{"product_id":"differential-and-integral-calculus-real-functions-of-one-or-several-real-variables-9798336080063","title":"Differential and Integral Calculus: Real Functions of One or Several Real Variables","description":"\u003cp\u003e • Author(s): William Kergroach\u003cbr\u003e • Publisher: Independently Published\u003cbr\u003e • Publisher Imprint: Independently Published\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book, \u003ci\u003eDifferential and Integral Calculus - Real Functions of One or Several Real Variables, \u003c\/i\u003e presents the fundamental concepts of differential and integral calculus. It is intended for advanced mathematics students as well as professionals requiring a solid command of mathematical analysis tools for technical or scientific tasks.\u003c\/p\u003e\u003cp\u003eThe book is divided into six major parts: \u003c\/p\u003e\u003col\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cb\u003eDifferential Calculus: \u003c\/b\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eChapters covering the fundamentals of real functions of one variable, normed vector spaces, and differential operators.\u003c\/li\u003e\n\u003cli\u003eEach section is accompanied by solved exercises to reinforce understanding.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cb\u003eIntegral Calculus: \u003c\/b\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eIn-depth discussions on integrals of multivariable functions, line integrals, and surface integrals.\u003c\/li\u003e\n\u003cli\u003ePractical exercises to illustrate physical and engineering applications.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cb\u003eCalculus of Variations and Differential Equations: \u003c\/b\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eExploration of the principles of calculus of variations, existence and uniqueness theorems, and dynamical systems.\u003c\/li\u003e\n\u003cli\u003eApplication of Fourier analysis to evolution equations, with solved exercises to strengthen comprehension.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cb\u003eAnalysis on Differential Manifolds: \u003c\/b\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to differential manifolds, tensor calculus, and Morse theory, with applications in general relativity and geometry.\u003c\/li\u003e\n\u003cli\u003eEach chapter is followed by solved exercises, allowing mastery of advanced concepts.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cb\u003eNumerical Methods and Integration Schemes: \u003c\/b\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003ePresentation of discretization methods, integration schemes, and advanced numerical methods such as finite elements and spectral methods.\u003c\/li\u003e\n\u003cli\u003ePractical exercises for solving problems in fluid dynamics and structural mechanics.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cb\u003eStochastic Calculus and Applications: \u003c\/b\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to stochastic processes and stochastic differential equations, with applications in finance, biology, and physics.\u003c\/li\u003e\n\u003cli\u003eExercises to apply stochastic calculus to random models and control processes.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ol\u003e\u003cp\u003e\u003cb\u003eConclusion and Appendices: \u003c\/b\u003e The book concludes with a chapter dedicated to multivariable integration theorems, including Green's, Stokes', and Gauss' theorems, and their extensions to higher dimensions. The appendices provide a review of fundamental theorems in functional analysis, such as the best approximation theorem, Riesz's lemma, and the Arzelà-Ascoli theorem.\u003c\/p\u003e\u003cp\u003eThis book is thus a comprehensive and structured guide for anyone seeking to master differential and integral calculus, with particular attention to practical applications in various scientific and technical fields.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46337762394263,"sku":"9798336080063","price":681.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9798336080063.webp?v=1768680441","url":"https:\/\/atlanticbooks.com\/products\/differential-and-integral-calculus-real-functions-of-one-or-several-real-variables-9798336080063","provider":"Atlantic Books","version":"1.0","type":"link"}