SC - 961 | Mathematical Control Theory: Deterministic Finite Dimensional Systems

Mathematical Control Theory: Deterministic Finite Dimensional Systems (Texts in Applied Mathematics) by Eduardo D. Sontag (Author)

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses.

The minimal mathematical background required is a working knowledge of linear algebra and differential equations.

The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

1998 | ISBN 978-1-4612-6825-3 | ISBN 978-1-4612-0577-7 | ID: SC - 961

Read More

SC - 998 | Combined Methods for Elliptic Equations

Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities (Mathematics and Its Applications) 1998th Edition by Zi Cai Li (Author)

In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together?

In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid. Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

1998 | ISBN-13: 978-1-4613-3340-1 | e-ISBN-13: 978-1-4613-3338-8 | ID: SC - 998

Read More

SC - 999 | Generalized Convexity, Generalized Monotonicity

Generalized Convexity, Generalized Monotonicity: Recent Results (Nonconvex Optimization and Its Applications) 1998th Edition by Jean-Pierre Crouzeix (Editor), Juan Enrique Martinez Legaz (Editor), Michel Volle (Editor)

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems.

A function is quasiconvex if its lower level sets are convex. Here again, the geo- metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man- agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob- lems.

1998 | ISBN-13: 978-1-4613-3343-2 | e-ISBN-13: 978-1-4613-3341-8 | ID: SC - 999

Read More

SC - 1047 | Calculus Made Easy Revised, Updated, Expanded Edition

Calculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

1998 | ISBN: 0312185480 | ID: SC - 1047

Read More

SC - 1150 | The Cauchy Problem for Higher Order Abstract Differential Equations

 The Cauchy Problem for Higher Order Abstract Differential Equations by Ti-Jun Xiao, Jin Liang

The main purpose of this book is to present the basic theory and some recent de­ velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ).

For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans­ lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties).

The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.

1998 | ISBN 978-3-540-65238-0 | ISBN 978-3-540-49479-9 | ID: SC - 1150

Read More

SC - 1202 | Handbook of Feynman Path Integrals

Handbook of Feynman Path Integrals by Christian Grosche, Frank Steiner

The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals.

The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals.

As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

1998 | ISBN: 9783540571353 | ID: SC - 1202

Read More