Mathematical Analysis: A Straightforward Approach 2nd Edition by K. G. Binmore (PDF)

Description

For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I enjoyed this book and this class.

⭐True its an older version (last printing 1999), but its straightforward style starts you out with explaining what a notation is, then never let’s go till you understand the hard stuff!

⭐I’m reading Walter Rudin’s “Principles of Mathematical Analysis” along with this one. If I cannot follow Rudin’s exposition, I refer to this book and try to get at least one version of the exposition that I can understand. Then, tackle again what Rudin has to offer. Binmore’s explanation is easy to follow. On the other hand, Rudin’s is a bit more abstract and has more surprisingly elegant proofs (and you have to fill in the gaps if they don’t strike you as logical).

⭐The book was in good condition.

⭐This book is really good for reviewing math analysis. I picked up this book to help me understand my course text and used this as a supplant. Good book. Lots of pictures.

⭐This is almost same as it was described except some black shade on the back cover. Inside the book, everything is OK. Moreover, it is a recent reprinted edition.

⭐Great book, but the price for the kindle version is ridiculous! Hey publisher, if you want to sell this book in electronic format, cut the price!I have a used one I got cheap.

⭐This book is ideal for self study. It has complete solutions to all the exercises in the book. A very good introduction to real analysis. Basic calculus is all that is needed to understand the book. Stirling’s approximation, Gamma and Beta functions are some of the topics in the book that are not generally found in a book at this level. This is an elementary book – but rigorous, in my opinion. If you want to get started in analysis this book would be an ideal place to start. And given the current price of the book, it is a steal. There are some typos but none too serious.

⭐* PhysicalThis book has ok paper, 361 pages and the fonts are an ok size to read with.* Target audience, H.N.D, Undergraduate, Post Graduate, Masters?It’s definitely in the first – year Mathematics degree level of helpfulness.* TopicsReal numbers, Continuum property, Natural numbers, Convergent series, Subsequences, Series, Functions, Limits of functions, Continuity, Differentiation, Mean values theorems, Monotone functions, Integration, Exponential and logarithm, Power series, Trigonometric Functions, the Gamma function, Vectors, Vector Derivatives. Worked examples (lots), further problems, , suggested further reading, Index* What’s the best bits then?This book looks like its been typeset in the 1980s. It removes the algebraic underpinning to real analysis, which in turn underpins the Calculus, and starts explaining the real analysis and Calculus topics only. You can view these algebraic topics in another book sometime later. So you accept this missing underpinning on faith with the author. I read another book on this same topic, so this is a refresher for me to be learning this. It’s straightforward and clear. It’s a big deal to master this when you’re starting out in this area topic. It’s as good as any other, given and accepting this simplification.* SummaryA clear explanation of real analysis is in its favour. The price for what its selling is against it somewhat. If you get this a lot cheaper for second – hand or other sources will swing it back into favour.

⭐it came in good condition though it did look like it was second hand which isn’t great for something sold as “New”

⭐Superb book, sender even wrote me a nice note wishing me luck with my studies!

⭐Laut Vorwort handelt es sich bei diesem kompakten Analysis-Buch um eine ‘unfussy and easy introduction to mathematical analysis’. Dem kann ich nur zustimmen.Der erste Teil des Buches ist den wesentlichen Elementen der eindimensionalen reellen Analysis gewidmet. Aufbauend auf den Ordnungseigenschaften und der Supremumseigenschaft der reellen Zahlen, behandelt der Autor zunächst Folgen, Reihen, Stetigkeit, sowie Differential- und Integralrechnung. Dann folgen Potenzreihen und analytische Entwicklungen der elementaren Funktionen (exp, log, sin und cos) und die Behandlung ihrer grundlegenden Eigenschaften. Den Abschluss des ersten Teils bildet ein Kapitel zur Gammafunktion, in dem auch die Stirlingsche Formel behandelt wird.Der zweite Teil beschäftigt sich mit der Anwendung von Resultaten des ersten Teils auf die Analysis im R^n. Das Kapitel ‘Vectors’ behandelt reelle Vektoren, den euklidischen Abstandsbegriff, Konvergenz und Stetigkeit. Das Kapitel ‘Vector derivatives’ behandelt partielle Ableitungen, die Ableitung im R^n, sowie stationäre Stellen und Extrema. Auf eine Einführung von grundlegenden topologischen Eigenschaften wird verzichtet.Mir gefällt sehr, dass die Entwicklung der Theorie weitgehend ‘self contained’ ist. So werden in Beweisen, Beispielen und Aufgaben -abgesehen von algebraischen Grundeigenschaften der natürlichen, ganzen und rationalen Zahlen- fast nur bereits bewiesene oder explizit aufgeführte Annahmen benutzt. So kommen zum Beispiel die elementaren Funktionen nicht vor (noch nicht einmal in Beispielen), bevor sie analytisch eingeführt wurden. Im zweiten Teil werden nur grundlegende Kenntnisse der linearen Algebra vorrausgesetzt, wobei an den entsprechenden Stellen ausdrücklich auf diese hingewiesen wird.Da ich dieses Buch zum Selbststudium nutze, war letztendlich aber das Vorhandensein von Lösungswegen zu den Aufgaben ausschlaggebend für meinen Kauf.

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