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Mitchell J: Boundary Value Problems and
Partial Differential Equations

Boundary Value Problems and Partial Differential Equations

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

This book explores the underlying concepts, physics and mathematics of wave scattering and wave field structures and self-consistently introduces a range of topics in scalar acoustics and quantum and vector electromagnetic scattering.

This book explores the underlying concepts, physics and mathematics of wave scattering and wave field structures and self-consistently introduces a range of topics in scalar acoustics and quantum and vector electromagnetic scattering.

Theory and Applications

Scattering of Waves

Integral Manifolds for Impulsive Differential Problems with Applications offers readers a comprehensive resource on integral manifolds for different classes of differential equations which will be of prime importance to researchers in applied mathematics, engineering, and physics. The book offers a highly application-oriented approach, reviewing the qualitative properties of integral manifolds which have significant practical applications in emerging areas such as optimal control, biology, mechanics, medicine, biotechnologies, electronics, and economics. For applied scientists, this will be an important introduction to the qualitative theory of impulsive and fractional equations which will be key in their initial steps towards adopting results and methods in their research.

Integral Manifolds for Impulsive Differential Problems with Applications

The book has two overarching goals. The first goal is to introduce different available numerical procedures for finding solutions to linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, differential equations, and error analysis. The second goal is to translate theory into practice through applying commonly used numerical methods in mathematics, physical sciences, biomedical sciences, and engineering.

This book was crafted in an informal and user-friendly manner to motivate the study of the material being covered. Ample figures and numerical tables are presented to enhance the reader's ease of understanding of the material under consideration.

Introduction To Applied Numerical Analysis, An

Trends in Abstract and Applied Analysis

The Stieltjes derivative is a modification of the usual derivative through a nondecreasing and left-continuous map. This change in the definition allows us to study several differential problems under the same framework.

This monograph is the first published book that offers a comprehensive view of the fundamentals of Stieltjes calculus and its applications, making it approachable to newcomers and experts. It aims to provide an integrated approach to the foundations and recent developments in the area of the Stieltjes derivatives and the qualitative theory of the Stieltjes differential equations. Through 10 pedagogically organized chapters, the authors examine a wide scope of the concept of the Stieltjes derivative and its applications. Each chapter focuses on theory, and proofs, and contains sufficient examples to enrich the reader's understanding.

The Stieltjes derivative contains the Hilger delta derivative on time scales. Thus, offering a new unification and extension of continuous and discrete calculus. Further, a study of differential equations in the sense of the Stieltjes derivative allows the study of many classical problems in a unique framework. This theory has the advantage that ordinary differential equations, ordinary difference equations, quantum difference equations, impulsive differential equations, dynamic equations on time scales, and generalized differential equations can be treated as particular instances of the Stieltjes differential equations. Hence, this book serves as a basic reference for researchers to harness this powerful technique further to unlock new insights and embrace the intricacies of natural processes. Researchers and graduate students at various levels interested in learning about the Stieltjes differential calculus and related fields will find this text a valuable resource of both introductory and advanced material.

Stieltjes Differential Calculus With Applications

Secret Life of

Unlock the mysteries of the most important, surprising and fascinating equations in history

Unlock the mysteries of the most important, surprising and fascinating equations in history

The 50 Greatest Equations and How They Work

The Secret Life of Equations

Recent Progress On Numerical Analysis For Nonlinear Dispersive Equations

Cambridge Monographs on Applied and Computational Mathematics

With Applications to Machine Learning and Image Analysis

Differential Equations and Variational Methods on Graphs

De Gruyter Studies in Mathematics

Orthogonal Polynomials

Textbooks in Mathematics

This book presents an opportunity to learn difference and differential equations through a modelling-first approach. The text is meant as an introduction to those equations and not as a text only for modelling courses. Modeling is presented as the vehicle for learning difference and differential equations.

This book presents an opportunity to learn difference and differential equations through a modelling-first approach. The text is meant as an introduction to those equations and not as a text only for modelling courses. Modeling is presented as the vehicle for learning difference and differential equations.

Introduction to Differential and Difference Equations Through Modeling

Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications

Analysis on fractals began to take shape as a mathematical field in the late 1980s. Traditionally, the focus of analysis has been on finitely ramified fractals -- those where copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive.This monograph outlines the theory of self-similar energies on finitely ramified self-similar fractals. Using these self-similar energies, one can construct Laplacians, harmonic functions, Brownian motion, and differential equations specific to these fractals.On finitely ramified fractals, self-similar energies are derived from eigenforms -- quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores conditions for the existence and uniqueness of these self-similar energies and addresses related problems. For certain cases, complete solutions are provided.

Self-similar Energies On Finitely Ramified Fractals

This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm-Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway.

Notes, Problems and Solutions in Differential Equations

Differential Geometry And Riemannian Manifolds

Boundary Value Problems and Partial Differential Equations

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Bibliografische Angaben

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