“…The book chapters are related to fast hybrid recursive FT based on Jacket matrix, acquisition algorithm for global navigation satellite system, determining the sensitivity of output parameters based on FFT, convergence of integrals of products based on Riemann-Lebesgue Lemma function, extending the real and complex number fields for treating the FT, nonmaterial structure, Gabor transform, and chalcopyrite bioleaching. …”

Tabla de Contenidos: “…5.6 The numerical solution to the model -- 5.6.1 The numerical outcomes -- 5.7 Illustrations with graphics -- 5.8 Conclusion -- Availability of data and materials -- References -- 6 Nonlinear fractional integro-differential equations by using the homotopy perturbation method -- 6.1 Introduction -- 6.2 Preliminaries -- Gamma function (GF) [22,23] -- Lipschitz condition (LC) [19] -- Riemann-Liouville fractional integral (RLFI) [22,23] -- Caputo fractional derivative (CFD) [22,23] -- Riemann-Liouville fractional derivative (RLFD) [23-25] -- 6.3 Model of the FVFIDE -- 6.4 HPM -- 6.5 Illustrative examples -- 6.6 Conclusion -- References -- 7 Fractional prey-predator model with fuzzy initial conditions -- 7.1 Introduction -- 7.1.1 Fuzzy differential equations -- 7.1.2 Fractional differential equations -- 7.1.3 Novelty in this chapter -- 7.2 Basic concepts -- 7.2.1 Fuzzy number -- 7.2.2 Fuzzy number in parametric form -- 7.2.3 Triangular fuzzy number -- 7.2.4 Fuzzy arithmetic operations -- 7.2.5 Riemann-Liouville fractional derivative -- 7.2.6 Generalized Hukuhara derivative -- 7.3 Main result -- 7.3.1 Fuzzy Riemann-Liouville fractional derivative -- 7.3.2 Fuzzy fractional prey-predator model -- 7.4 Numerical illustration -- 7.5 Results and discussion -- 7.6 Conclusion -- References -- 8 Taylor series expansion approach for solving fractional order heat-like and wave-like equations -- 8.1 Introduction -- 8.2 Taylor series expansion method -- 8.2.1 Fundamental approach to solve space-fractional PDEs -- 8.2.2 Fundamental approach to solve time-fractional PDEs -- 8.3 Illustrative applications -- 8.3.1 Solution of HLEs -- 8.3.1.1 One-dimensional HLE [9] -- 8.3.1.2 Two-dimensional HLE [9] -- 8.3.2 Solution of WLEs -- 8.3.2.1 One-dimensional WLE [6] -- 8.3.2.2 Two-dimensional WLE [6] -- 8.4 Conclusion -- References…”

Tabla de Contenidos: “…Frontmatter -- Contents -- Fractional Dynamics / Local Fractional Calculus on Shannon Wavelet Basis / Discretely and Continuously Distributed Dynamical Systems with Fractional Nonlocality / Temporal Patterns in Earthquake Data-series / An Integral Transform arising from Fractional Calculus / Approximate Solutions to Time-fractional Models by Integral-balance Approach / A Study of Sequential Fractional q-integro-difference Equations with Perturbed Anti-periodic Boundary Conditions / Fractional Diffusion Equation, Sorption and Reaction Processes on a Surface / Fractional Order Models for Electrochemical Devices / Results for an Electrolytic Cell Containing Two Groups of Ions: PNP - Model and Fractional Approach / Application of Fractional Calculus to Epidemiology / On Numerical Methods for Fractional Differential Equation on a Semi-infinite Interval / From Leibniz's Notation for Derivative to the Fractal Derivative, Fractional Derivative and Application in Mongolian Yurt / Cantor-type spherical-coordinate Method for Differential Equations within Local Fractional Derivatives / Approximate Methods for Local Fractional Differential Equations / Numerical Solutions for ODEs with Local Fractional Derivative / Local Fractional Calculus Application to Differential Equations Arising in Fractal Heat Transfer / Local Fractional Laplace Decomposition Method for Solving Linear Partial Differential Equations with Local Fractional Derivative / Calculus on Fractals / Solutions of Nonlinear Fractional Differential Equations Systems through an Implementation of the Variational Iteration Method / Fractional-order Nonlinear Systems: Chaotic Dynamics, Numerical Simulation and Circuits Design / Fractional Derivative of the Riemann Zeta Function / A Treatment of Generalized Fractional Differential Equations: Sumudu Transform Series Expansion Solutions, and Applications…”

Tabla de Contenidos: “…Quotidian and monadological ontologies -- 4. Application to the Riemann Hypothesis -- Introduction -- Riemann's Hypothesis -- Afterword -- Note -- References -- 7. …”

