Differential calculus and equations

This book presents papers surrounding the extensive discussions that took place from the 'Variational Analysis and Aerospace Engineering' workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015.

This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria.

This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and  3-manifolds.

This book offers an essential introduction to the mathematical theory of compressible viscous fluids.

This book presents a comprehensive overview of the modeling of complex fluids, including many common substances, such as toothpaste, hair gel, mayonnaise, liquid foam, cement and blood, which cannot be described by Navier-Stokes equations.

Now in its second edition, this monograph explores the Monge-Ampere equation and the latest advances in its study and applications.

In this book we analyze  relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics.

The book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "e;Dynamical Systems: Theory and Applications,"e; held in Lodz, Poland on December 7-10, 2015.

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "e;Dynamical Systems: Theory and Applications,"e; held in Lodz, Poland on December 7-10, 2015.

Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow.

This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015.

This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium "e;Building bridges: connections and challenges in modern approaches to numerical partial differential equations"e;.

This book collects recent research papers by respected specialists in the field.

Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup.

This book deals with mathematical problems arising in the context of meteorological modelling.

This text is the first of its kind to bring together both the thermomechanics and mathematical analysis of Reiner-Rivlin fluids and fluids of grades 2 and 3 in a single book.

This book focuses on the approximation of nonlinear equations using iterative methods.

This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance.

This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes).

This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "e;max-product"e; type operators.

Presenting the latest findings in topics from across the mathematical spectrum, this volume includes results in pure mathematics along with a range of new advances and novel applications to other fields such as probability, statistics, biology, and computer science.

This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Rene Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis.

This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function.

The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganes, Spain, from July 3 to July 6, 2018.

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries.

This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field.

This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems.

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces.

In this volume a theory for models of transport in the presence of a free boundary is developed.

This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities.

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities.

Aimed at the community of mathematicians working on ordinary and partial differential equations, difference equations, and functional equations, this book contains selected papers based on the presentations at the International Conference on Differential & Difference Equations and Applications (ICDDEA) 2015, dedicated to the memory of Professor Georg Sell.

This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results.

This textbook covers the main results and methods of real analysis in a single volume.

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology.

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics.

This book presents lecture notes from the XVI 'Jacques-Louis Lions' Spanish-French School on Numerical Simulation in Physics and Engineering, held in Pamplona (Navarra, Spain) in September 2014.

The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields.

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations.

This book investigates the mathematical analysis of biological invasions.

This work collects the most important results presented at the Congress on Differential Equations and Applications/Congress on Applied Mathematics (CEDYA/CMA) in Cadiz (Spain) in 2015.

This is a monograph covering topological fixed point theory for several classes of single and multivalued maps.

This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula).

This monograph presents a synopsis of fluid dynamics based on the personal scientific experience of the author who has contributed immensely to the field.

This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author.

This volumebrings together four lecture courses on modern aspects of water waves.

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.

This textbook provides and introduction to numerical computing and its applications in science and engineering.

The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way.