Vector Calculus & Applications
, axb
Hision 12
-
1 a x b =
lalising E
E
↑
1 -
7
Time
*"T
(
I
& I
v = rector
scalar unit rector in direction
↑
3
↑ of axb
>
- >
Ex
1
a
?
Basis rectors 2, E
~=
(
~
:
-j
y
1
Exc
1
y position
=
-
↳
0 rector
-
-
2 15 ↑
+
1 = +
r
X 1
Opposite ? Change sign
[x] =
E
-
↳
b lallb/cost
1
I a =
Right hand
* rule !
- a + (b + 2)
,Annotation ajbj a suffix notation
crepeated
2 =
a + b ↳ 3
anbet Abs
↳= ai + bi jbjab + =
↳ Vie : 1 ,
2
,
31 (a ·
b) (c d) ·
⑧ has one free siffix .
i ajbj .
Cadk
Repeated stix appears ajbilj =
abi =
[(a -b)
-
exactly twice
& + 11 :
b) =
1a/"(bv)
Einstein Summation convention
says that a
repeated soffit =>
(n + (a ·
b) =
[al(6 1):
:
is to be summed from
=> : + (4 bIvi
.
= 1/ (b · ai
1 to 3
.
, => Hi + Lajbj)v = Andrbjujai
= An Arb , a
:
=FAAAI
that is
Matrices : Tensors :
objects can be it
in Suffix notation
Hij A3]
Rank : number of free soffices in a
trace(N) An + Az + Ass
=
tensor
= Ajj
, axb
Hision 12
-
1 a x b =
lalising E
E
↑
1 -
7
Time
*"T
(
I
& I
v = rector
scalar unit rector in direction
↑
3
↑ of axb
>
- >
Ex
1
a
?
Basis rectors 2, E
~=
(
~
:
-j
y
1
Exc
1
y position
=
-
↳
0 rector
-
-
2 15 ↑
+
1 = +
r
X 1
Opposite ? Change sign
[x] =
E
-
↳
b lallb/cost
1
I a =
Right hand
* rule !
- a + (b + 2)
,Annotation ajbj a suffix notation
crepeated
2 =
a + b ↳ 3
anbet Abs
↳= ai + bi jbjab + =
↳ Vie : 1 ,
2
,
31 (a ·
b) (c d) ·
⑧ has one free siffix .
i ajbj .
Cadk
Repeated stix appears ajbilj =
abi =
[(a -b)
-
exactly twice
& + 11 :
b) =
1a/"(bv)
Einstein Summation convention
says that a
repeated soffit =>
(n + (a ·
b) =
[al(6 1):
:
is to be summed from
=> : + (4 bIvi
.
= 1/ (b · ai
1 to 3
.
, => Hi + Lajbj)v = Andrbjujai
= An Arb , a
:
=FAAAI
that is
Matrices : Tensors :
objects can be it
in Suffix notation
Hij A3]
Rank : number of free soffices in a
trace(N) An + Az + Ass
=
tensor
= Ajj