Tabla de Contenidos: “…Cálculo Integral; Página Legal; Contenido; Unidad 1 Teorema fundamental del cálculo; 1.1 Notación sumatoria; 1.2 Suma de Riemann; 1.3 Primer teorema fundamental del cálculo; 1.4 Segundo teorema fundamental del cálculo; 1.5 Teorema de existencia; 1.6 Teorema del valor medio del cálculo integral; Problemas para resolver; Unidad 2 Métodos de integración Parte 1; 2.1 Propiedades lineales de la integración; 2.2 Integrales inmediatas; 2.3 Integral por cambio de variable; 2.5 Integral de funciones exponenciales; 2.6 Integral de funciones que dan como resultado un logaritmo natural…”

“…Part 1, The Emergence of Sets within Mathematics, surveys the initial motivations for a mathematical notion of a set within several branches of the discipline (geometry, algebra, algebraic number theory, real and complex analysis), emphasizing the role played by Riemann in fostering acceptance of the set-theoretic approach. …”

“…Les dix-sept chapitres de cet ouvrage abordent ces questions à partir des discours qu’ont tenu philosophes et mathématiciens depuis les Sophistes jusqu’à Thom en passant par Galilée, Hobbes, Locke, Diderot, d’Alembert, Hume, Gergonne, Riemann, Houel, Nietzsche, Borel, Poincaré, Einstein, Lautman, Gonseth. …”

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Tabla de Contenidos: “…I.12 Physical commentI.13 Solutions of selected exercises; I.14 Problems; I.14.1 Liouville theorem; I.14.2 Codifferential δ and Laplacian of an exterior form; I.14.3 Geodesic normal coordinates; I.14.4 Cases d=1, 2, and 3; I.14.5 Wave equation satisfied by the Riemann tensor; I.14.6 The Bel-Robinson tensor; I.14.7 The Weyl tensor; I.14.8 The Cotton-York tensor; I.14.9 Linearization of the Riemann tensor; I.14.10 Second derivative of the Ricci tensor; II Special relativity; II.1 Introduction; II.2 Newtonian mechanics; II.2.1 The Galileo-Newton Spacetime…”

“…A lo largo de la obra encontraremos problemas resueltos -como la Conjetura de Poincaré, resuelto por el genio excéntrico Grigori Perelman, que rechazó los honores académicos y un premio del millón de dólares por su trabajo- y otros que, como la Hipótesis de Riemann, siendo desconcertante después de siglos. …”

“…The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. …”

Tabla de Contenidos: “…CAUCHY Y LAS SERIES DE FUNCIONES -- 1.4. LA INTEGRAL DE RIEMANN Y LA REPRESENTACIÓN DE FUNCIONES -- 1.5. CANTOR Y LA REPRESENTACIÓN DE FUNCIONES -- 1.6. …”

Tabla de Contenidos: “…8 Prime Numbers 8.1 Prime Number Generators; 8.2 The Prime Number Theorem; 8.3 Products of Geometric Series; 8.4 The Riemann Zeta Function; 8.5 Real Numbers; 9 Logic and Meta-Mathematics; 9.1 The Collection of All Sets; 9.2 Other Than True or False; 9.3 The Logic of A Theory of Everything; 9.3.1 Gödel's Incompleteness Theorem; 9.3.2 Logically Closed Sets; 9.3.3 Applications; Bibliography; Index…”

Tabla de Contenidos: “…CONDICIONES DE CAUCHY-RIEMANN -- 3.4. CONSECUENCIAS DE LA DERIVACIÓN COMPLEJA -- 3.5. …”

