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\centerline{Mathematics 242 -- Principles of Analysis}
\centerline{Information on Exam 2}
\centerline{November 8, 2000}
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\noindent
{\it General Information}
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The second exam for the course will be given in class on
Friday, November 17.  This will 
be an individual, in-class, closed book exam.  I will be happy 
to hold a late afternoon or evening review session to help you 
prepare.  Scheduling is going to be rather difficult, though:
I have commitments (the Holy Cross Chamber Orchestra concert, and 
another orchestra rehearsal) in the evening both Wednesday and Thursday, 
November 15 and 16.  It may be that the only possible times for a review
session turn out to be Tuesday evening or late Wednesday afternoon.
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\noindent
{\it Topics to be Covered}
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The exam will cover the material we have covered since the first exam
up to and including class on November 10 (the Fundamental Theorem of 
Calculus).  This is material from Chapters 3, 4, 5 of the text (but
only the sections we covered in class -- not 3.6, 4.4, or 5.5):
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\item{1)}  Limits of functions, the limit theorems (sum, product, quotient,
``squeeze'' rules, one-sided limits
\item{2)}  Continuity
\item{3)}  Definition and properties of the derivative, the Mean Value Theorem
\item{4)}  The definite integral, integrability, the Fundamental Theorem
of Calculus
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\noindent
{\it What to Expect}
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The exam will have four or five questions, each possibly with several
parts.  Some questions will ask for a precise statement of a 
definition or a theorem we have discussed.  Be prepared to give
careful statements of 
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\item{1)}  The definitions of $\lim_{x\to c} f(x) = L$ and $f$ is 
continuous at $c$
\item{2)}  The Intermediate and Extreme Value Theorems
\item{3)}  The Mean Value Theorem
\item{4)}  The Fundamental Theorem of Calculus
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\noindent
Also know and be able to give proofs of:
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\item{1)}  Statements of the form $\lim_{x\to c} f(x) = L$ using the 
definition
\item{2)}  The Extreme Value Theorem
\item{3)}  The Mean Value Theorem (proof via the special case 
$f(a) = f(b)$ -- Rolle's Theorem)
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The other questions will be similar to questions from the problem sets
and discussions.  Some good review problems to look at are
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\item{} Section 3.1/2, 7, 9
\item{} Section 3.3/1, 5, 8 
\item{} Section 3.4/1, 9, 10 
\item{} Section 3.5/9, 15, 20
\item{} Section 4.1/10, 11, 12, 13
\item{} Section 4.3/10, 14, 19, 21
\item{} Section 5.1/ 3, 9, 
\item{} Section 5.3/2, 4, 5
\item{} Section 5.4/3, 4, 8
\bye
