Bücher der Reihe Mathematical Concepts and Methods in Science and Engineering

Our purpose in writing this book is to provide a description of some of the applications of optimal control techniques to practical power system problems. It begins with an introductory chapter that briefly reviews the history of optimal control and its power system applications and also provides an outline of the text.

This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc.

" In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers.

This book is to serve as a text for engineering students at the senior or beginning graduate level in a second course in dynamics.

As an outgrowth of the advancement in modern control theory during the past 20 years, dynamic modeling and analysis of economic systems has become an important subject in the study of economic theory.

The primary objective of the course presented here is orientation for those interested in applying mathematics, but the course should also be of value or in using math to those interested in mathematical research and teaching ematics in some other professional context.

This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

Multicriteria optimization has its roots in mathematical economics, in particular, in consumer economics as considered by Edgeworth and Pareto. Today, such an optimum is variously called "Pareto optimum" (after the Italian-French welfare economist who continued and expanded Edgeworth's work), "effi.

The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7.

Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach, but the author uses it to advantage in this two-volume set. Students gain a mastery of kinematics first ¿ a solid foundation for the later study of the free-body formulation of the dynamics problem.A key objective of these volumes, which present a vector treatment of the principles of mechanics, is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results. In the first volume, the elements of vector calculus and the matrix algebra are reviewed in appendices. Unusual mathematical topics, such as singularity functions and some elements of tensor analysis, are introduced within the text. A logical and systematic building of well-known kinematic concepts, theorems, and formulas, illustrated by examples and problems, is presented offering insights into both fundamentals and applications. Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis, advanced kinematics of mechanisms and analytical dynamics, mechanical vibrations and controls, and continuum mechanics of solids and fluids.Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics.

This book introduces two most important aspects of modern analysis: the theory of measure and integration and the theory of Banach and Hilbert spaces. It can serve as a text for a solid one-year course entitled "Measure and Integration Theory" or a com prehensive one-year course entitled "Banach Spaces, Hilbert Spaces, and Spectral Theory.

The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7.

This book deals with a very important problem in power system planning for countries in which hydrogeneration accounts for the greatest part of the system power production.

For many years it has been an article of faith of numerical analysts that the evaluation of derivatives of complicated functions should be avoided. The recent developments described in this text allow the evaluation of derivatives using simple automatic derivative evaluation subroutines pro grammed in FORTRAN or BASIC.

Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry.

Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light.It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems.

Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed.

Presents six lectures on the use of mathematics in the conceptual design of various types of aircraft and spacecraft. This book covers the following topics: design of rocket-powered orbital spacecraft (Miele/Mancuso), design of Moon missions (Miele/Mancuso), design of Mars missions (Miele/Wang), and more.

Provides the basis for a one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. This book offers a practical review of questions involving basic kinematics.

This book is devoted to the mathematical optimization theory and modeling techniques that recently have been applied to the problem of controlling the shape and intensity of the power density distribution in the core of large nuclear reactors.

Considerably simplified models of macroscopic material behavior, such as the idealization for metals of elastic-time independent plastic response with a yield (onset) criterion, have served the engineering profession well for many years.

Proceedings of a Meeting held in Erice, Italy, September 3-10, 1991