Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
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Engineering Mathematics - II - <strong>Vector</strong> Calculus - 2007<br />
Let<br />
<br />
t<br />
be<br />
the<br />
unit<br />
tan gent<br />
vector<br />
at<br />
P.<br />
Consider<br />
d.w.r.t s<br />
<br />
t . t<br />
1<br />
<br />
t<br />
.<br />
<br />
d t<br />
ds<br />
<br />
<br />
d t <br />
. t<br />
ds<br />
<br />
0<br />
<br />
<br />
d t<br />
2 t . <br />
ds<br />
0<br />
<br />
<br />
t<br />
<br />
d t<br />
.<br />
ds<br />
<br />
0<br />
<br />
d t<br />
ds<br />
is<br />
a normal<br />
to<br />
the<br />
space<br />
curve<br />
<strong>and</strong><br />
<br />
n<br />
<br />
<br />
d t<br />
ds<br />
<br />
d t<br />
| |<br />
ds<br />
is<br />
called<br />
the<br />
unit<br />
normal to<br />
the<br />
curve.<br />
Scalar <strong>and</strong> <strong>Vector</strong> Fields<br />
Scalar Valued Function<br />
Let P(x,y,z) which is a scalar is called a scalar point function.<br />
Note: A scalar point function is also called a scalar fixed . = (x,y,z)<br />
Ex.: (x,y,z) = x 2 + y 2 + z 2<br />
<strong>Vector</strong> Valued Function<br />
Page 7 of 72
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