Differential calculus and equations

Readers may question why non-Newtonian calculus should be used when Newtonian calculus is already available and many scientists are familiar with it.

The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines.

This book is designed as an introduction to neural dynamics through an intuitive exploration of fundamental "e;dynamic motifs"e;- the recurring dynamical concepts essential for understanding computational neuroscience.

This book is designed as an introduction to neural dynamics through an intuitive exploration of fundamental "e;dynamic motifs"e;- the recurring dynamical concepts essential for understanding computational neuroscience.

This book addresses problems driven by differential operators that lack monotonicity.

This book addresses problems driven by differential operators that lack monotonicity.

This book begins by exploring the fundamental concepts of dynamical systems and machine learning modeling, elucidating the workflow of these two modeling approaches.

This book begins by exploring the fundamental concepts of dynamical systems and machine learning modeling, elucidating the workflow of these two modeling approaches.

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises.

Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

 Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

 Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

This monograph offers an overview of the active research area involving the class of PDEs known as Oskolkov equations.

Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

This monograph provides new functional analytic developments on spectral problems in various applied fields such as jump equations, Kolmogorov differential equations, weighted graphs, neutron transport theory, population dynamics, linearized non-local Allen–Cahn equations and perturbed convolution semigroups.

This monograph provides new functional analytic developments on spectral problems in various applied fields such as jump equations, Kolmogorov differential equations, weighted graphs, neutron transport theory, population dynamics, linearized non-local Allen–Cahn equations and perturbed convolution semigroups.

This book provides the very first comprehensive and self-contained introduction to hedgehog theory, which is born of the desire to visualize the formal differences of convex bodies.

This book provides the very first comprehensive and self-contained introduction to hedgehog theory, which is born of the desire to visualize the formal differences of convex bodies.

This book provides a comprehensive overview of the latest achievements in the field of optical fiber lasers, covering the basics, technology, and numerous applications.

This book provides a comprehensive overview of the latest achievements in the field of optical fiber lasers, covering the basics, technology, and numerous applications.

The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field.

This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids.

This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability.

This volume presents a review of advanced technological problems in the glass industry and of the mathematics involved.

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Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste.

The aim of this work is to present a broad overview of the theory of hyperbolic c- servation laws, with emphasis on its genetic relation to classical continuum physics.

A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm.

This book could have been entitled "e;Analysis and Geometry.

In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations.

Biomedical imaging is a fascinating research area to applied mathematicians.

This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets.

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation.

Equations of state are not always effective in continuum mechanics.

Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level.

This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension.

The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance.