Chapter 1: The
Real Numbers
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Discussion
Some
Preliminaries
Chapter 1: The Real Numbers
The Axiom of
Completeness
Consequences of
Completeness
Cantors Theorem
Epilogue
Peter W. White
white@tarleton.edu
Initial development by
Keith E. Emmert
Departmen
Chapter 2:
Sequences and
Series
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Discussion
The Limit of a
Sequence
The Algebraic and
Order Limit
Theorems
MCT & Innite
Series
BolzanoWeierstrass
The Cauchy
Criterion
Properties of
Innite Series
Double Sums &
Products
Epilogue
Chapter 2: Sequences a
Chapter 3: Basic
Topology of R
PWhite
Discussion
Open and Closed
Sets
Chapter 3: Basic Topology of R
Compact Sets
Peter W. White
white@tarleton.edu
Initial development by
Keith E. Emmert
Department of Mathematics
Tarleton State University
Fall 2011 / Real
Chapter 4:
Functional Limits
and Continuity
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Discussion
Functional Limits
Combinations of
Continuous
Functions
Continuous
Functions on
Compact Sets
The IVT
Sets of
Discontinuity
Chapter 4: Functional Limits and
Continuity
Peter W. White
white@tarlet
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MATH 4093-010
Exam 1
You must show all your work in a clear, clutter free format to receive full credit on
each problem. This is a closed book test. Please do your nal work on either the paper
provided or clean lined paper and staple this cover
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MATH 4093-010
Exam 2
You must show all your work in a clear, clutter free format to receive full credit on
each problem. This is a closed book test. Please do your nal work on either the paper
provided or clean lined paper and staple this cover
MATH 4093 Advanced Analysis
Catalog Description: A study of the theory of the calculus of functions of a single variable.
Topics may include the topology of the real line, functions, sequences and their limits,
continuity, differentiation, and integration
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MATH 4093-010
Final Exam
You must show all your work in a clear, clutter free format to be eligible to receive
full credit on each problem. Please do your nal work on either printer paper or
clean lined paper and staple this cover sheet to the