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In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function , the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.
Pages in category "Theorems in real analysis" The following 45 pages are in this category, out of 45 total. ... Taylor's theorem; Titchmarsh convolution theorem; U.
Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis focuses on the real numbers, often including positive and negative infinity to form the extended real line.
A function defined on some subset of the real line is said to be real analytic at a point if there is a neighborhood of on which is real analytic. The definition of a complex analytic function is obtained by replacing, in the definitions above, "real" with "complex" and "real line" with "complex plane".
An Introduction to Complex Analysis in Several Variables. Van Nostrand. Rudin, Walter (1976). Principles of Mathematical Analysis. Walter Rudin Student Series in Advanced Mathematics (3rd ed.). McGraw-Hill. ISBN 9780070542358. Rudin, Walter (1986). Real and Complex Analysis (International Series in Pure and Applied Mathematics). McGraw-Hill.
Taylor's theorem – gives an approximation of a times differentiable function around a given point by a -th order Taylor-polynomial. L'Hôpital's rule – uses derivatives to help evaluate limits involving indeterminate forms; Abel's theorem – relates the limit of a power series to the sum of its coefficients
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Danskin's theorem (convex analysis) Darboux's theorem (real analysis) Darboux's theorem (symplectic topology) Davenport–Schmidt theorem (number theory, Diophantine approximations) Dawson–Gärtner theorem (asymptotic analysis) de Branges's theorem (complex analysis) de Bruijn's theorem (discrete geometry) De Bruijn–Erdős theorem ...