Differential calculus and equations

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.

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.

Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form.

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions.

Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory.

Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner.

Revised and updated, this second edition provides an accessible introduction to both chaotic dynamics and fractal geometry for readers with a calculus background.

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).

Until the authors' recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues.

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.

Covers ODEs and PDEs-in One TextbookUntil now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn't exist.

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus.

With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs).

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.

This book presents a detailed development of the divergence theorem.

Currently, the techniques of operation research are widely used in every aspect of day-to-day life.

The Italian school of Mathematical Analysis has long and glo- rious traditions.

The calculus has been one ofthe areas of mathematics with a large number of significant applications since its formal development in the seventeenth century.

Mathematicians often face the question to which extent mathematical models describe processes of the real world.

The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations.

This book provides an upto date information on metric, connection and curva- ture symmetries used in geometry and physics.

In volume I we developed the tools of "e;Multivalued Analysis.

Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays.

In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators.

The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday.

This book provides a complete and exhaustive study of the Green's functions.

This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study.

Impulsive Control in Continuous and Discrete-Continuous Systems is an up-to-date introduction to the theory of impulsive control in nonlinear systems.

Computational Techniques for the Summation of Series is a text on the representation of series in closed form.

This book considers signal processing and physical modeling meth- ods for sound synthesis.

At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies.

Lectori salutem!

This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods.

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Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration.

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This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties.

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Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments.

This book presents as its main subject new models in mathematical neuroscience.

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This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces.

Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations.