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Calculus

  • Kartonierter Einband
  • 124 Seiten
Source: Wikipedia. Pages: 121. Chapters: Continuous function, Series, Complex analysis, List of mathematical functions, Geometric... Weiterlesen
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Source: Wikipedia. Pages: 121. Chapters: Continuous function, Series, Complex analysis, List of mathematical functions, Geometric series, Taylor's theorem, Uniform convergence, Uniform continuity, Mean value theorem, Infinitesimal calculus, Periodic function, Calculus with polynomials, Newton's notation, Monotone convergence theorem, Partial fractions in integration, Differential of a function, Fundamental theorem of calculus, Madhava of Sañgamagrama, Limit of a function, Non-standard calculus, Fractional calculus, Leibniz and Newton calculus controversy, The Method of Mechanical Theorems, Yuktibha a, Rolle's theorem, Leibniz integral rule, Maxima and minima, Euler spiral, Binary logarithm, Extreme value theorem, Time scale calculus, Advanced Placement Calculus, Hyperbolic angle, Related rates, Even and odd functions, Binomial series, Change of variables, Berezin integral, Operational calculus, Fresnel integral, Timeline of calculus and mathematical analysis, Tractrix, Louis Leithold, Regiomontanus' angle maximization problem, First derivative test, Semi-differentiability, Gabriel's Horn, Alternating series, Functional integration, Evaluating sums, Root test, Quantum differential calculus, Leibniz formula for pi, Visual calculus, Integral of secant cubed, C. M. Whish, Thomae's function, Elementary Calculus: An Infinitesimal Approach, List of calculus topics, Term test, Dirichlet integral, Outline of calculus, List of types of functions, Viète's formula, Racetrack principle, Reduction, Infinitely near point, Slope field, Ghosts of departed quantities, Hermitian function, Perron's formula, General Leibniz rule, Calculus on Manifolds, Hyperinteger, Quasi-continuous function, Bohr-Mollerup theorem, Reflection formula, Focaloid, Standard part function, Increment theorem, Cauchy's convergence test, Homoeoid, Limits of integration, Maplets for Calculus, Higher-order derivative test. Excerpt: A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely. In mathematics, given an infinite sequence of numbers , a series is informally the result of adding all those terms together: a1 + a2 + a3 + · · ·. These can be written more compactly using the summation symbol . An example is the famous series from Zeno's dichotomy The terms of the series are often produced according to a certain rule, such as by a formula, or by an algorithm. As there are an infinite number of terms, this notion is often called an infinite series. Unlike finite summations, infinite series need tools from mathematical analysis to be fully understood and manipulated. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics and computer science. Series can be composed of terms from any one of many different sets including real numbers, complex numbers, and functions. The definition given here will be for real numbers, but can be generalized. Given an infinite sequence of real numbers , define Call SN the to N of the sequence , or partial sum of the series. A series is the sequence of partial sums, . Observe that partial summation takes as input a sequence, , and gives as output another sequence, - partial summation is thus an unary operation on sequences. Further, this function is linear, and thus is a linear operator on the vector space of sequences, denoted S. The inverse operator is the finite...

Produktinformationen

Titel: Calculus
Untertitel: Continuous function, Series, Complex analysis, List of mathematical functions, Geometric series, Taylor's theorem, Uniform convergence, Uniform continuity, Mean value theorem, Infinitesimal calculus, Periodic function
Editor:
EAN: 9781157592006
ISBN: 1157592007
Format: Kartonierter Einband
Anzahl Seiten: 124
Gewicht: 671g
Größe: H246mm x B189mm x T7mm
Jahr: 2011
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