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This book introduces the main ideas and fundamental methods of iso-differential calculus for iso-functions of several variables. Introduced are the iso-functions of the first, second, third, fourth and fifth kind, and iso-partial derivatives of the first, second, third, fourth, fifth, sixth and seventh kind. In this book, the main conceptions for multiple, line and surface iso-integrals for iso-functions of several variables are given. The book is provided with examples and exercises making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects o

Differential calculus. --- Calculus, Differential --- Calculus

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Dinàmica --- Sistemes borrosos --- Optimització matemàtica --- Mètodes de simulació --- Jocs d'estratègia (Matemàtica) --- Optimització combinatòria --- Programació dinàmica --- Programació (Matemàtica) --- Anàlisi de sistemes --- Lògica borrosa --- Cinètica --- Matemàtica --- Mecànica analítica --- Aerodinàmica --- Cinemàtica --- Caos (Teoria de sistemes) --- Dinàmica molecular --- Electrodinàmica --- Estabilitat --- Matèria --- Moviment --- Moviment rotatori --- Pertorbació (Matemàtica) --- Teoria quàntica --- Termodinàmica --- Estàtica --- Física --- Energia --- Mecànica --- Dynamics. --- Lògica difusa

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"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"--

Calculus

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This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

Mathematics. --- Functional analysis. --- Integral equations. --- Differential equations. --- Numerical analysis. --- Ordinary Differential Equations. --- Integral Equations. --- Numerical Analysis. --- Functional Analysis. --- 517.91 Differential equations --- Differential equations --- Functional calculus --- Equations, Integral --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Differential Equations. --- Mathematical analysis

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This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations