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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis
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Introduction to Analysis in One Variable (Paperback)
Loot Price: R2,181
Discovery Miles 21 810
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Introduction to Analysis in One Variable (Paperback)
Series: Pure and Applied Undergraduate Texts
Expected to ship within 12 - 17 working days
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This is a text for students who have had a three-course calculus
sequence and who are ready to explore the logical structure of
analysis as the backbone of calculus. It begins with a development
of the real numbers, building this system from more basic objects
(natural numbers, integers, rational numbers, Cauchy sequences),
and it produces basic algebraic and metric properties of the real
number line as propositions, rather than axioms. The text also
makes use of the complex numbers and incorporates this into the
development of differential and integral calculus. For example, it
develops the theory of the exponential function for both real and
complex arguments, and it makes a geometrical study of the
curveĀ (expit)(expit), for realĀ tt, leading to a
self-contained development of the trigonometric functions and to a
derivation of the Euler identity that is very different from what
one typically sees. Further topics include metric spaces, the
StoneāWeierstrass theorem, and Fourier series.
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