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Calculus

Calculus

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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 summary, Calculus Michael Spivak 4th Edition is a renowned textbook written by mathematician Michael Spivak that covers a wide range of topics in calculus, including limits, derivatives, integrals, sequences and series, and multivariable calculus. For the moment we consider only addition: this operation is performed on a pair of numbers—the sum a + b exists for any two given numbers a and b (which may possibly be the same number, of course). It also includes challenging exercises and proofs to help students develop a deeper understanding of the material.

The answer section contains solutions to about half the examples from an assortment of problems that should provided a good test of technical competence. It is then possible to find the solution of certain simple equations by a series of steps (each justified by Pl, P2, or P3) similar to the ones just presented for the equation a + x = a. One can first add b and c, obtaining b + c, and then add a to this number, obtaining a + (b + c); or one can first add a and b, and then add the sum a + b to c, obtaining (a + b) + c.I have had time to make only a few changes to the Suggested Reading, which after all these years probably requires a complete revision; this will have to wait until the next edition, which I hope to make in a more timely fashion. Regarding its frequent recommendation to beginning Calculus students, it is far from an ideal book to learn from. It might seem reasonable to regard addition as an operation which can be performed on several numbers at once, and consider the sum a\ + • • • + an of n numbers a\,.

Finally, there is a Suggested Reading list, to which the problems often refer, and a glossary of symbols. If anyone has it or knows where I can download it from it would be much appreciated if you can help! I have often been told that the title of this book should really be something like “An Introduction to Analysis,” because the book is usually used in courses where the students have already learned the mechanical aspects of calculus—such courses are standard in Europe, and they are becoming more common in the United States.The reason for this is suggested by the final item of the reading list: where the author suggests that one could learn as much from all of the other items on the reading list by simply reading the “Oeuvres complètes de Niels Henrik Abel”, Abel being the same mathematician who lends his name to the 'Nobel' in mathematics, the Abel Prize. About half of this course was devoted to algebra and topology, while the other half covered calculus, with the preliminary edition as the text. I was both startled and somewhat dismayed when I realized that after allow­ ing 13 years to elapse between the first and second editions of the book, I have allowed another 14 years to elapse before this third edition. Eso está muy bien porque las matemáticas son teorías de formas puras en las que cada concepto está saturado de teoría. Except "Suggested Reading", I think there is almost no difference between 3rd edition and 4th edition.

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.

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. These can be helpful for students who want additional practice and support in understanding the material.

The basic properties of multiplication are fortunately so similar to those for ad­ dition that little comment will be needed; both the meaning and the consequences should be clear.Considerable attention is paid to motivating the discussion, showing why each result is important (though mainly in the pure mathematics context, applications of calculus being mainly found in the problems at the end of each chapter). Naturally, such elaborate solutions are of interest only until you become convinced that they can always be supplied. The Trigonometric Functions 303 *16 7T is Irrational 324 *17 Planetary Motion 330 18 The Logarithm and Exponential Functions 19 Integration in Elementary Terms 363 Appendix.



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