MA211
Properties of Functions of
Several Variables
1
Example
Describe and sketch the domain of z = x 2 + y 2 ,
and sketch the graph of z.
y
Solution
Domain
Since x 2 + y 2 > 0 for all ( x, y ) R 2 , the
x
domain of z consists of all points ( x, y ) in
the

MA211
Polar Coordinate System
1
Tests for Symmetry
[1] About the x-axis
We get back r f if we replace by .
[2] About the y-axis
We get back r f if we replace by .
[3] About the pole axis (or origin)
We get back r = f () if we replace by + .
2
Example Use

MA111
Week 2
Lecture 1
KSR
1
Example
Solve using the Gauss-Jordan
Elimination method
x1 x2 2 x3 9
2 x1 4 x2 3x3 1
3x 6 x 5 x 0
2
3
1
KSR
2
Applications of Systems of
Linear Equations
KSR
3
Example
A chemistry laboratory can be
used by 38 students at one

MA111
Week 2 Lecture 2
Example
The flow of traffic (in vehicles/ hr)
through a network of streets is
shown.
Solve the system for xi
Polynomial Curve Fitting
Given a set of data represented by n points
x1 , y1 , x2 , y2 ,K , xn , yn
in the xy-plane, we w

Solving Systems of Linear Equations by
the Gaussian Elimination and
Gauss-Jordan Elimination Methods
J. Vanualailai
April 26, 2013
School of Computing, Information & Mathematical Sciences, University of the South Pacific, Suva, Fiji.
Systems of Linear Equ

SCHOOL OF
COMPUTING,
INFOMATION AND
MATHEMATICAL
SCIENCES
MA111: Linear Algebra
and Calculus
Week 1 : Lecture 3
KSR
1
1. No solution
Parallel lines
Inconsistent system
Example: Solve
x y 1
x y 2
04/11/16
KSR
2
2. Exactly one solution
Intersecting lines
Co