For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises. A few other changes and renumbering of Problems result from corrections, and elimination of incorrect problems. More Hamburger icon An icon used to represent a menu that can be toggled by interacting with this icon. It is more convenient, however, to consider addition of pairs of numbers only, and to define other sums in terms of sums of this type.

A favor tiene el enfoque matemático que no desestima las aplicaciones ingenieriles, pero prioriza la teoría formal pura.However, it is recommended for students who have a strong foundation in algebra and trigonometry and are comfortable with abstract mathematical concepts. Only after picking it up I figured why my Math professors said math is a beautiful and logical subject, I really can't stress how much this book changed my perspective. There are now separate Appendices for many topics that were previously slighted: polar coordinates, uniform continuity, parameterized curves, Riemann sums, and the use of integrals for evaluating lengths, volumes and surface areas. But if you are looking to learn mathematics--in this case, calculus--then get your ass over this book and start engaging the grey matter.

As other posters have said, if you are going to be a mathematics or physics major, there is no reason to even look at another calculus text. Has a lot of explainig clear graphics,give examples of bizarre functions for clearing concepts,give a original introduction to complex variable by convergent complex power series,makes a formal costruction of the real numbers field, and make at this level unusual excursions in more advanced results as the demostration of the irracionality of pi or the demostration of the trancendence of e.

As well as being a fine description of the basics of analysis (mostly real, with a toe in the deep water of complex functions), it is an excelent book to ease the transition from mathematics as taught at school level to the rigours of university mathematics.

Considering that this book is a bit old and consequently uses unusual notations, the explanations are extremely good and the author's approach reminds me of the best Leonard Euler's texts. In practice, it is usually just a waste of time to solve an equation by indicating so explicitly the reliance on properties Pl, P2, and P3 (or any of the further properties we shall list).

I am especially grateful to my friends Michael Freeman, Jay Goldman, Anthony Phillips, and Robert Wells for the care with which they read, and the relentlessness with which they criticized, a preliminary version of the book. Si hay convergencias entre estos mundos formales y el mundo humano es más sorprendente que necesario, como lo sugirió Bertrand Russell en su Autobiografía. In fact, this short chapter is simply an explanation of what is meant by the “basic properties of numbers,” all of which—addition and multiplication, subtraction and division, solutions of equations and inequalities, factoring and other algebraic manipulations—are already familiar to us. Like putting an everyday object under a microscope: very interesting, but now there are many more interesting objects I want to put under a microscope. But seriously--if you're looking for practical application or pragmatic knowledge then this book isn't exactly for you.