,5 Gr
oupTheor
y 33
5
.0.
1 Su bg
roups...
.... .
....
.....
.......
... 34
5
.0.
2 Ab el
ia
n(Commu t
ati
ve)Gr
oups...
.......
..... 34
5
.0.
3 L i
e(Cont
inu
ous)Groups...
.......
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. 35
i
, 5
.1 Coor
din
ateTr
ans
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mat
ion
Gr
oup
s.....
...
.....
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5
.1.
1 TheTran
sla
tionGr
oup ... ...
......
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.. 36
5
.1.
2 Th
eRota
tionGroup....
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...
..
.
... 36
5
.1.
3 TheI
nver
s i
onGroup...
.....
...
...
..
..
... 37
6Sca
lara
ndVe ctorCalculus 39
6.
1 Sc al
a rDifferentiat
ion. ..... ..
.. .....
...... .... 40
6.
2 Ve ctorDifferentiat
ion. ....................... 41
6.
2.1 Th ePa rti
al Deri
vati
ve. ................... 41
6.
3 Th eGr adient.. ........ .
. ................. 42
6.
4 Ve ctorDe ri
vati
v e
s. ....... .................. 42
6.
4.1 Th eSu mRu les.... .................... 43
6.
4.2 Th ePr oduc tRules.. ...........
.... ..... 43
6.
5 Se condDe r
ivati
ves. .... .
. ................... 44
6.
6 Sc al
a rI
n tegr
ation. ....... ................... 45
6.
6.1 Th eF undame nt
alTh eor
emofCa l
cul
us. ......... 45
6.
7 Ve ctorIntegrat
ion. ....... ...........
.... ... 45
6.
8 Th eF undame ntalTh eorem(s)ofVe ct
orCalcul
us. .
....... 46
6.
8.1 ASc alarFu ncti
onofVe ctorCoordi
nates.........
. 46
6.
8.2 Th eDi vergenceTh eorem. ................. 47
6.
8.3 St okes’The orem. . ..................... 48
6.
9 Integrati
onb yPa rts. ..... ................... 49
6.
9.1 Sc alarIntegrati
onb yPa r
ts. .......
.. ....... 49
6.
9.2 Ve ctorInteg r
ati
onb yPa r
ts.......... .
...... 49
6.
10 I
ntegrati
onByPa rtsinE l
ectrodynamics.............. 51
7Coor
din
ateSyste
ms 55
7
.1Ca r
tesi
an. .
.....
.......
.......
.......
... 57
7
.2Sp her
ic
alPol
ar.....
.......
.......
.......
.. 58
7
.3Cy l
in
dri
cal....
.......
.......
.......
..... 60
8 Th
eDi
racδ-
Fun
cti
on 63
9 Ma
thRe
fer
enc
es 67
I
INo
n-Re
lat
ivi
sti
cEl
ect
rod
yna
mic
s 69
10Maxwe
ll
’sEquat
ions 71
1
0.1TheMaxwe l
lDi
spl
ace
me ntCurr
ent.
.....
.....
...
... 71
1
0.2Pote
nti
al
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......
.. ..
........
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... 75
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