I L

" I' - - p' - pIe r(. w<.

" 0( " I II ~" II' 1/"'( II I •

Tables

Table 1

Page 3

Titles

IX, II,,}

1/ h II I'

" , II

JI I- II I'

II y II I ::::

1

c. A f /I II, /) 1\ h /I

r ~ i' .

Tables

Table 1

Table 2

Page 4

Titles

t.

=

(Tj< n (~) =

Page 5

Titles

It I-

Tables

Table 1

Table 2

Table 3

Page 6

Titles

r f ~.

[

]

t [(

I~ (;) .~·_I C

I

2008_10_27_APM421_Lecture7_Diffusion_Equation

Page 1

Titles

-

Tables

Table 1

Page 2

Titles

- -;-;- J;;? j f .

(5e-lt -j IN\: IN)

N~te :

~~ ~ r)·

1 [~I Q I( I II ]

Tables

Table 1

Table 2

Page 3

Titles

e- d p.

5 1

e df

c,

---

Tables

Table 1

Page 4

Tables

Table 1

Table 2

Table 3

Table 4

Page 5

Titles

- J .

Tables

Table 1

Table 2

Page 6

Titles

+.b

Tables

Table 1

Page 7

Titles

f.r

( _.i .9, v ~ f ().v

11:~

PI'~W!. fl,., '\ f -h.v.. t~ MV { ~ ® 3 ,. V~ 5

.('.r .,·ct. e...v,,~ , ... :It.[ dAI-A +.

Tables

Table 1

Table 2

Table 3

Page 8

Titles

(.) v~ C,) ..... rJ. Uv>v."'~· t'Fr .I F. T. -{. 5~v

5,/'>/*' A n.... d,'({v~;,"" eJ"~Ivb..

I. -Iw"" 01- fI,... M :Iv- ,I J.h. ~ . TiN. f.,_I. @

-n. rr rr ( l t 1\ I .... V

,Jok. fkJ I e. ~ (n =- 14 (r) I . f O?

1J,w', by PI ..... ot.w£/.;· ~ I U V (f) /I ~ II 4> II

-

c { H+IJ,

Page 9

Tables

Table 1

2008_11_03_APM421_Lecture8_Harmonic_Oscillator_Hydrogen_Atom

Page 1

Titles

<f /Y" .. v. z· ... ~

",t:({ 5Af.>.~r"/ Ik d"Fv< kC'T'

A

Tables

Table 1

Table 2

Table 3

Page 2

Titles

,

__ >. v .

.

A =- 1 !

_x1t

I -xX (

+2.w ~ -l<)..j...

A- 5.t...1v;" 5' of!- -/k.. V ~JV4 µ""-

_ xy~

Tables

Table 1

Table 2

Page 3

Titles

t:l. Ci, J tk-- .... , (L.. j",-, w< frj,: '- -fr

Tables

Table 1

Table 2

Table 3

Page 4

Titles

A

~ f~-h,,~ ~J,h..,,'1 ~

c" 1101 a.. fO I r ,.,0""",',,,1 ?

r-frc. (t I )t. ]

e. H" (~) e

Tables

Table 1

Table 2

Page 5

Tables

Table 1

Table 2

Table 3

Table 4

Page 6

Titles

o I- ~ Covlo.,.../:? f-1-tN. ~ .. I V (J' I -

({ -

Tables

Table 1

Table 2

Table 3

Page 7

Titles

"

t~ p.

- R.tr

N,.kc( 12.,) Jl~ I -/ tJtt?

Page 8

Titles

(- WN

I

+ '-

+ (I_~) W ~O.

riC :: D

1

C!A.fOA\j f vev,'.J, r.J

r

I< -) /<. ~ I.

+ I< J a ~ {' 1<'/

Z [-f (£< -r) + ({-~)] qK-r rl<-I =-0.

