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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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Calculus.

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Calculus of tensors. --- Engineering mathematics.

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Sans le calcul infinitésimal, il n'existerait ni téléphone portable, ni GPS. Nous n'aurions pas découvert l'ADN, pas plus que Neptune, et jamais quitté la Terre pour voyager dans l'espace. S'il impressionne par sa puissance, le principe du calcul infinitésimal est pourtant celui de la simplicité : pour résoudre un problème complexe, il suffit en effet de le décomposer en une infinité d'éléments plus simples. L'assemblage du nombre infini de solutions apportera alors comme par miracle la réponse recherchée. Puissance infini retrace l'évolution du calcul infinitésimal depuis Archimède jusqu'aux percées actuelles en matière de théorie du chaos ou d'intelligence artificielle. Cette formidable saga scientifique et humaine, jalonnée de noms illustres comme ceux de Pythagore ou de Fourier et accessible à tous, laissera ses lecteurs émerveillés du monde. Cet essai a connu un large succès outre-Atlantique dans sa version originale. Il a été nominé par la Royal Society of London comme l'un des meilleurs livres scientifiques grand public jamais publiés. Steven Strogatz est Professeur de mathématiques appliquées à l'université Cornell (New York). Il est l'un des mathématiciens les plus renommés et cités au monde. Il tient également des blogs sur les mathématiques pour le New York Times et le New Yorker.

Calculus --- Calculus. --- Differential calculus. --- Counting --- Philosophy --- Calcul infinitésimal. --- Calcul différentiel. --- Calcul --- Philosophie --- History. --- Histoire. --- Calcul infinitésimal. --- Calcul différentiel.

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This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.

Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal