Tentative list of textbook homework problems for Math 311, spring 2003

Text
Introduction to Real Analysis, 3rd edition, by Robert G. Bartle and Donald R. Sherbert, John Wiley & Sons (ISBN 0-471-32148-6).

Note
Some problems have hints in the back of the book.

Comments
I've selected problems from various sections of the book. As we cover the sections, I will indicate which problems students should write up and hand in. I almost surely will not cover all of the sections listed below, and I may not cover them in the order indicated.
Students should certainly look at the problems listed in any section which is covered and steps toward solution of most of these problems should be made.

Meeting times & places
All classes are 4:30-5:50 (sixth period). Classes meet in SEC 205 on Monday and Wednesday and in SEC 212 on Thursday except when otherwise noted.

SectionSection titleSuggested problems
1.1 Sets and Functions 10, 11, 12, 13, 20
1.2 Mathematical Induction 5, 14, 18, 20
1.3 Finite and Infinite Sets 8, 12  
2.1 The Algebraic and Order Properties of R 2, 7, 8, 15, 15, 17, 22  
2.2 Absolute Value and the Real Line 2, 4, 7, 16  
2.3 The Completeness Property of R 1, 3, 5, 6, 8, 9, 11, 12  
2.4 Applications of the Supremum Property 2, 3, 4, 6, 8, 9, 12, 13, 15, 18  
2.5 Intervals 1, 3, 7, 8, 9  
3.1 Sequences and Their Limits 2b, 3d, 4, 5a,d, 6b, 8, 10, 14, 15, 16  
3.2 Limit Theorems [MORE TO COME!]  
3.3 Monotone Sequences  
3.4 Subsequences and the Bolzano-Weierstrass Theorem  
3.5 The Cauchy Criterion  
3.6 Properly Divergent Sequences  
3.7 Introduction to Infinite Series  
4.1 Limits of Functions  
4.2 Limit Theorems  
4.3 Some Extensions of the Limit Concept  
5.1 Continuous Functions  
5.2 Combinations of Continuous Functions  
5.3 Continuous Functions on Intervals  
5.4 Uniform Continuity  
5.5 Continuity and Gauges  
5.6 Monotone and Inverse Functions  
6.1 The Derivative  
6.2 The Mean Value Theorem  
6.3 L'Hospital's Rules  
6.4 Taylor's Theorem  
7.1 The Riemann Integral  
7.2 Riemann Integrable Functions  
7.3 The Fundamental Theorem  
7.4 Approximate Integration  
8.1 Pointwise and Uniform Convergence  
8.2 Interchange of Limits  
8.3 The Exponential and Logarithmic Functions  
8.4 The Trigonometric Functions  
9.1 Absolute Convergence  
9.2 Tests for Absolute Convergence  
9.3 Tests for Absolute Convergence  
9.4 Series of Functions  

The final exam for this course is scheduled for 12:00 PM to 3:00 PM on Tuesday, May 13, 2003.

Maintained by greenfie@math.rutgers.edu and last modified 1/15/2003.