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  2. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    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.

  3. Real analysis - Wikipedia

    en.wikipedia.org/wiki/Real_analysis

    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.

  4. Analytic function - Wikipedia

    en.wikipedia.org/wiki/Analytic_function

    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".

  5. Category:Theorems in real analysis - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in_real...

    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.

  6. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    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–ErdÅ‘s theorem ...

  7. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...

  8. Linear approximation - Wikipedia

    en.wikipedia.org/wiki/Linear_approximation

    Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case = states that = + ′ () + where is the remainder term. The linear approximation is obtained by dropping the remainder: () + ′ ().

  9. Category:Real analysis - Wikipedia

    en.wikipedia.org/wiki/Category:Real_analysis

    Real analysis is a traditional division of mathematical analysis, along with complex analysis and functional analysis. It is mainly concerned with the 'fine' (micro-level) behaviour of real functions, and related topics. See Category:Fourier analysis for topics in harmonic analysis.