integral forms and their conection with physical equations
TRANSCRIPT
-
\- \ssts-$t R
EC{i:- ss-X.=6d\
3'-
* t - ^ - - - - > o q.:: -;E I iT : :; .
=- i - ^:
= Q = =p= p a: - 5:1 > i7Fg-: { g"',"{: aiE !a;"; c '- t
==- s
-.u =c, E-;_- e - = E
g' i. i.:;= i i=;i-r.F +=; iniiE r --!+ i = EE;':= i=s t-i=?== :. S
='=: a 'g=il* i:= 3;tr:= ,; EE6 o o i"=3-=' ,u,, i ;;fa a =,: +
-; =. =
; N -.: : -= =.P =:6 e r i!!_[; -ii_l l\qEi2
oIXX
'==
l/,k;,a.Ina:-:
I
&l5sina".!tu:
3G
6 \i!4XE 'Ei^9di:@ rnrc'--d@^@,,t5
*- o!.ti o=@;aia9'*
oc -";_!D
+:*T@-=-
Y
-
=i= =:'== n ? ;L? i:: =r a
= 1;
== - = = e 1
= i: : .
= - S G
'i=- -.= a -- -
= 31?
=.
---.- r: > 1=:i=. := -,j 0; : ::ii;) r ;'=; i: i -:i.-i="\i i!::L s i E;=;;?:= iili. 1 =^;_l1=Ir =-.';;i c : ^ i ="-:i'= i;:;=, i =-i=ri
= =
i:i=S ;:.- , z '-.:i =
:;= i: ; r =i:;:t .'.ii:= --..-1:G::;:"=i :?=-!' pEi l-i
=i-i= r'-=iiil-=i"=_li=I I ii..,;= *i'_,._=..=E3 pS'= i.{ I pii i-Sj* .l; ? .:: L-;!.. ?. .: . : r_t:= o- jo ll; : ; j S ,, _ _-;:"t i
=:; a: i i-.. ? " i3 i ^ l^ r+ : . - a " =
.' =
: ir =
-
" i-t 1='= ' : !.=. i - a :* : v >
s.;ir: r"i=;1.i [' j;; iliil; ^'-lijj*i ;: ; =;ii=- j=, i itj i =; : : _:;ljr..i.. ri';.-''l =,.1 - : r ,,"-==f .j:3J: l.:'ir=-"t-3=='=.....i=-;..: -l:< ?; o
,=?! - i: i;;
=:, ..j i=- i:;1t.'ili..-= i t ;-,:ii1; t i = 1il i - ., : i 1;;* i i;; =i' :i =' = E
.ll;! i=i;:t is i E:;t':.';i.i;l;i I ';7;i:i : : ;'""1=-: i -l 1; lF=3S '
:.i ! * "l ? 2**i=:= i
== :1i; : : : j li: -' , :r',
= = : 3- =c-e".P-.=+G
=i;:; i==!7=_; ' f :,;i i:li:? , ;_l;i= t, =:fri + ;
!: i z ' :::
=
.
