he - Differential Equations 1

The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. ……続きを見る

This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advance……続きを見る

Second volume of a highly regarded two-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order. Examples are drawn from a wide ran……続きを見る

This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial ……続きを見る

This book provides a comprehensive study of numerical techniques for solving integral and integro-differential equations using wavelet-based approximation methods. It combines both theoretical insig……続きを見る

This book provides a systematic summary and condensation of research on infinite-dimensional Hamiltonian operator spectrum theory over the past thirty years, and offers simple and concise proofs for……続きを見る

Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the……続きを見る

This second volume of the multi-volume Fractional Calculus for Skeptics explores the concept of “roughness” and its applications in complex systems. It demonstrates how fractional calculus offers va……続きを見る

This book is based on lecture materials originally developed by Harald E. Krogstad for the MSc course Mathematical Modelling at the Norwegian University of Science and Technology (NTNU) and later ad……続きを見る

The book focuses on the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equat……続きを見る

For over fifty years, Boundary Value Problems and Partial Differential Equations, Seventh Edition has provided advanced students an accessible and practical introduction to deriving, solving, and in……続きを見る

Classification of Lipschitz Mappings, Second Edition presents a systematic, self-contained treatment of a new classification of Lipschitz mappings and its applications, particularly to metric fixed ……続きを見る

This book develops the properties of monotone rearrangement and relative rearrangement (sometimes called pseudo-rearrangement). It introduces applications to variational problems involving monotone ……続きを見る

This book introduces qualitative methods for understanding differential equations, especially when analytical solutions are not possible. Aimed at second-year undergraduate students in mathematics o……続きを見る

Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is th……続きを見る

This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on “Computational Variational Flows in Machine Learning and Optimal Transport”. Variational and stochastic f……続きを見る

Entropies and Fractionality: Entropy Functionals, Small Deviations and Related Integral Equations starts with a systematization and calculation of various entropies (Shannon, Rényi, and some others)……続きを見る

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into considera……続きを見る

This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singu……続きを見る

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and ……続きを見る

Over the past two decades, the method of fundamental solutions (MFS) has attracted great attention and has been used extensively for the solution of scientific and engineering problems. The MFS is a……続きを見る

This book explores the design and analysis of fractional-order and active disturbance rejection control, examining both the theoretical foundations and their practical applications. It covers fracti……続きを見る

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functio……続きを見る

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis.……続きを見る

This text presents a comprehensive and unified treatment of nonlinear filtering theory, with a strong emphasis on its mathematical underpinnings. It is tailored to meet the needs of a diverse reader……続きを見る

This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of man……続きを見る

Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey……続きを見る

"Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, ineq……続きを見る

Since its publication more than 15 years ago, Heat Conduction Using Green’s Functions has become the consummate heat conduction treatise from the perspective of Green’s functionsーand the newly revi……続きを見る

Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the fina……続きを見る