The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations.
Pocket Book of Integrals and Mathematical Formulas, 5th Edition covers topics ranging from precalculus to vector analysis and from Fourier series to statistics, presenting numerous worked examples to demonstrate the application of the formulas and methods.
Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals.
This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals.
This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals.
Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century.
"e;Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability.
A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems.
A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif
This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011).
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.
Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability.
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction.
This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions.
With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs).
Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems.
This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field.
Differential equations with "e;maxima"e;-differential equations that contain the maximum of the unknown function over a previous interval-adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval.
Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory.
The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics.
Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research.
Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation.
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations.
Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems.
A Course in Ordinary Differential Equations, Second Edition teaches students how to use analytical and numerical solution methods in typical engineering, physics, and mathematics applications.
The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories.
Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions.
Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs.
