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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis
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Approximately Calculus (Hardcover, Illustrated Edition)
Loot Price: R1,944
Discovery Miles 19 440
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Approximately Calculus (Hardcover, Illustrated Edition)
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Is there always a prime number between $n$ and $2n$? Where,
approximately, is the millionth prime? And just what does calculus
have to do with answering either of these questions? It turns out
that calculus has a lot to do with both questions, as this book can
show you. The theme of the book is approximations. Calculus is a
powerful tool because it allows us to approximate complicated
functions with simpler ones. Indeed, replacing a function locally
with a linear - or higher order - approximation is at the heart of
calculus. The real star of the book, though, is the task of
approximating the number of primes up to a number $x$. This leads
to the famous Prime Number Theorem - and to the answers to the two
questions about primes. While emphasizing the role of
approximations in calculus, most major topics are addressed, such
as derivatives, integrals, the Fundamental Theorem of Calculus,
sequences, series, and so on.However, our particular point of view
also leads us to many unusual topics: curvature, Pade
approximations, public key cryptography, and an analysis of the
logistic equation, to name a few. The reader takes an active role
in developing the material by solving problems. Most topics are
broken down into a series of manageable problems, which guide you
to an understanding of the important ideas. There is also ample
exposition to fill in background material and to get you thinking
appropriately about the concepts. ""Approximately Calculus"" is
intended for the reader who has already had an introduction to
calculus, but wants to engage the concepts and ideas at a deeper
level. It is suitable as a text for an honors or alternative second
semester calculus course.
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