The student of calculus is entitled to ask what calculus is and what it can be used for. This short book provides an answer. The author starts by demonstrating that calculus provides a mathematical tool for the quantitative analysis of a wide range of dynamical phenomena and systems with variable quantities. He then looks at the origins and intuitive sources of calculus, its fundamental methodology, and its general framework and basic structure, before examining a few typical applications. The author's style is direct and pedagogical. The new student should find that the book provides a clear...

In recent years works done by most researchers towards building autonomous intelligent controllers frequently mention the need for a methodology of design and a measure of how successful the final result is. This monograph introduces a design methodology for intelligent controllers based on the analytic theory of intelligent machines introduced by Saridis in the 1970s. The methodology relies on the existing knowledge about designing the different subsystems composing an intelligent machine. Its goal is to provide a measure of the performance applicable to any of the subsystems, and use that...

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse...

A concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action is regarded as the geometric organization of the totality of non-commutativity of a given compact connected Lie group, while the...

An introduction to the theory of compact connected Lie groups and their representations, and a presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a balance between the algebraic and geometric aspects of Lie theory.

This volume discusses the classical subjects of Euclidean, affine and projective geometry in two and three dimensions, including the classification of conics and quadrics, and geometric transformations. These subjects are important both for the mathematical grounding of the student and for applications to various other subjects. They may be studied in the first year or as a second course in geometry. The material is presented in a geometric way, and it aims to develop the geometric intuition and thinking of the student, as well as his ability to understand and give mathematical proofs. Linear...

This present book comes from the first part of the lecture notes the author used for first-year graduate algebra course at the University of Minnesota, Purdue University and Peking University. The aim of this book is not only to give the student quick access to the basic knowledge of algebra, either for future advancement in the field of algebra, or for general background information, but also to show that algebra is truly a master key or "skeleton key" to many mathematical problems. The author wishes to present this book as an attempt to re-establish the contacts between algebra and other...

This present book comes from the first part of the lecture notes the author used for first-year graduate algebra course at the University of Minnesota, Purdue University and Peking University. The aim of this book is not only to give the student quick access to the basic knowledge of algebra, either for future advancement in the field of algebra, or for general background information, but also to show that algebra is truly a master key or "skeleton key" to many mathematical problems. The author wishes to present this book as an attempt to re-establish the contacts between algebra and other...

This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartans' theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we...

This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartans' theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we...