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Tensors, Differential Forms, and Variational Principles
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
The Significance of Nonlinearity in the Natural Sciences
In accordance with the established tradition of these annual meetings under the aegis of Orbis Scientiae we have, this year, included the very important field of "The Significance of Non linearity in the Natural Sciences." We are pleased to join many scientists in recognizing the nonlinearity arising from the under lying interaction of all natural phenomena. It is tempting to say that in the long run things are nonlinear and that we shall have to design new techniques and methods to solve nonlinear equations. This year's Orbis Scientiae did include four sessions on nonlinear equations pertaining to elementary particle physics, molecular physics, fluid dynamics, and also to biology. Our Cente...
The Differential Geometry of Finsler Spaces
The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of inte...
Projective Geometry
Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition.
A Concise History of Mathematics
This compact, well-written history — first published in 1948, and now in its fourth revised edition — describes the main trends in the development of all fields of mathematics from the first available records to the middle of the 20th century. Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating. Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their begi...
Differential Geometry, Calculus of Variations, and Their Applications
This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
A First Course in the Calculus of Variations
This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.
An Investigation of the Laws of Thought
"A classic of pure mathematics and symbolic logic ... the publisher is to be thanked for making it available." — Scientific American George Boole was on of the greatest mathematicians of the 19th century, and one of the most influential thinkers of all time. Not only did he make important contributions to differential equations and calculus of finite differences, he also was the discoverer of invariants, and the founder of modern symbolic logic. According to Bertrand Russell, "Pure mathematics was discovered by George Boole in his work published in 1854." This work is the first extensive statement of the modern view that mathematics is a pure deductive science that can be applied to variou...
Branching Processes
A unified treatment of the limit theory of branching processes, this volume focuses on basics and is appropriate for graduate and advanced undergraduate students. The authors cover basic Galton-Watson process, potential theory, one dimensional continuous time Markov branching processes, age-dependent processes, multi-type branching processes, and special processes. Exercises. 1972 edition.
