Sökning: "Integrals of Riemann"

Hittade 3 uppsatser innehållade orden Integrals of Riemann.

  1. 1. Complex Multiplicative Calculus and Mixed Problems

    Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Axel Lokrantz; [2022]
    Nyckelord :multiplicative integrals; multiplicative calculus; product integrals; geometric mean; continuous geometric mean; geometric mean of non-negative random variables; inequality of arithmetic and geometric means; A_G-G_A inequality; generalized Hölder s inequality; multiplicative vector spaces; multiplicative function spaces; exponential transition functor; logarithmic Riemann surface; lift; function lift; projection; function projection; lift-projection method; multivalued complex multiplicative integrals; geometric expectation; mixed differential equation; Lambert W function; W; M; w and m functions; Mathematics and Statistics;

    Sammanfattning : In this thesis we consider multiplicative integrals and derivatives on functions on the positive numbers, the logarithmic Riemann surface and the punctured complex numbers. Additive structures on the real and complex numbers are related to their multiplicative counterparts on the positive numbers and the logarithmic Riemann surface by defining exponential transition functors. LÄS MER

  3. 2. The Henstock–Kurzweil Integral

    Kandidat-uppsats, Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Författare :Manolis David; [2020]
    Nyckelord :Henstock–Kurzweil integral; generalized Riemann integral; gauge integral; Denjoy–Perron integral; narrow Denjoy integral; Perron integral; non-absolute integration; Lebesgue outer measure; absolute integrability; fundamental theorem of calculus; convergence theorems; single variable calculus;

    Sammanfattning : Since the introduction of the Riemann integral in the middle of the nineteenth century, integration theory has been subject to significant breakthroughs on a relatively frequent basis. We have now reached a point where integration theory has been thoroughly researched to a point where one has to delve quite deep into a particular subject in order to encounter open conjectures. LÄS MER

  4. 3. Generalized Riemann Integration : Killing Two Birds with One Stone?

    Kandidat-uppsats, Matematik och tillämpad matematik; Tekniska högskolan

    Författare :David Larsson; [2013]
    Nyckelord :Measure and integration; Special integrals; Henstock-Kurzweil integral; gauge integral; generalized Riemann integral; Denjoy and Perron integrals; Integrals of Riemann; Stieltjes and Lebesgue type; Antidifferentiation; One-variable calculus; Functions of bounded variation; Functions of several variables; Absolute integrability; Convergence theorems;

    Sammanfattning : Since the time of Cauchy, integration theory has in the main been an attempt to regain the Eden of Newton. In that idyllic time [. . . LÄS MER