Focus on Calculus


Svetlin G. Georgiev (Editor)
Sorbonne University, Paris, France
Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

Series: Mathematics Research Developments
BISAC: MAT005000

This book is devoted to some recent aspects of calculus. The book contains seven chapters. Chapter 1 introduces the conception for conformable delta (Hilger) derivative and some of its properties. Results in this chapter include basic conformable delta derivative, the conformable exponential function, conformable trigonometric and hyperbolic functions, conformable delta integral and integral rules and Taylor’s formula. They are considered first order conformable dynamic equations on time scales. Chapter 2 is devoted to some classes second order quadratic difference equations. They are given criteria for existence of a unique equilibrium point that is stable and unstable, existence of prime period-two solutions. Chapter 3 is aimed to develop two calculi over the specific algebraic operations, preserving the preceding relativistic addition formula and having all ordinary properties. Chapter 4 is devoted to principles of hypercomplex random function calculus.


Generalized Gaussian-type hypercomplex valued measures are studied. Random functions controlled by these measures are investigated. Solutions of hyperbolic PDEs over hypercomplex numbers such as the octonion algebra and Cayley-Dickson algebras are scrutinized. Chapter 5 covers the interesting historical aspects of the spreadsheets and their distinct advantages. It is described how the ubiquitous Microsoft Excel spreadsheets can be used to implement well-known numerical methods such as Simpson’s Rule and Trapezoidal Rules. Appropriate examples are presented in substantial detail. The aim of Chapter 6 is to show some didactic tools that can be suggested by professors so that students can recall those issues saved in the deepest part of their minds. In Chapter 7, based on fractional differences, a fractional calculus is developed which complies with most of the properties that is to say non-differentiability, non-commutativity of derivative and long-range memory. The book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers and biologists.



Table of Contents


Chapter 1. Conformable Dynamic Calculus on Time Scales
(Svetlin G. Georgiev, Sorbonne University, Paris, France)

Chapter 2. General Second Order Quadratic Fractional Equation
(Yevgeniy Kostrov, Manhattanville College, Purchase, NY, US)

Chapter 3. Relativistic Velocity Addition and Calculi Based on Hyperbolic Tangent
(Agamirza E. Bashirov and Sinem Genc, Department of Mathematics, Eastern Mediterranean University Gazimagusa, Turkey)

Chapter 4. Principles of Hypercomplex Random Function Calculus
(S. V. Ludkovsky)

Chapter 5. Microsoft Excel for Numerical Calculus
(Sameen Ahmed Khan, Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah, Oman)

Chapter 6. Keeping Alive Calculus Outstanding Issues While Studying Engineering Careers
(Marta Caligaris, Georgina Rodríguez and Lorena Laugero, Grupo Ingeniería and Educación, Facultad Regional San Nicolás, Universidad Tecnológica Nacional, San Nicolás, Buenos Aires, Argentina)

Chapter 7. Focus on Non-Commmutative Fractional Calculus
(Guy Jumarie, Department of Mathematics, University of Quebec at Montreal, Downtown Station, Montreal, QC, Canada)


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