Solutions to Assignment 8
Math 217, Fall 2002
4.6.26 If A is 6 4, what is the smallest possible dimension of Nul(A)? Well, we know that rank(A)+dim(Nul(A) = 4. It is possible that rank(A) = 4, that is, that dim(Col(A) = 4 because A is 6 4. We conclude the
MATH 2100ALGEBRA II
Fall 2013 and Winter 2014
Instructor: Paul Mezo
4217 HP
Tel: 520-2600 ext. 2156
e-mail: mezo@math.carleton.ca
Prerequisites: MATH 1102 with a grade of C+ or higher, or MATH 2107 with
a grade of B+ or higher, or permission of the School
Part IIB. Maxima and Minima
1. Relative Maxima and Minima (12.10)
Figure 1- Relative minimum, relative maximum, and inflection point of a single variable function
Figure 1 shows critical points of a single variable function
, critical points can be identi
MOMENTUM EQUATION IN RECTANGULAR COORDINATES
avx avx 6vx avx
+, y I
at 6x 6y ()2
x-component: p<
Com onent av + V aVy + V aVy + avy
I x ' V _
y P P at ax y (9)} az
6P 6 a a
= - - + 1x2: _TY_X _1;'}_ + pgy
65 ax 6y 62
6V2 avz aVz av:
z-com
Part II. Multivariable Functions and
Differential Calculus
Multivariable functions (12.1)
A function which has more than one independent variable is a multivariable function. A variable
is said to be a function of two independent variables
a)
and
if:
are
MATH 217 PROJECT 1: EXTREMES OF FUNCTIONS
Due Date: Thursday, March 1, 2012
Part I:
Functions representing terrains are usually very complex but can provide important
information such as the volume of the surface and the degree and orientation of the
slop
Part IV Vector calculus
Vector fields
A vector field is a vector, which is a function of position as well as possibly other variables, as
opposed to the position vector
( )
( ( ) ( ) ( ) ,
(1)
which is a function of parameter t (not necessarily time) only
Microscopic Momentum Balance
Viscous stresses vs total stresses
Newtons second law for this control volume:
Sum of Forces
Rate of
Rate of
Rate of
Momentum = Momentum Momentum + Acting on
System
Output
Accumulation Input
Let us consider th