RealAnalysisResources

Companion Notes for Advanced Calculus
Title & Table of Contents (in pdf format)
The Field of Reals and Beyond (in pdf format)
From Finite to Uncoutable Sets (in pdf format)
Metric Spaces and Some Basic Topology (in pdf format)
Sequence and Series--First View (in pdf format)
Functions on Metric Spaces and Continuity (in pdf format)
Differentiation: Our First View (in pdf format)
Riemann-Stieltjes Integration (in pdf format)
Sequences and Series of Functions (in pdf format)
Some Special Functions (in pdf format)
Index (in pdf format)
https://www.math.ucdavis.edu/~emsilvia/math127/math127.html


Introduction to Analysis
 Chapter 1: Sets and Functions
Chapter 2: Numbers
Chapter 3: Sequences
Chapter 4: Series
Chapter 5: Topology of the Real Numbers
Chapter 6: Limits of Functions
Chapter 7: Continuous Functions
Chapter 8: Differentiable Functions
Chapter 9: Sequences and Series of Functions
Chapter 10: Power Series
Chapter 11: The Riemann Integral
Chapter 12: Applications of the Riemann Integral
Chapter 13: Metric, Normed, and Topological Spaces
https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.html

Metric_Spaces Proofs
https://www.math.utah.edu/~tan/6710_FA/Chapter_1_Metric_Spaces

Metric Spaces
https://faculty.math.illinois.edu/~mjunge/metricmas.pdf

Notes on Metric Spaces
https://sites.math.northwestern.edu/~scanez/courses/320/notes/metric-spaces.pdf

Metric, Normed, and Topological Spaces
https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/ch13.pdf

Real Analysis
Notes on Supremums and Infimums
Notes on the Point-Set Topology of R
Notes on Compactness
Notes on Metric Spaces
The Completion of a Metric Space
Notes on Analytic Functions
The Riemann-Lebesgue Theorem
https://sites.math.northwestern.edu/~scanez/courses/320/

What to remember about metric spaces
http://www.its.caltech.edu/~kcborder/Notes/MetricSpaces.pdf

THEORY OF METRIC SPACES
LECTURE NOTES AND EXERCISES
http://www.macs.hw.ac.uk/~jim/F13YE2/analysis_notes.pdf