This course is the first half of a year long course in the theory of
functions on the real line. Most of the first semester will be spent on
a careful examination of sequences, limits of functions, continuity and
their applications to differentiation and integration. This analysis
will produce strong results about real functions that surpass the
calculus, as well as a rigourous recovery of those theorems. A central
methodological theme will be the development of mathematical intuition
and proof-writing, by exercising these abilities in unfamiliar contexts.
Textbook
A Friendly Introduction to Analysis Single and Multivariable
by Witold A.J. Kosmala, 2nd Edition, Prentice Hall.
Homework will be assigned on Friday and due on Friday in two weeks
after it has been assigned. Late homework will in general not accepted.
Homework will consist of two parts: assigned problems and suggested
problems. You do not have to turn in the suggested problems, but will
be responsible for these problems on the exam. It is important to do
all
homework in order to gain a better understanding of the course
material.
Homework # 2
(assigned 9/12) - due on Friday, September 26
Assigned problems:
section 2.3: # 8, 12
section
2.4: # 11(a,b,j)
section 2.5: # 16, 17 (hints: consider
a_{n+2}-a_{n+1} and use an idea of telescoping series
or use an approach from Remarks 1.3.11 and 1.3.12 on pg. 27, Section
1.3)
Suggested problems:
section 2.3: # 5, 6, 7, 17, 19
section
2.4: # 1, 3, 4, 6
section 2.5: # 1, 3, 8
Exam
# 1: Friday, September 26 - covers sections 2.1-2.5
There will be three in class midterm exams and take home final exam.
Before each exam, we will dedicate one entire class period for review
and preparation for the exam.
Midterm Exam 1: Friday,
September 26
Exam # 1 covers sections 2.1-2.5. Review also sections 1.2, 1.3,
1.7 and 1.8.
Midterm Exam 2: Wednesday,
November 5
Midterm 2 Review Session: Tuesday, November 4, 6 - 7
pm, TLC 041
Midterm Exam 3: Friday,
December 5
Midterm 3 Review Session: Wednesday, December 3, 6-7
pm, TLC 041
Final Exam assignment will be
distributed on Friday, December 12 and due on Tuesday, December
16 by 2:30 pm.
Final exam - due on Tuesday,
December 16 by 2:30 pm