K (1< 4- I)

Tables

Table 1

Page 9

Tables

Table 1

2008_11_10_APM421_Lecture9_Spectral_Theory

Page 1

Titles

?\

I,

f..f,.. ~ c Irl

,.

J .~

Page 2

Titles

-0.......- .3 r- .~.-r' f'f, , -, <: [,yo. 1 ~' - ~r-...f -+. E If{ •• ~

«A -.d, 1, ') ~ ).., < (~-~) J,-+. > = j,'" O.lA -wf.) -- "

Page 3

Titles

0·

A- -' ..l .

... ,.,!z..o ...... " ...... 1 t' s- /r .. I

Y/~ c( -C.... A-- --' ,.f

,-, __ -<) v--V' .. I.,..q it- /

t1A-" 1I1;',r~.' f r I ~.o A e- v:; (..-t ) .

~ 7, ....... ',w"). .1e.1-~... ~

IS .} ...... ,_,/ _.I c,..,w--f" w.K{y

(.w~~.II~)

.....

( A- .... }I....-. l.,f.... ~ 0 .6.< (&V H.

(A _ -;,)-1 I'> "",:f-,,,,,{y ~.I'" ...,.

Ir 4. (I " II ( A _ ~.r' ( ... - •. 1:t. II ! ( ,,~IJ I~ _,\..YLII~·

.c, -(~, Ai )

",l..,.c;L (:..- "

.(',~k~~ .. r

... IN-cr (

II _ ~:;r..."'t.,..

v-:v fA l .

1I ( j.. - A) -, (,4'- >'1 ,fA 1/

u -

.. -:r;f 3- "fAA fA-!"'- ~

~ ~ ~ ~ ,I II..- p ..... 1e' l;I tI

-h ~~

-/w. ""~fr.M"') , .. ~.J:,J <IJ~ y< c.f. ' .

,.....

......

Tables

Table 1

Table 2

Page 4

Titles

It ~J ~'>I) .-fA " _')J «, .,-.,;0

u.. W:, ... ,/. • .1 • ";-" "(I,...,...·w.. .,.'

II il '-"" I. tJ.W -/.I--.{.f.. .... µ.1<.{L .f,

---- - -

LJ

Tables

Table 1

Table 2

Page 5

Titles

II {p -A )rf- ... /I -7'"

c;, /1 -I.. II = 11..£ II -;;- I

J (r- ,\) -f .. 1/ .::.

L-' (;;l.J 1 ,~ <r (V) 0 ,....,-<- (VI

,,(A') C 1]2..-

Tables

Table 1

Table 2

Table 3

Page 6

Titles

~-'

.. ,

J A ).

Tables

Table 1

Table 2

Page 7

Titles

~~#ocL. -4-1 ~ ~ (,.

,.,

Tables

Table 1

Table 2

Page 8

Titles

vJ- ~ffNd ?

wL.r<.. :, fk UA; /or,...}! .

?

Tables

Table 1

Table 2

2008_11_24_APM421_Lecture10_Spectral_Theorem

Page 1

Titles

• ,A-,.~v,w. -/I.,.~

1,""':;- ,,(- I,,-k., " .. i-n,. ;"- 5 ~ .M

i1-- ,,...,,,1 ./Lf,.;'1 ~(~) ,.. • ).,'dli·,)

..... c" -h / f'" Iv , .. ' f v 5<'/ -/. ./L-r;,.,

>." <. " . -n... d", ". v (A ) '" A ~,," I ,,,Ii,)

'fl.1~ k.~I"'.I"'~ .. r..- .J {,{ltd -fI....

•

•

Tables

Table 1

Table 2

Page 2

Titles

3~t;S e. 1°'1 ($ .... ,..,. ...... -/.1" .. Py r-h)

D.. f, "'- "pp'" r;.1< lv, d-I;~' ,. f1... r n.... 5 OM ~ ,.f.J.. p"

~ ~K+t ak~I,-.fk ')

Page 3

Titles

}~

).<A1',+> .f- I<A+,+) == ()J.,41') +- <-f, ~A+)

~ >: <+IA--+> + >'<"""1 A-~>.

