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{\course}         \hfill {Instructor: Russell Brown}\\ 
{\daytime }	  \hfill {Office: POT741} \\
{\room}	          \hfill	{Phone: 257-3951}\\
{\semester}	  \hfill	{Messages: 257-3336}\\
        	  \hfill	{M2--3, W2--3, F 10--11}\\
                  \hfill {and by appointment.}

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\hd{Grading}  \begin{tabular}[t]{l}3 exams 300 \\ Homework 150\\
Final 150 
\end{tabular}

\hd{Text} {\it Introduction to analysis, }Maxwell Rosenlicht.


The aim of this course is to give a complete development of calculus
beginning from the basic properties of the real numbers. Thus, we will
begin with some notation from set theory, then list the basic
properties of the real numbers.  These properties will be used in
Chapter 3 to establish important topological facts  of the reals in
the context of complete metric spaces.  Chapter 4 is devoted to
continuous functions.  The intermediate value theorem and the theorem
asserting that a continuous function on a closed and bounded interval
attains a maximum are extremely important in the rest of the course. 
Finally, in Chapter 5, we will introduce the derivative of a function
of one variable and study its properties. The most important result
here is Taylor's theorem which gives one way of approximating a
differentiable function by a polynomial.  

While the material may sound familiar, many of you will find our
approach  to be new. The difference is that rather than concentrating on
the computational aspects of calculus (e.g.~How do I find the minimum
value of a function?), we will emphasize more  fundamental  
 questions
(e.g.~When do I know that a function has a minimum value?).

\hd{Homework} 
Students will be given written homework assignments.
Students may collaborate on their homework assignments, but one 
should not copy completed solutions from other students. 

\hd {Exams}  There will be 3 hour exams and a final. Tentative dates
 for each exam are given below. The final will be
cumulative. The exams will consist of questions similar to those given
on homework. You will be expected to know the main theorems, proofs
and definitions of this course.  You should not only commit these to
memory, but you should be able to provide examples to illustrate them.




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Exam 1: Monday, September 25.

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Exam 2: Friday, October 27.

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Exam 3 Friday, December 1.  

\smallskip
Final: 10:30 am, Monday 11 December 1995.

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