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\centerline{\bf Math 335, Section 1, Real Analysis}
\centerline{\bf Fall 1996}
\centerline{\bf Nancy Stanton}
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\centerline{\bf Text: Protter $\&$ Morrey, A First Course in Real Analysis,
2nd Ed.}
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I consider the book appropriate for a year long course in real analysis
which spends about a semester on analysis in 1 variable and about a
semester on analysis in several variables.  It has an excellent choice of
topics, is well-written, and includes lots of examples.  The problems
range from easy to medium in level of difficulty.  I would use it again.

The students find the book hard to read; they would find any analysis book
hard to read.  Among analysis books, I would rank this as fairly easy.
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{\bf Contents}
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CHAPTER 1
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The Real Number System

1.1  Axioms for a Field

1.2  Natural Numbers and Sequences

1.3  Inequalities

1.4  Mathematical Induction
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CHAPTER 2
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Continuity and Limits

2.1  Continuity

2.2 Limits

2.3  One-Sided Limits

2.4  Limits at Infinity; Infinite Limits

2.5  Limits of Sequences
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CHAPTER 3
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Basic Properties of Functions on $\bf{R}^1$

3.1  The Intermediate-Value Theorem

3.2  Least Upper Bound; Greatest Lower Bound

3.3  The Bolzano-Weierstrass Theorem

3.4  The Boundedness and Extreme-Value Theorems

3.5  Uniform Continuity

3.6  The Cauchy Criterion

3.7 The Heine-Borel and Lebesgue Theorems (Lebesgue Theorem
skipped)
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CHAPTER 4
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Elementary Theory of Differentiation

4.1  The Derivative in $\bf{R}^1$

4.2  Inverse Functions in $\bf{R}^1$
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CHAPTER 5
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Elementary Theory of Integration

5.1  The Darboux Integral for Functions on $\bf{R}^1$

5.2  The Riemann Integral

5.3  The Logarithm and Exponential Functions
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CHAPTER 9
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Infinite Sequences and Infinite Series

9.1  Tests for Convergence and Divergence

9.2  Series of Positive and Negative Terms; Power Series

9.3  Uniform Convergence of Sequences


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{\bf Math 335, Section 1, Syllabus}

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August 28,30 Chapter 1
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September 2,4,6 Sections 2.1, 2.2
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September 9 Section 2.3 
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September 11 Section 2.4
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September 13,16 Section 2.5
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September 18,20 Section 3.1
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September 23 Section 3.2
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September 25 review for exam
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September 27 Exam I
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September 30 Section 3.3
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October 2 Section 3.4
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October 4,7 Section 3.5
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October 9,11,13 Sections 3.6, 3.7
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October 16,18,28 Section 4.1
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October 30 Section 4.2
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November 1,4 Section 5.1
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November 6 review for exam
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November 8 Exam II
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November 11,13 Section 5.2
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November 15,18 Section 5.3
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November 20,22 Section 9.1
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November 25,27 Section 9.2
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December 2,4 Section 9.3
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December 6,9 Section 9.4
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December 11 review for final


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