Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rot...more
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 ...more
1) If you are thinking of reading this book because you are attracted to its "pure" approach, learn some logic. Seriously, just get your head around what deductions are and what the principle of mathematical induction is. I recommend a Fitch-style natural deductive system. Spivak will teach you about calculus but if you don't have the prerequisite logic, you won't really ...more
I was extremely lucky to spot ...more
Very well written, well motivated introduction to analysis, with good problems. I also absolutely love the little annotated bibliography near the end, which you can find here :
Calculus was the very first textbook I read for my university degree. 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.
Unlike many writers of textbooks in mathematics, Spivak makes a big effort to give more than a dry exposition: theorem - proof - ...more
One day I will return to Spivak's Calculus to complete all the exercises; the suggested reading offers some reassurance that readers who have got as far as completing all the exercises probably know a lot more about advanced mathematics (e.g. functional analysis) than is covered by this book. The reason for this is suggested by the final item of t ...more
Many calculus texts motivate the study of the material with physics problems. Spivak does not, although he does point out the applications. Rather, the development of the calculus here proceeds from mathematical considerations. Because of this, the book is certain to be useful to mathematics students--those approaching calculus for the first time, or those who wish to gain deeper insig ...more
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His book Calculus takes a very rigorous and theoretical approach to ...more