Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs.
Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs).
Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications.
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.
Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.
Classroom-tested, Advanced Mathematical Methods in Science and Engineering, Second Edition presents methods of applied mathematics that are particularly suited to address physical problems in science and engineering.
Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales.
Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations.
Deepen students' understanding of biological phenomenaSuitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeli
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books.
This book focuses on explaining the fundamentals of the physics and mathematics of chaotic phenomena by studying examples from one-dimensional maps and simple differential equations.
Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature.
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics.
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators.
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways.
This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs).
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.
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.
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.
Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice.
A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations.
Methods for Solving Mixed Boundary Value ProblemsAn up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary.
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.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators.
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
This book is a comprehensive and time-tested guide to the mathematical theory of Fourier series and boundary value problems, with a strong emphasis on engineering applications.
This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020.
Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species).
The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions.
Audience: This book would be of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods.
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional.
