This course is aimed at developing proficiency,
with an
understanding of the ideas behind the methods, in the following
specific
subjects:
Infinite Series and Power Series
Numerical Integration
Linear Algebra, the theory of linear functions and equations in several variables
The first three topics complete the coverage of
single
variable calculus, and the fourth, on which we shall spend roughly two
thirds
of the course is the basis of the calculus
of
functions of several variables, as well as a fundamental subject in its
own
right.
The textbook for the Calculus part is Calculus
, by Salas, Hille and Etgen,
Ninth edition. This part of the course covers selected parts of
Chapters 8 and
10, and all of 11.
In
the remainder of the course we will work with the text `Beginning
linear
algebra' by Carlen and Carvalho. This text
is
available at the Georgia Tech bookstore but you can also download it
from Prof. Carlen's website.
The readings can be roughly broken into five sections:
Block 1:
Block 2: Power Series and Numerical Integration, and
elementary
differential equations. Sections 11.7-11.8
and 8.7-8.9 in Salas, Hille
and Etgen
Block 3: Introduction to Matrices, Row Reduction and Solution of
Linear
Systems.
Block 4: Linear Independence,
Block 5: Determinants, Eigenvectors, Eigenvalues.
(3)
COURSE CALENDAR:
This is a VERY rough guideline, and will be altered by the pace at
which the
material is covered in class:
Week 1: 11.5-11.6 in Salas Hille and Etgen
Week 2: 10.5-10.7, 11.1-11.2 in Salas Hille
and Etgen
Week 3: 11.3-11.4 in Salas Hille and Etgen
Week 4: 11.7-11.8 in Salas Hille and Etgen
Week 5: 8.7-8.9 in Salas Hille and Etgen
Week 6: Sects. 1.4-1.6, in Carlen and Carvalho
Week 7: Sects. 2.1-2.3 in Carlen and Carvalho
Week 8: Sects. 2.4-2.6 in Carlen and Carvalho
Week 9: Sects. 3.1-3.3 in Carlen and Carvalho
Week 10: Sects. 3.4-3.7 in Carlen and Carvalho
Week 11: Sects. 4.1-4.4 in Carlen and Carvalho
Week 12: Sects. 5.1-5.2 in Carlen and Carvalho
Week 13: Sects. 5.3-5.4 in Carlen and Carvalho
Week 14: Sects. 5.5 in
Carlen and Carvalho