Differential calculus and equations

Reports and expands upon topics discussed at the International Conference on [title] held in Colorado Springs, Colo.

Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods.

One of the masters in the differential equations community, the late F.

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.

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems.

This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators.

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods.

Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs.

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.

This volume documents the results and presentations relating to the use of wavelet theory and other methods in surface fitting and image reconstruction of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993.

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.

, Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems.

Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering.

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.

Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems.

This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis.

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.

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.

Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines.

Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences.

Reconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography.

Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance.

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.

A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.

Fundamental to the study of any mathematical structure is an understanding of its symmetries.

Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering.

Based on the Working Conference on Boundary Control and Boundary Variation held in Sophia-Antipolis, France, this work provides important examinations of shape optimization and boundary control of hyperbolic systems, including free boundary problems and stabilization.

Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly.

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).

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.

Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville.

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.

The concept of higher order derivatives is useful in many branches of mathematics and its applications.

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.