Tag: Differential

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 Reduced Basis Methods for Partial Differential Equations: An Introduction by Alfio Quarteroni , Andrea Manzoni , Federico Negri
English | PDF (True) | 2016 | 305 Pages | ISBN : 3319154303 | 2.7 MB
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization.

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.

Free Download Ethan Cowan, "Hands-on Differential Privacy: Introduction to the Theory and Practice Using Opendp (Early Release)"
English | ISBN: 1492097748 | 2024 | 275 pages | EPUB | 3 MB
Many organizations today analyze and share large, sensitive datasets about individuals. Whether these datasets cover healthcare details, financial records, or exam scores, it’s become more difficult for organizations to protect an individual’s information through deidentification, anonymization, and other traditional statistical disclosure limitation techniques. This practical book explains how differential privacy (DP) can help.

Free Download Fundamentals of Differential Geometry by Serge Lang
English | PDF | 1999 | 553 Pages | ISBN : 038798593X | 63.9 MB
The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a threat). At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differen tiable maps in them (immersions, embeddings, isomorphisms, etc. ). One may also use differentiable structures on topological manifolds to deter mine the topological structure of the manifold (for example, it la Smale [Sm 67]). In differential geometry, one puts an additional structure on the differentiable manifold (a vector field, a spray, a 2-form, a Riemannian metric, ad lib. ) and studies properties connected especially with these objects. Formally, one may say that one studies properties invariant under the group of differentiable automorphisms which preserve the additional structure. In differential equations, one studies vector fields and their in tegral curves, singular points, stable and unstable manifolds, etc. A certain number of concepts are essential for all three, and are so basic and elementary that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginnings.

Free Download Differential Diagnosis of Fracture by Yingze Zhang
English | PDF | 2021 | 902 Pages | ISBN : 9811383383 | 124.2 MB
This book covers diagnostic images of common and rare fractures for nearly every part of the human body, based on a large number of clinical cases. The highlight of this book is that both of three-dimensional X-ray images and CT/MRI images of thousands of fracture cases are presented for comparison and further discussion, according to the framework of AO classification.

Free Download Atlas of Retinal Detachment: Diagnosis and Differential Diagnosis by Wenbin Wei
English | EPUB (True) | 2018 | 262 Pages | ISBN : 9811082308 | 355 MB
This atlas and textbook aims to provide diverse pictures, facilitating the readers to learn fundus diseases. Retinal detachment is a common group of vitreo-retinal diseases that causes blindness. The diagnosis and differential diagnosis are dependent mostly on ophthalmolscopy and fundus imaging technology. With the development of imaging technology, it is getting easier for ophthalmologist to make quick and accurate decision on the diagnosis.

Free Download Applications of Lie Groups to Differential Equations by Peter J. Olver
English | PDF | 1986 | 524 Pages | ISBN : 0387962506 | 105.9 MB
This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations.

Free Download Partial Differential Equations: Qualitative Studies of Linear Equations
English | 2023 | ISBN: 3031336992 | 706 Pages | PDF (True) | 7 MB
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. 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.