MA211
Functions of Several Variables
1
Techniques in Partial Differentiation
Using the definition can be tedious.
Thus, we develop some techniques.
z f ( x, y )
z
x
The t-Chain Rule
z
y
y (t )
x(t )
If
x x(t )
y y (t )
dx
dt
dy
dt
z f ( x, y )
t
then
dz z

MA211
Parametric Equations of Lines
1
Lines determined by a point and a
vector
A line in 2 or 3 space can be determined
uniquely by specifying a point on the line
and a nonzero vector parallel to the line.
2
Theorem
The parametric equation of a line in 2(

SCHOOL OF COMPUTING,
INFORMATION & MATHEMATICAL
SCIENCES
MA111: CALCULUS I &
LINEAR ALGEBRA
Week 1 : Lecture 2
KSR
1
Example
A farmer rears ducks and goats.
He counts 70 heads and 178 legs.
How many ducks and goats does he have ?
Let x be the number of du