The
MA 2071 Linear
Algebra D '03
Join the Quest for Maw in the Math Awareness Week contest!! Follow this
link to
find out how to begin the hunt!!!!
All
Project #2s due on Thursday, April 10 at the start of class. Please let me know
well before then if you need help!!!
ME Project
#2 has rewording on Problem #6…
Instructional Staff
instructor:
John Goulet Stratton 201 A goulet@wpi.edu
office hours
Monday 9:15-12, 1-3
( 10:30-11 today 3/18)
Tuesday
9:15-12, 12:30-2
Thurs
9:15-12, 12:30-2
Friday
9:30-12, 12:30-2
or
by appointment
Sections: (all conferences
meet in Stratton 106 on Weds)
section D01 – 3:00 Joanna Begin (jbegin@wpi.edu)
section D02 – 1:00 Jeff Simone (jss328@wpi.edu)
section D03 – 12:00 Iavor Trifonov (trifonov@wpi.edu)
section D04 – 11:00 Sidharth Rupani (sidrup@wpi.edu)
section D05 – 8:00 Matt Black (mblack@wpi.edu)
Text: Kolman, Linear Algebra with
Applications ,7th ed
Grade:
quizzes (5)
35% each Friday
projects
30%
final
exam 25%
homework
10%
5 point bonus for
perfect attendance!
Bonus: the team with the highest quiz average does not have to take the final exam
Quizzes
#1 – 3/14/03
#2 – 3/21/03
notes from class 3/20 on matrix algebra
rules
2. vector form
of solutions to systems
homogeneous, particular parts
1. terminology
(definitions): “homogeneous, particular
solutions”
#3 –
1. matrix algebra
2. inverses
under what conditions
does a matrix have an inverse?
what relation does that
have to solutions of Ax = b ? Ax = 0?
3. determinants
compute, relate result
to inverses
#4 4/4/03
1.
solution sets of homogeneous systems as vector spaces
bases and dimension of
2.
vector spaces
showing
a set is a vector space
finding
counterexamples
you
must know the definition
of a vector space!
#5 4/11/03
(
so be able to set up, solve the
problem Pc = x )
you must know the definition of a bases!
Groups 60,70 and 110 are tied for first place after 4
quizzes. Groups 45 and 53 are
close behind!!! Winner gets to skip the Final Exam!!
assignments given daily at the beginning
of class, by section
see the following file
follow this link for an overview of
what this course is about
a paper discussing the evolution of
this course is at this link.
Essentially, upon completion of the
course, you will have worked on
Core Linear Algebra material
* learned basic definitions from linear algebra
* developed skills in linear algebra computations
(solving
linear systems, matrix arithmetic, use of linear transformations…)
* related computations
to general linear algebra concepts (what a linear transformation is,
how a basis
is used,…)
Projects
* used linear algebra
for applications within your major via
projects
* worked in teams. Follow this link
for group paper due Thursday 3/20
* presented project materials as teams which involves writing
Time Investment
As with any 1/3 unit course, it is
assumed that the total time spent per week, including class and
all activities, will be about 14 hours, on the average. Aside from class, you will to a certain
extent need to work in parallel on both core linear
algebra material (homework and quiz
preparation)
and your
projects.
Conferences
Each Weds in conference, skill areas
will be covered, in a cooperative format. That means that the
students
in the conference will work on problems to try and get their computational
skills in order. The
PLAs managing the conferences will critique
their work so that they are up to speed, so to speak,
on
the skills covered.
The specific skills covered in each
conference may be found at this link.
Core Material Covered:
Linear Systems
types
of problems
types
of solutions
arbitrary
variables
the
Gauss-Jordan algorithm
Matrix Arithmetic and Algebra
matrix
arithmetic
matrix
algebra
diagonal
and symmetric matrices
A =
PDP-1
inverses
and powers of matrices
relation
of matrices to solutions of systems – rank
change
of coordinates
Ax thought of as a linear combination of the columns
of A
Vector Spaces
basis
concept
of building blocks
determining
if a set is a basis or not
coordinates
and coordinate changes x = Pc
how
to build and use the P matrix for coordinate changes
orthogonal
basis
basis
where all vectors in it are perpendicular to each other (0 dot product)
at
the heart of Fourier analysis
key
formula: ci = xvi/vivi
special
case: orthonormal basis (all unit vectors)
real and abstract vector
spaces
“closure” requirements
Rn
planes and lines through the origin
solutions to homogeneous systems
solutions to homogeneous 2nd order
differential equations
sets of functions
Determinants
Basic Properties
Relation to inverses, to
solutions of systems, to rank
Useful Theorems
Product
Rule, Det(At) = Det(A) etc
Computing by hand:
XXX rule,
Cofactor Expansion
Cross Products
Linear Transformations
definition
Laplace
and Fourier; derivatives and integrals
matrix
of
application
to rotations, reflections
determined
entirely by effect on basis for domain
when
is a linear transformation 1-1??
Diagonalization and the Principal Axis Theorem
eigenvalues
and eigenvectors – recognizing, computing
when
can a matrix be diagonalized?
how
do you diagonalize?
applications:
powers of matrices
behavior
of dynamical systems
conic
sections
Adobe Acrobat
Reader for .pdf files will be
needed. Please install it if you don’t have it already.
go to the following link to download
Maple
this link has information
on installing Maple over the college’s network as well as using
Maple to do linear
algebra computations such as Gauss-Jordan, matrix arithmetic and
eigenvalue analysis.
This link
goes to the Maple site at the University of Waterloo and has numerous sheets
with linear algebra
applications.
Matlab
This link is to a WPI site
with 3 purposes:
Follow this link to
see how Matlab solves linear algebra problems such as matrix
multiplication
and eigenvalue/vector computations.
Projects
A primary component of the
WPI approach to education is the project.
As all of you know,
you will participate in
team projects at junior and senior level (the IQP and MQP, respectively).
These will require many
things of you: working in a team, communicating orally and in writing,
planning, using technology
and other resources, learning things you knew nothing about before,
and finally, providing a
solution to a complex problem of society or in one’s major.
(links not in place yet for IE….)
Industrial Engineering
Mechanical
Engineering meeting Monday
(4/7) with Matt – 5 pm, PLC (Daniels)