Lecturer: Arthur Mattuck 2-241 3-4345 mattuck@mit.edu
TA: TBA
18.100A follows the textbook
closely. The best way of getting a feeling for the difference
between 18.100A and 18.100B is to look at the corresponding
textbooks
(at Quantum or the Coop). The book for 18.100B is Rudin's
"Principles of Mathematical Analysis"; the book for 18.100A is given below.
Textbook: Mattuck --- Introduction to Analysis, (Prentice-Hall)
For corrections to the current and previous printings, see
textbook
This course is an introduction to devising mathematical proofs
and learning to write them up. It is primarily for students with
no prior experience with this. The class usually contains
students from years 2,3,4,G in approximately equal numbers,
and from a wide spectrum of
courses -- about 1/4 math majors, the others
mathematically inclined-or-needy students from courses like 2,6,7,8,12,14,15,16,22.
The subject matter for the first
2/3 of the syllabus (up to Exam 2) is the proofs of one-variable
calculus theorems and arguments which use these theorems. The
emphasis is on estimation and approximation, two basic tools of
analysis.
The last third goes beyond calculus, getting into uniform
convergence of series of functions and improper integrals, which
involves several simultaneous limiting processes. The last
theorem for example gives the justification for differentiating the Laplace
transform under the integral sign, which involves interchanging
the order in which three limits are taken.
In addition. there is a very brief
introduction to point-set topology, which is used in upper-level courses
having an analysis prerequisite.
The homework link above starts out empty, but fills up as
the problem assignments
are given out during the term (in class, and posted on
this site in the link above around the same time). This allows
for some
flexibility in content and difficulty, and for feedback from the
class members.
Homework is collected two or three times weekly,
and returned graded at the following class. There
are from 3-6 problems, depending on their difficulty or length.
Sometimes "Questions" are included (exercises having model solutions at
the end of the chapter), as an aid in learning how to write up solutions.
The textbook is by and large an adequate substitute for class
attendance; students in the past have found it sufficiently
clear. A few just read the book, get the assignments here, and slip the homework under
my door before or during class, retrieving the returned homework
from a box outside my door.
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