Differential calculus and equations

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics.

This fourth issue on "e;progress in turbulence"e; is based on the fourth ITI conference (ITI interdisciplinary turbulence initiative), which took place in Bertinoro, North Italy.

This work gathers a selection of outstanding papers presented at the 25th Conference on Differential Equations and Applications / 15th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017.

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

This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals.

This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design.

This textbook is designed with the needs of today's student in mind.

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties.

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis.

The purpose of the volume is to provide a support for a first course in Mathematics.

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A Collection of Problems on a Course of Mathematical Analysis is a collection of systematically selected problems and exercises (with corresponding solutions) in mathematical analysis.

Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.

This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.

A comprehensive introduction to modern applied functional analysis.

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area.

This mathematical monograph details the authors' results on solutions to problems governing the simultaneous motion of two incompressible fluids.

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing.

This volume provides a short summary of the essentials of Lagrangian dynamics for practicing engineers and students of physics and engineering.

This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior.

Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems.

This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian.

This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017.

Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations.

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems.

Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).

A collection of articles on operator-theoretic methods for boundary-value problems.

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation.

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.

An accessible treatment of the main results in the mathematical theory of the Navier–Stokes equations, primarily aimed at graduate students.

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This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition.

In analysing nonlinear phenomena many mathematical models give rise to problems for which only nonnegative solutions make sense.

Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering.

In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincare center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories).

This text emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations.

This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background.

This gives comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems across the field -- alongside a more advance volume on applications.

This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense.