Tag: Equations

Free Download Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms by Chuchu Chen , Jialin Hong , Lihai Ji
English | PDF EPUB (True) | 2024 | 293 Pages | ISBN : 981996685X | 40.8 MB
The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.

Free Download Brigitte Lucquin, "Partial Differential Equations: Modeling, Analysis and Numerical Approximation"
English | 2016 | ISBN: 3319270656, 3319800663 | PDF | pages: 406 | 4.1 mb
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Free Download R. Nagle, Edward Saff, Arthur Snider, "Fundamentals of Differential Equations"
English | 2017 | ISBN: 0321977068, 0321977157, 1292240997 | PDF | pages: 728 | 13.7 mb
For one-semester sophomore- or junior-level courses in Differential Equations.

Free Download A Short Introduction to Partial Differential Equations by Arian Novruzi
English | PDF EPUB (True) | 2023 | 225 Pages | ISBN : 3031395239 | 32 MB
This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods.

Free Download A Short Introduction to Partial Differential Equations by Arian Novruzi
English | PDF EPUB (True) | 2023 | 225 Pages | ISBN : 3031395239 | 32 MB
This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods.

Free Download On Modern Approaches of Hamilton-jacobi Equations and Control Problems With Discontinuities:
A Guide to Theory, Applications, and Some Open Problems
English | 2024 | ISBN: 3031493702 | 569 Pages | PDF (True) | 6 MB

Free Download The Stationary Semiconductor Device Equations by Peter A. Markowich
English | PDF | 1986 | 202 Pages | ISBN : 3211818928 | 16.1 MB
In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician’s point of view. I shall derive the device equations – as obtained for the first time by Van Roosbroeck in 1950 – from physical principles, present a mathematical analysis, discuss their numerical solu tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress. Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Those readers who are not interested in the mathemati cal methodology and rigor can extract the desired information by simply ignoring details and proofs of theorems. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts.

Free Download Santanu Saha Ray, "Stochastic Integral And Differential Equations In Mathematical Modelling"
English | ISBN: 1800613571 | 2023 | 318 pages | PDF | 17 MB
The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes – either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations. Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes. This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.

Free Download Singular Integral Equations: Linear and Non-linear Theory and its Applications in Science and Engineering by E. G. Ladopoulos
English | PDF | 2000 | 569 Pages | ISBN : 3540672303 | 32.3 MB
The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Free Download Partial Differential Equations III: Nonlinear Equations, Third Edition by Michael E. Taylor
English | PDF (True) | 2023 | 774 Pages | ISBN : 3031339274 | 10 MB
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.