LINEAR ALGEBRA: APMA 308-01, FALL 2009
INSTRUCTOR:
Prof. Marek-Jerzy Pindera, email:
mp3g@virginia.edu
, office phone: 924-
1040, office: Thornton Hall D214
TA:
Simon E. Mushi, email:
sem5t@virginia.edu
, Office hours: M @ 4:00-6:00 pm in Thornton
Hall C248
LECTURES
:
MWF @ 12:00-12:45 pm in Olsson Hall 005
OFFICE HOURS
: MW @ 10:30 am-11:45 pm in Thornton Hall D-214
TEXT
: Gareth Williams, Linear Algebra with Applications, 6
th
Edit. We will be covering
Chapters 1-7.
AN OVERVIEW
: The course is an introduction to the basic topic of matrix theory and linear
algebra. It will be targeted to the needs of SEAS students. The student will learn how to
manipulate matrices, how to solve systems of linear equations; how to compute determinants,
eigenvalues/eigenvectors; etc. These topics will be put on the unifying setting of vector spaces,
in particular inner product spaces, and linear transformations.
These abstract concepts are
essential ingredients towards developing an understanding of the different situations
encountered in the solution of linear systems of equations, and thus will form a major part
of the course. In light of this, it is essential that the student attends each lecture and comes
to class prepared – the pace of the course will be quick and the student is expected to be
familiar with the basic concepts of high-school level matrix algebra.
Illustrations to
Engineering and Science will be highlighted as required.
COURSE OBJECTIVES
: The specific course objectives are listed below.
•
To understand the theory of systems of linear equations, and to know how to set up and solve
a system of linear equations in matrix form
•
Understand the nature of a best-possible solution (in the least-squares sense) to an unsolvable
system
b
Ax
=
when
b
is not in the range of
A
, and how to obtain it
•
Know the basic algebraic operations on vectors and matrices and their properties, and how to
compute them efficiently
•
Understand the theory of abstract vector spaces, and know the archetypal examples,
Euclidean spaces, spaces of matrices, and the spaces of functions (including polynomial
functions, continuous functions, and integrable functions)
•
Understand the concept of abstract linear transformations, and what properties to expect of