Chapter 4-Vector-Valued Functions

Chapter 4 :
Vector-valued Functions


U 1
.
:
Acceleration and Newton's Second Law


Differentiation of Paths :




i
Rules :




1 . /b(t) + TH) :
b) + It is sum rule



P(tclt)
.&(pHH)]
2 =
pCt(t) + scalar multiplication a
re




.
3 (Ct . H :
(t) · (t) + b() . (t) dot product re o



.
4 (t)xJ(t)] :
bt)xi(t) + b) x cross product rule



q't) Iql
5
d([19(t))) chain rule
:
.




velocity
:
['It)

acceleration :
"(t)

ex :
(0) =
-


i , alt) -u :




Y(0) i + Y
=




[10) :
i

- (t) =
(x (t) y(t) , ,
z (t))



& (t) :
(X (t) Y'() z'(t)
, ,
>
-
<110) (1 :

,
1, 01


& "It) :
(X"(t) Y"(t) z" (t))
, ,
+
5 "10) =
10 , 0 , -1)


" (t) 10 =

,
0 , -1)


GE (t) (1 :
,
1
,
+)

6 i (t) (t =

, t ,
1-1/2) original position


1 t
-
=
0
Z

E =
t


↑ (2) (2 82 0)
=
, ,




Newton's second law :




Force :
E

E([(t) malt) =