# Elementary Analysis: The Theory of Calculus by Ross

• Analysis
• micromass
In summary, Kenneth Ross' book "Elementary Analysis: The Theory of Calculus" is a good introductory book for undergraduate students with a background in proofs and set theory. Ross covers a good amount of material and explains it thoroughly, making it a useful supplement for struggling students. However, the book is not the most advanced and may not cover enough topics for students planning to pursue graduate studies in mathematics. Additionally, some topics, such as the construction of the real numbers and exponential and logarithmic functions, are not covered in enough depth. Overall, it is a sufficient book for introductory analysis, but other books such as Abbott's "Understanding Analysis" may be more suitable for students looking for a more rigorous and comprehensive approach.

## For those who have used this book

• ### Strongly don't Recommend

• Total voters
2
micromass
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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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SrVishi said:

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.

bacte2013 said:
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.

I bought this book 35 years ago and still have it today. This was my introduction to rigorous maths. How difficult some of those concepts seemed back then. And how exciting when the light went on one day and it all started to make sense.

The strength of the book is its clarity in presenting material that is probably very different from anything the student has come across before. Other books I considered at the time seemed to assume a general familiarity with rigorous concepts, which I didn't have.

For me it represented a whole new way of thinking. Where would I have been without it!

A nostalgic rather than objective review perhaps.

## 1. What is "Elementary Analysis: The Theory of Calculus by Ross" about?

"Elementary Analysis: The Theory of Calculus by Ross" is a textbook that covers the fundamental concepts and principles of calculus, including limits, derivatives, integrals, and applications of these concepts.

## 2. Who is the author of "Elementary Analysis: The Theory of Calculus by Ross"?

The author of "Elementary Analysis: The Theory of Calculus by Ross" is Kenneth A. Ross, a mathematician and professor at the University of Oregon.

## 3. Is "Elementary Analysis: The Theory of Calculus by Ross" suitable for beginners?

Yes, the textbook is designed for students who are new to calculus and have a basic understanding of algebra and trigonometry.

## 4. What sets "Elementary Analysis: The Theory of Calculus by Ross" apart from other calculus textbooks?

"Elementary Analysis: The Theory of Calculus by Ross" is known for its clear and concise explanations, numerous examples and exercises, and emphasis on building a solid foundation in calculus.

## 5. How can "Elementary Analysis: The Theory of Calculus by Ross" be used in a classroom setting?

The textbook can be used as a primary resource for a calculus course, or as a supplement to other textbooks. It also includes helpful features such as chapter summaries and review exercises for students to practice and reinforce their understanding of the material.

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