Differential calculus and equations Books

This book covers applications of fractional calculus used for medical and health science.

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a...

Phaser is a sophisticated program for IBM personal com- puters, developed atBrown University by the author and some of his students, which enables usersto experiment with differential and difference equations and dynamical ...

The world abounds with introductory texts on ordinary differential equations and rightly so in view of the large number of students taking a course in this subject. However, for some time now there is a growing need for a...

Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which...

Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist­ ence and asymptotic behavior of solutions of certain classes of singularly perturbed...

My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present...

In Chapter One we review the foundations of statistieal physies and frac­ tal functions. Our purpose is to demonstrate the limitations of Hamilton's equations of motion for providing a dynamical basis for the statistics of...

Jerry Marsden, one of the world's pre-eminent mechanicians and applied mathematicians, celebrated his 60th birthday in August 2002. The event was marked by a workshop on "Geometry, Mechanics, and Dynamics"at the Fields...

This is the most thorough treatment of normal forms currently existing in book form. There is a substantial gap between elementary treatments in textbooks and advanced research papers on normal forms. This book develops all the...

This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key...

This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. From the mathematical viewpoint the closest...

This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization...

Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in...

The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu­ ral" invariant measures. We wanted to bring together a coherent...

This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon...

Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to...

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. This volume describes that technique, which...

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. Operational Calculus and...

With the collapse of Demographic Transition Theory, new theories of population must not just be explanations, but should be falsifiable theories which can compute the number of occurrences of marriages and births. This book reviews computable marriage...

When a dynamical system has a large number of parameters it is not possible to get a completely comprehensive picture of all the types of behavior that it may display and one must be content with surveying the system along various corridors of lower...

This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including equations and systems of elliptic and parabolic type and various applications in physics,mechanics and...

Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics. The five papers appearing in this volume are centred around the mathematical theory of the...

This Monograph contains a collection of problems arising in partial differential equations investigated by means of complex analysis approached in elementary ways.

This monograph has two main purposes, first to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable,...

This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by...

This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer­ Verlag, 1981). We present the material at a level that assumes some...

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob­ lems and we hope to convert the reader to this view. In this preface we will...

My Love Affair with the Sobolev Inequality, D.R. Adams.- Maximal Functions in Sobolev Spaces, D. Aalto, J. Kinnunen.- Hardy Type Inequalities Via Riccati and Sturm-Liouville Equations, S. Bobkov, F. Götze.- Quantitative Sobolev and Hardy Inequalities and...

In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads...

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of...

The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's...

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical...

This IMA Volume in Mathematics and its Applications MODELING, MESH GENERATION, AND ADAPTIVE NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of the 1993 IMA Summer Program "Modeling, Mesh...

The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As...

This monograph develops the Hamilton-Jacobi-Bellman theory via dynamic programming principle for a class of optimal control problems for stochastic hereditary differential equations (SHDEs) driven by a standard Brownian motion...

The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is...

The topics covered in this volume include Sobolev's fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because...

This book attempts to give a presentation of the advance of our knowledge of phase portraits of quadratic systems, paying special attention to the historical development of the subject. This the only book that organizes the...