Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
Equation of line :
Equations of a line pas sin g through (x1, y1, z1)
and
direction
ratios
a, b, c are
x x1 y y1
z z
1
a b c
Equation of a plane : is of the form
ax + by + cz + d = 0 where a,b,c are the DR's of the normal.
Introduction
In this chapter the basic concepts of Differential Calculus of scalar functions are
extended to vector functions.
Here we study vector differentiation, gradient, divergence, curl, solenoidal and
irrational fields.
Also we study about vector integration and verification of the integral theorems.
Vector Function of a Scalar Variable
Let f f1
i f2
j f3
k where f1, f2
and f3
are
functions
of
a
var iable
t
is called a vector function.
If f1, f2 and f3 are differentiable then we define
d f f(t t) f(t)
df
1 df
2 df
lim i j
3
k
dt t0
t dt dt dt
Similarly higher order derivatives can also be defined.
Note:
d f
0
dt
iff
f
is
a
cons tan t
vector .
Page 2 of 72