Written by an engineer and sharply focused on practical matters, Solution of Ordinary Differential Equations by Continuous Groups explores the application of Lie groups to the solution of ordinary differential equations.
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles.
This book documents the results of a workshop held at the Geometry Center (University of Minnesota, Minneapolis) and captures the excitement of the week.
, Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems.
Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics.
Thoroughly revised and updated, The Art of Modeling in Science and Engineering with Mathematica, Second Edition explores the mathematical tools and procedures used in modeling based on the laws of conservation of mass, energy, momentum, and electrical charge.
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.
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.
This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces.
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs).
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis.
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.
Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Levy type of noise.
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).
Of considerable importance to numerical analysts, this text contains the proceedings of the 18th Dundee Biennial Conference on Numerical Analysis, featuring eminent analysts and current topics.
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.
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved.
The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps.
A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems.
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.
Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field.
Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms.
A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type.
Mathematical Techniques for Wave Interaction with Flexible Structures is a thoughtful compilation of the various mathematical techniques used to deal with wave structure interaction problems.
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.
In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences.
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.
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.
Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications.
The book treats two topics in the theory of stochastic partial differential equations: space-regularity of solutions and existence of stochastic flows.
Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc.
Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences.
The book compiles works presented at a seminar aiming to attract global experts in differential equations, mathematical modeling, and integration methods.
