# Elementary Analysis: The Theory of Calculus by Ross

• Analysis

## For those who have used this book

• ### Strongly don't Recommend

• Total voters
2

Code:
[LIST]
[*] Preface
[*] Introduction
[LIST]
[*] The Set N of Natural Numbers
[*] The Set Q of Rational Numbers
[*] The Set R of Real Numbers
[*] The Completeness Axiom
[*] The Symbols +\infty and -\infty
[*] A Development of R
[/LIST]
[*] Sequences
[LIST]
[*] Limits of Sequences
[*] Limit Theorems for Sequences
[*] Monotone Sequences and Cauchy Sequences
[*] Subsequences
[*] lim sup's and lim inf's
[*] Some Topological Concepts in Metric Spaces
[*] Series
[*] Alternating Series and Integral Tests
[*] Decimal Expansions of Real Numbers
[/LIST]
[*] Continuity
[LIST]
[*] Continuous Functions
[*] Properties of Continuous Functions
[*] Uniform Continuity
[*] Limits of Functions
[*] More on Metric Spaces: Continuity
[*] More on Metric Spaces: Connectedness
[/LIST]
[*] Sequences and Series of Functions
[LIST]
[*] Power Series
[*] Uniform Convergence
[*] More on Uniform Convergence
[*] Differentiation and Integration of Power Series
[*] Weierstrass's Approximation Theorem
[*] Differentiation
[*] Basic Properties of the Derivative
[*] The Mean Value Theorem
[*] L'Hospital's Rule
[*] Taylor's Theorem
[/LIST]
[*] Integration
[LIST]
[*] The Riemann Integral
[*] Properties of the Riemann Integral
[*] Fundamental Theorem of Calculus
[*] Riemann-Stieltjes Integrals
[*] Improper Integrals
[*] A Discussion of Exponents and Logarithms
[/LIST]
[*] Appendix on Set Notation
[*] References
[*] Symbols Index
[*] Index
[/LIST]

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I also recommend the "Analysis I-II" by Terrence Tao. He starts by building up the comprehensive and detailed construction of the real numbers and set theory. Proofs are also covered in detail, including what proof technique will be best for proving certain theorems and also providing valuable hints about proving on your own. I actually started studying the analysis by studying the first few chapters on Analysis I and jumping to Apostol and Pugh. Tao's brilliant yet clear exposition and treatment of the real number system and set theory made the transition very smooth. Another books I recommend are "Real Numbers and Real Analysis" by Ethan Bloch and "Introduction to Analysis" by Mattuck.

By the way, Tao also keeps the ongoing errata list on his blog.

I also recommend the "Analysis I-II" by Terrence Tao. He starts by building up the comprehensive and detailed construction of the real numbers and set theory. Proofs are also covered in detail, including what proof technique will be best for proving certain theorems and also providing valuable hints about proving on your own. I actually started studying the analysis by studying the first few chapters on Analysis I and jumping to Apostol and Pugh. Tao's brilliant yet clear exposition and treatment of the real number system and set theory made the transition very smooth. Another books I recommend are "Real Numbers and Real Analysis" by Ethan Bloch and "Introduction to Analysis" by Mattuck.

By the way, Tao also keeps the ongoing errata list on his blog.
I would love to read Tao's books but I can't seem to find them online. Whenever I go to his website, it seems to be a broken link!

Oh, boy. I remember this book from when I was starting to learn advanced math (proofs) and had no training in proof-writing. In fact, when I took Real Analysis in grad school, I wasn't even sure I had undergraduate-level analysis back then. It turns out I did; it was under the name "Advanced Calculus" and silly me couldn't make the connection.

Now that I have some type of analysis background (one semester in Real Analysis and one in Functional Analysis), I'm willing to give this book another try.

PeroK