MT2
, MT2 - Maths induction
Charlie, first half of lectures.
James, second half.
Pls do tutorial questions.
Each week new quiz for recap.
Schnums advanced calculus - books for this unit
Mary Boas general text book
Revision on vectors—
* vector colours .
A vector quantity has both direction 13 magnitude →
displacement
velocity .
A scalar only has magnitude / size → distance [will have a notation
speed a→ a- or a
]
Vectors can be written w.r.t, a basis which may density
,
temperature
be natural for coordinate system.
E.g cartesian coordinates- x,y,z,
= " " " " °
"
unit vector
magnitude = 1
magnitude of
a→ is →
/ I'M =
ai+aj
ñ
_g÷
given then
,
unit vector in the air
Ñ
is a. of
Eg ñ +3¥ foil
=
+
+5=145
.
=
IT =¥⇐÷rE+¥ñ
, Scalar product
B→
defined by
F. Ñ =
IF/ / BY -
Gso
⇐¢ =Ñ E -
it
A-Y.coso.fi?-5ii--r-i.--:i-.
this means if is a hit vector then
*ñ
=/ AT / II. cosa =/
length of E. u→
projection onto
the air oefñ
if I p B→ perpendicular A?Ñ=o ( o will
Cesaro
are =
go ,
)
.IE/-qsg--la-?i(I+-B).E--A-?EtB?E
F- A- =/ AT
>
in cartisesn -
÷
-
i -
I
E. I j I E. I
- -
= .
= =\
F. I =
Jic = I = 0
Angle between vectors Cosa
Ñ¥;§-
=
Example
on
find angle between the
diagonal of the cube Pa side
=
i+J+É I;v÷ (F) IF I E) + + = 1+0.0--1
Ñ=
.
'
Ii? / =ti+=rs viii. ri l -
-
•so
ѵ,+¥- ¥ ¥ 0--65%1
-
-
=
=
=
,
, r
vector product
I'RE (IATIBT sinon
→
given vectors define another vector by XB = .
But still
÷;÷ : agnes
have I' x ⑤ E) +
.mmriatnE¥÷÷ = FIB
+ Axe
in cart'sear basis
I x K I XI '
-
I ex I
¥
a- x be =
I I k
÷ :÷ :: !
-
Az by AJ will be minus in the
:
on .
.am
I
=
flu by -
ay bx)
E g (I t
21) x (I t 5k ) I I i 2×5-3×0 101
tzj ±
-
.
I 2 O
j 5 - o 5J
-
i 3 5
K 3 2
I
-
tk
IOI -
5J
Tutorial sheet will have triple vectors -
F
/ ÷; )
-
scale rtripu product =
± LEXI =
Exit ) . . .
o
-
-
:L:÷÷÷÷i÷
Gc Any Azz
"
m. in
:* .
, MT2 - Maths induction
Charlie, first half of lectures.
James, second half.
Pls do tutorial questions.
Each week new quiz for recap.
Schnums advanced calculus - books for this unit
Mary Boas general text book
Revision on vectors—
* vector colours .
A vector quantity has both direction 13 magnitude →
displacement
velocity .
A scalar only has magnitude / size → distance [will have a notation
speed a→ a- or a
]
Vectors can be written w.r.t, a basis which may density
,
temperature
be natural for coordinate system.
E.g cartesian coordinates- x,y,z,
= " " " " °
"
unit vector
magnitude = 1
magnitude of
a→ is →
/ I'M =
ai+aj
ñ
_g÷
given then
,
unit vector in the air
Ñ
is a. of
Eg ñ +3¥ foil
=
+
+5=145
.
=
IT =¥⇐÷rE+¥ñ
, Scalar product
B→
defined by
F. Ñ =
IF/ / BY -
Gso
⇐¢ =Ñ E -
it
A-Y.coso.fi?-5ii--r-i.--:i-.
this means if is a hit vector then
*ñ
=/ AT / II. cosa =/
length of E. u→
projection onto
the air oefñ
if I p B→ perpendicular A?Ñ=o ( o will
Cesaro
are =
go ,
)
.IE/-qsg--la-?i(I+-B).E--A-?EtB?E
F- A- =/ AT
>
in cartisesn -
÷
-
i -
I
E. I j I E. I
- -
= .
= =\
F. I =
Jic = I = 0
Angle between vectors Cosa
Ñ¥;§-
=
Example
on
find angle between the
diagonal of the cube Pa side
=
i+J+É I;v÷ (F) IF I E) + + = 1+0.0--1
Ñ=
.
'
Ii? / =ti+=rs viii. ri l -
-
•so
ѵ,+¥- ¥ ¥ 0--65%1
-
-
=
=
=
,
, r
vector product
I'RE (IATIBT sinon
→
given vectors define another vector by XB = .
But still
÷;÷ : agnes
have I' x ⑤ E) +
.mmriatnE¥÷÷ = FIB
+ Axe
in cart'sear basis
I x K I XI '
-
I ex I
¥
a- x be =
I I k
÷ :÷ :: !
-
Az by AJ will be minus in the
:
on .
.am
I
=
flu by -
ay bx)
E g (I t
21) x (I t 5k ) I I i 2×5-3×0 101
tzj ±
-
.
I 2 O
j 5 - o 5J
-
i 3 5
K 3 2
I
-
tk
IOI -
5J
Tutorial sheet will have triple vectors -
F
/ ÷; )
-
scale rtripu product =
± LEXI =
Exit ) . . .
o
-
-
:L:÷÷÷÷i÷
Gc Any Azz
"
m. in
:* .
