1
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Gii tích vectơ(cont)
Lecture 2
EE 2003: Trường đin t
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tgradient
1 2 3
( , , )u u u
1 2 3
( , , )P u u u
1 1 2 2 3 3
( , , )Q u du u du u du
1 2 3
1 2 3
d du du du
u u u
 
Xét vô hướng và hai đim lân cn
. Ta có:
1 2 3
1 1 2 2 3 3
1 1 1
d a a a d
h u h u h u
 

1 2 3
1 1 2 2 3 3
1 1 1
grad a a a
h u h u h u
 
Toán tgradient: (VH VT)
.d grad d

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2
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tgradient
d

0
0d
.d a
Ý nghĩa ca toán tgradient:
P
Q1
Q2
Q3
Q4
4
d

3
d

2
d
1
d
0
hướng ca gradti P Đln ca gradti P bng tc đ
tăng cc đi ca ti P
n
grad a
n

. .grad a a

n
dn dna
2
Q
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tDivergence
Đnh nghĩa toán tDivergence:
0
lim S
V
AdS
div A A
V

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3
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tDivergence
Ý nghĩa ca toán tDivergence: mt đngun
Không có MĐ ngunCó MĐ ngun dương Có MĐ ngun âm
0div A
0div A
0div A
V 0
V 0
V 0
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tDivergence
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4
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tDivergence
Biu thc tính toán tDivergence:
2 3 1 1 3 2 1 2 3
1 2 3 1 2 3
1
h h A h h A h h A
div A A h h h u u u
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tDivergence
Đnh lý Divergence: trường liên tc trong thtích V
S V
AdS divAdV
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5
EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tRotation (Curl)
Đnh nghĩa toán trotation:
0
lim
n
S
Max
Ad
rot A A a
S

EE 2015 : Signals & Systems Tran Quang Viet FEEE - HCMUT
Tran Quang Viet – FEEE – HCMUT Electromagnetics Field
Toán tRotation (Curl)
Ý nghĩa ca toán trotation: mt đngun ca trường có
tính cht xoáy
0rot A
0;rot A IN
0;
rot A OUT
S 0
S 0
S 0
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