“…The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. …”
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“…This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: •The p-norms on vector space and their equivalence •The Weierstrass and Stone-Weierstrass approximation theorems •The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables •The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem •Applications to Ordinary Differential Equations •Line integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. …”
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“…This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. …”
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“…Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. …”
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“…Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. …”
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“…Elementary knowledge of vector calculus is the only prerequisite.…”
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“…Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.…”
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“…Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. …”
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“…In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. …”
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“…The text uses tools of calculus and real analysis to get solutions in explicit form. …”
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“…Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. …”
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“…Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. …”
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“…The appendices can be understood by someone who has taken one or two semesters of calculus.…”
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“…Aimed at undergraduate and graduate students as well as researchers, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains forty-one original problems with very detailed solutions, progressing from dimensional estimates and intuitive arguments to detailed computations to help readers understand fluid mechanics.…”
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“…Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. …”
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“…Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. …”
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“…It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. …”
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“…The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. …”
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“…On the one hand, we propose a general approach for approximating ideal filters based on fractional calculus from the point of view of systems of fractional order. …”
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“…Worldwide this is only the fourth case of a bladder calculus causing a vesicocutaneous fistula.…”
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