Classical Electrodynamics

Cl
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rodynami
cs

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0.1Th
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ink
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I Ma
the
mat
ica
lPh
ysi
cs 5
1 Ma
the
mat
ica
lPr
elu
de 7

2 Numb
ers 9
2.
1 RealNumbe
rs...
...
...
...
...
...
...
...
...
.. 9
2.
2 Comp l
exNumb
ers..
...
...
...
...
...
...
...
... 1
0

3 Vect
orsandVe ctorProduct
s 15
3.
1 Sc al
a r
sa ndVe ct
ors.........
..........
....... 16
3.
2 Th eSc a
lar,orDotProduct........
..........
... 16
3.2
.1 Th eL awofCosin
e s.........
..........
.. 18
3.
3 Th eVe ct
or,orCrossProduct....
..........
...... 18
3.
4 Tr i
pleProdu c
tsofVector
s. ..
..........
......... 20
3
.5 δ
ijan
dǫk.
i
j ......
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.. 2
1
3
.5.
1 Th eKr
oneckerDel
taFuncti
onandtheEin
stei
nSumma
tionCon
ven
tion21
3
.5.
2 Th eLe
vi-
Civ
itaTensor........
........... 2
2
3
.5.
3 Th eEps
il
on-Del
taIdent
it
y. ..
...........
... 2
2

4 Tens
ors 25
4.
1 Th eDy
adandN-a
dicF
orms....
.....
.....
.....
. 25
4.
2 Coordi
nat
eTra
nsf
ormat
ion
s..
.....
.....
.....
.... 28

,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...
.......
.......
. 35

i

, 5
.1 Coor
din
ateTr
ans
for
mat
ion
Gr
oup
s.....
...
.....
.... 35
5
.1.
1 TheTran
sla
tionGr
oup ... ...
......
.....
.. 36
5
.1.
2 Th
eRota
tionGroup....
.....
...
...
..
.
... 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
s. ....
......
.. ..
........
.....
... 75