t,
ii;: " =1=;=; r i l:; " g=:r c !;l;3 Y 'i:F; F 5 7 ii * E*4: : ;
1 ;;liil =e ,=?;; ==i:1 ? ;iitP"*-llLiiE** iit i 7: + =-: i =i
; r ?- =l =
= iSS .=-!i el{;)=*i i:'=-:ilt:
=
i i,:=r e=:; - iill!== i|:t:t-; ;_+7 r.Ei_.,=si_E"- ?=:: ,=*5tr:: =1;[.:f : i;==--i ='"sS-=-E .+=: ir =iJi;==;'r-7E-'= ;.. 7 2s l ii = r o. -,= :-;,' = =i.: -- :SS :.= i" l i i :i E
'= . :;, *Zz ;l i 1,-=: 9 : ;
= -a l,' : i-*"1:;; i :=11 -
..! 1;:-_l=l;:..:i=l::i:: a =.irJ;:1=iEii e-+ 1=i=='.-.== t.-t7".,n I:_:" | - ii.:*i;-.ia_;= z1i :'n< -c^-r 5;_?=:piP : - i:.lJ'= oi s.'_-=G
=- . : ===rs:!= i;=t :i ::1 =i : ;:iil=:til=, za- Ii:11;="=::ili ll?l.j : ,iil". =:j?=,
'i; =1?,?t! i: t; I I i t:?+ i ?!ii 1ii ,=rfE+ =-r'i i=i=:: ;:!:7; l;f;_ =uti;i;=--t+;;;i =
la E;=_2 ,. =
-z = - i t:,i *,=-L ,=ii:i=i E=3== ;=
r;rg;r. i:i-a5:ii=-r ri=l:;1iii,;; i=
=i + ".-. z= i ,- L= ! i_ :==; : r' =;.- i =*
f 1=Jig =a i!=l=V :; ':'== I:t-: * i =?r==i;i?=;iii E: it,1 li: ?:tt-t i::" = i:ii'==;?;;1 =? ? i"s i =; 7 L7- 7 ;--= -: -- :.:,i;1: u .!?7i ,7'=;=i-? 7:;ii= Tir ', iri;;=i:-:r,i
r ii?=;i? =;*.t- :i' | ?=Sa1; ;;;=i =i;.:i. : iii;=
7;." . 1:s;! =E== =a --':7
=:,i' z 1=;:i
=r.. ;rS:=,- d?ea -
ll
tt,
r!Lt !st k+
' l"J)1
oP
i-
:
-
F;
ozz,
XHz
E
Eaoti
5/tsE.oz!)
;Yhh.:- .:"lilli*h
-
PE :lf =: its L Ir ? il =* :'cf =lii=i= ='== = +1 =' .)-* 1 Fi?=.A==;'i ,7i - E- E +=-
=- = i.a: " a i ,; = i= : =i
7-< i {;l=E!=Is i;I 1' , i - ;= \t:": i;i i = = I i -i 4. =-1- ,.'
-
i i'J ; i =, I I : z i i. " i.' ="
5 '7u'- ' Y c:' r ; : l' =+ : =; =.
* Erii=_t7_- i;;i'"'.';: t=:-r=I c._;;; = i" =-::l=_lTl,--:?i:i i -r =: =,it-*i3.=
--fs= 1S'
-
7c. ^. ij i z : {: J.J - e.ej-:- sli j=t. i.?-I iiiilli=,= FEl.::i
-:;.: ki5==i =i::7 .t * J * ol-t,==!:= : I i Sf-=i-- - Vd, iiI s ? .+i=Y='=13tLu: +;f 1i--
s:. Pe ? ",-- t.A:=n=! I i=S ^i= 2
=
-- lt I 5 =E =t= ig;E11 Y ='rs + =2r ;r -* * ttr : I e:= i I =iP :5:" " = [ t 'zi'|g , : I i, d 6'
"' T = i. -. -y, , , 3-' :
.
=2 1_ ; : '=:. ii= = - ii IE s.i.: 3 E : 5=" * .s. S=i:':'n:j----Y7A : g-
= a'{ o :
i ? ,P : 1 ? ? ?! =i : =.:4 s.
-q: = n = = il -. == .E F = =+
=
:"": ! r 6= + ii z i L i6 -."- + S i r- i +* p - - ft H= =
* =
A' | -= i =e s 17.
=..', ) =.
9 -6 ' /= = i ? .oo lB i? 3 , 3 :e i)' 7i-= r-i =
'i r_ :. -- =
=_= ; - - = - :
=='I=-i--i: i i =-'
; ==
==- rstl r'* 1p ; rc: ! i =- =
l^,
-
-i-;-=ia--i=". i' -
*f*. r : f 4==-6=- i -
i -: i olcr-={:I=k=-