Differential calculus and equations

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions.

This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21-23 December 2021.

A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others.

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.

Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source.

The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years.

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems.

The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics.

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science.

The volume covers most of the topics addressed and discussed during the Workshop INdAM "e;Recent advances in kinetic equations and applications"e;, which took place in Rome (Italy), from November 11th to November 15th, 2019.

This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics.

This book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions.

This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier-Stokes equations.

The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable.

A First course in Ordinary Differential Equations provides a detailed introduction to the subject focusing on analytical methods to solve ODEs and theoretical aspects of analyzing them when it is difficult/not possible to find their solutions explicitly.

This book is an invaluable resource for applied researchers to find the analytical solution of differential equations describing the dynamical system with less computational effort and time.

Technical problems often lead to differential equations with piecewise-smooth right-hand sides.

This volume is a collection of research papers on nonlinear partial differential equations and related areas, representing many aspects of the most recent developments in these important areas.

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011.

This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015.

A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics.

Compressible Flow with Application to Shocks and Propulsion is part of the series "e;Mathematics and Physics for Science and Technology"e;, which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results.

These proceedings gather selected, peer-reviewed papers presented at the IV International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2023, held on July 12-14, 2023 by the University Center of Technology and Digital Arts (U-tad) in Madrid, Spain.

Functional differential equations have received attention since the 1920's.

The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point.

Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities.

This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera- tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.

This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved.

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics.

This volume is on initial-boundary value problems for parabolic partial differential equations of second order.

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry.

First published in 1990.

These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas.

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems.

Cardiovascular diseases have a major impact in Western countries.

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions.

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established.

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines.

This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization.

This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics.

This book provides probabilists with sufficient background to begin applying PDEs to probability theory and probability theory to PDEs.