Tables

Table 1

Page 4

Titles

A" ;:: A

lit. _ A~) fit> UA. - j\.", Q \HU .

ik ~v""( t .I- OF"" A, - A~ ].!v • .(J.. r D ~ A. - A~ £(ji - M):r:

";:t!jv,,",C( ,./ AO} ",,~W5 I """ct ,f ,0.,. Wl~voJ. {µ... ~t

< eo +, t> S <. g'f, 'f )'k < 8 ~, !> '/~ V f, + "HI wi-- a ... o.

Page 5

Titles

, (v.)2...::= A

A : IH -? IH

A~O

, ? 1'4 <, .. f< " :x: 2 "" A we 1 • .1< .f.,. y- "" ::r: -:lC. IJ<.. w" /I

'2.. . -rT J.. / "2.. B ) r /- ~ C"- f.t.....,{ ~

'OJ

l-'-I) c~/",I.'" . ,==;;: B I V ~

u,J{iJe,,,,,,,fr. ~ t, - h ~ ] I g~ - l' ) ta, - 0) !.,.f h""'fv~

-f,.,r ,,1/ A. )')rJ"') g. f. r..., 'fY'dPc'" A r"'~·"Y{ qt,· ~.

Tables

Table 1

Page 6

Titles

AB:;- 1JA

< .H l' I 1- > ::: < JA' J4 B 1/ 'i' > := < $ 8 + I J7;' -1-:> ~ (B J/, +, J;i>r> i?:D

(If fJ" -/ IJ \10\: (",..,1, (l~ [""li1-1t- M UlJ("A.) -lJA{AI~

Page 7

Titles

("" {..,'. ,,{\ .,.(..,. _ w<,..x-l-, f, ~""'" f.., ~ ,..,.1 "" ./, ,:. J ,! I. ,

dtvU<j<f f1/I.<M).' ".iff -(.. vlf) .r ~-, (X> V x ~ L"'" ...I4-J '

11M' J w<- .'r- -h...1 ... , ,.1,.,-,·.1 pex I ". 0 V X € [~, aJ .... ""US

r-~A;:~·

fAN 1~/1: (t "". ",+" {)Jo.I.. 04 .,,;ov t .

-n...... ~ •. ' .... ,'} cf .... """s

",-s~~... ® .,')Lf

<t.

Tables

Table 1

Table 2

Page 8

Tables

Table 1

Table 2

Table 3

2009_02_04_CFT_Stang_Differential_Maxwell.pdf

Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

2009_02_12_CFT_Lin_Magnetic_monopoles_h-star.PDF

2009_03_19_CFT_Lie_Algebras_and_Spin.pdf

2009_08_Schlein_Tutorial_BIRS.pdf

Introduction

Mean Field Systems

Heuristic Discussion

Marginal Densities

BBGKY Approach (Spohn 1980)

Uniqueness for GP hierarchy (Erdös-Yau 2000)

Dynamics of Bose-Einstein Condensates

Theorem (Erdös-Schlein-Yau)

Uniqueness of Infinite Hierarchy

Coherent States Approach (Hepp 1973)

Bosonic Fock Space

Coherent States

Theorem (Rodnianski-Schlein)

2009_09_10_MAT194_Intro.pdf

Course Information

Calculus Distilled

Smooth Structure on Small Scales

2010_02_Huron_School_Grade2_Presentation.pdf

2010_03_PDE2_Picture.pdf

PDE_Overview

pde0

PDE1

PDE2

PDE3

PDE4

PDE5

PDE2_Marked_Painted

PDE_View_MarkedUp

PDE_View_Painted

2010_03_Vector.html

2010_04_Lagrange.html

2010_08_Istanbul_Notes.html

2010_09_Oberwolfach_Notes.html