Tabla de Contenidos: “…6.5.1 Lebesgue Integrals on a Measurable Set -- 6.5.2 Fuzzy Riemann Integrals Using the Expression in the Decomposition Theorem -- 6.5.3 Fuzzy Riemann Integrals Using the Extension Principle -- Chapter 7 Arithmetics of Fuzzy Sets -- 7.1 Arithmetics of Fuzzy Sets in R -- 7.1.1 Arithmetics of Fuzzy Intervals -- 7.1.2 Arithmetics Using EP and DT -- 7.1.2.1 Addition of Fuzzy Intervals -- 7.1.2.2 Difference of Fuzzy Intervals -- 7.1.2.3 Multiplication of Fuzzy Intervals -- 7.2 Arithmetics of Fuzzy Vectors -- 7.2.1 Arithmetics Using the Extension Principle -- 7.2.2 Arithmetics Using the Expression in the Decomposition Theorem -- 7.3 Difference of Vectors of Fuzzy Intervals -- 7.3.1 α‐Level Sets of A ̃⊖EPB ̃ -- 7.3.2 α‐Level Sets of A ̃⊖DT⋄B ̃ -- 7.3.3 α‐Level Sets of A ̃⊖DT⋆B ̃ -- 7.3.4 α‐Level Sets of A ̃⊖DT†B ̃ -- 7.3.5 The Equivalences and Fuzziness -- 7.4 Addition of Vectors of Fuzzy Intervals -- 7.4.1 α‐Level Sets of A⊕EPB ̃ -- 7.4.2 α‐Level Sets of A⊕DTB ̃ -- 7.5 Arithmetic Operations Using Compatibility and Associativity -- 7.5.1 Compatibility -- 7.5.2 Associativity -- 7.5.3 Computational Procedure -- 7.6 Binary Operations -- 7.6.1 First Type of Binary Operation -- 7.6.2 Second Type of Binary Operation -- 7.6.3 Third Type of Binary Operation -- 7.6.4 Existence and Equivalence -- 7.6.5 Equivalent Arithmetic Operations on Fuzzy Sets in R -- 7.6.6 Equivalent Additions of Fuzzy Sets in Rm -- 7.7 Hausdorff Differences -- 7.7.1 Fair Hausdorff Difference -- 7.7.2 Composite Hausdorff Difference -- 7.7.3 Complete Composite Hausdorff Difference -- 7.8 Applications and Conclusions -- 7.8.1 Gradual Numbers -- 7.8.2 Fuzzy Linear Systems -- 7.8.3 Summary and Conclusion -- Chapter 8 Inner Product of Fuzzy Vectors -- 8.1 The First Type of Inner Product -- 8.1.1 Using the Extension Principle -- 8.1.2 Using the Expression in the Decomposition Theorem…”

Tabla de Contenidos: “…Simpson's rule -- Building the Riemann Sum Formula -- Approximating the definite integral with the area formula for a rectangle -- Widening your understanding of width -- Limiting the margin of error -- Summing things up with sigma notation -- Heightening the functionality of height -- Finishing with the slack factor -- Chapter 5 There Must Be a Better Way - Introducing the Indefinite Integral -- FTC2: The Saga Begins -- Introducing FTC2 -- Evaluating definite integrals using FTC2 -- Your New Best Friend: The Indefinite Integral -- Introducing anti-differentiation -- Solving area problems without the Riemann sum formula -- Understanding signed area -- Distinguishing definite and indefinite integrals -- FTC1: The Journey Continues…”

Tabla de Contenidos: “…Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- About the Authors -- Chapter 1 Introduction to Fractional Calculus -- 1.1 Introduction -- 1.2 Birth of Fractional Calculus -- 1.3 Useful Mathematical Functions -- 1.3.1 The Gamma Function -- 1.3.2 The Beta Function -- 1.3.3 The Mittag-Leffler Function -- 1.3.4 The Mellin-Ross Function -- 1.3.5 The Wright Function -- 1.3.6 The Error Function -- 1.3.7 The Hypergeometric Function -- 1.3.8 The H-Function -- 1.4 Riemann-Liouville (R-L) Fractional Integral and Derivative -- 1.5 Caputo Fractional Derivative -- 1.6 Grünwald-Letnikov Fractional Derivative and Integral -- 1.7 Riesz Fractional Derivative and Integral -- 1.8 Modified Riemann-Liouville Derivative -- 1.9 Local Fractional Derivative -- 1.9.1 Local Fractional Continuity of a Function -- 1.9.2 Local Fractional Derivative -- References -- Chapter 2 Recent Trends in Fractional Dynamical Models and Mathematical Methods -- 2.1 Introduction -- 2.2 Fractional Calculus: A Generalization of Integer-Order Calculus -- 2.3 Fractional Derivatives of Some Functions and Their Graphical Illustrations -- 2.4 Applications of Fractional Calculus -- 2.4.1 N.H. …”

Tabla de Contenidos: “…8.3 Propiedades generales de polinomios ortogonales clásicos -- 8.4 Ejercicios y problemas -- 9 Singularidades en ecuaciones diferenciales lineales -- 9.1 Puntos singulares de una ecuación diferencial lineal -- 9.2 Ecuación diferencial de Riemann -- 9.3 Función hipergeométrica de Gauss -- 9.4 Ejercicios y problemas -- 10 Funciones elípticas -- 10.1 Definiciones y propiedades generales -- 10.2 La función de Weierstrass -- 10.3 Las funciones theta -- 10.4 Las funciones elípticas de Jacobi -- 10.5 Ejercicios y problemas -- Apéndice -- Bibliografía -- Símbolos utilizados -- Índice analítico…”