The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.
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The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.
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Most Helpful Customer Reviews
5.0 out of 5 stars
Great Intro Analysis book,
By Towert7 (MA, USA) - See all my reviews
This review is from: Fundamental Ideas of Analysis (Paperback)
This book is aimed at the advanced undergraduate course (not the graduate level).
I worked through most of the book in an advanced undergraduate course in real analysis (one semester). I later finished the chapters we skipped on my own. Prior to taking the course I had almost no prior knowledge of mathematical reasoning (induction, contradiction, contrapositive, etc). Thankfully the book does a very good job of explaining each proof and what techniques are used. The book uses very simple and clear notation which made learning the material easier. A lot of the homework problems apply the section material to harder problems than are featured in the examples. Thankfully the basics are covered nicely, leaving the student prepared to think about the more complicated problems. Some of the projects take a good deal of effort though. The book is a great size and the text is very easy to read (great layout). I am very happy to have used this book and would recommend it to others.
4.0 out of 5 stars
good book,
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This review is from: Fundamental Ideas of Analysis (Paperback)
this is a very good book if you are new to real analysis; the examples provided by the author are extremely helpful. if you already have basic knowledge about analysis or proof, do not get this book but Rudin's "Principles of Mathematical Analysis," which is very concise with no example or detailed explanations.
If you are not a math major (or just a BA math like me), I highly suggest you to get this book instead of the Rudin's book; writing rigorous proofs are hard for beginners, but this book definitely sets a solid foundation for you.
11 of 18 people found the following review helpful:
5.0 out of 5 stars
Reed,
By A Customer
This review is from: Fundamental Ideas of Analysis (Paperback)
This book is an excellent introduction to real analysis. It is written in a fairly informal style which allows the topics to sink in. If I were a student new to analysis, I would recommend buying this book along with one of the more formal texts (ex. Rudin).
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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nth check, starred sections, orthonormal family, harmonic series diverges, sup norm, finite expectation, contraction mapping principle, twice continuously differentiable function, difference quotient Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mean Value Theorem, Fundamental Theorem of Calculus, Intermediate Value Theorem, Weierstrass M-test New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
nth check, starred sections, orthonormal family, harmonic series diverges, sup norm, finite expectation, contraction mapping principle, twice continuously differentiable function, difference quotient Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mean Value Theorem, Fundamental Theorem of Calculus, Intermediate Value Theorem, Weierstrass M-test New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
1
book
cites this book:
- Complex Variables and Applications by James Ward Brown in Back Matter
- Calculus of Variations (Dover Books on Mathematics) by I. M. Gelfand in Back Matter
- The History of Mathematics: A Reader by John Fauvel in Back Matter
- Advanced Calculus of Several Variables (Dover Books on Mathematics) by C. H. Edwards Jr. in Back Matter
- Computing Examples Supplement to Models in Biology: Mathematics, Statistics and Computing by D. Brown in Back Matter
- Basic Real Analysis by Houshang H. Sohrab in Back Matter
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