free Geometry eBooks

Page: 371-380 results of 1704
This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other... more...
The recent revolution in differential topology related to the discovery of non-standard ("exotic") smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry.... more...
In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II.... more...
Leonardo da Pisa, perhaps better known as Fibonacci (ca. 1170 – ca. 1240), selected the most useful parts of Greco-Arabic geometry for the book known as De Practica Geometrie. This translation offers a reconstruction of De Practica Geometrie as the author judges Fibonacci wrote it, thereby correcting inaccuracies found in numerous modern histories. It is a high quality translation with supplemental text to explain text that has been... more...
This monograph presents the basic theorems of differential geometry in three-dimensional space, including a thorough coverage of surface theory. By means of a series of carefully selected and representative mathematical models this monograph also explains at length how these theorems are used in three-dimensional elasticity and in shell theory. The presentation is essentially selfcontained, with a great emphasis on pedagogy. In... more...
Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from... more...
The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions. Contents: Multiscale Singular Perturbations and Homogenization of Optimal Control Problems (M Bardi et al.); Patchy Feedbacks for Stabilization and Optimal Control: General Theory and Robustness Properties (F Ancona... more...
The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to this subject was proposed by Ch. Ehresmann 60 years ago, attracting first mathematicians and later physicists by its transparent geometrical simplicity. Unfortunately, it does not extend well to a number of... more...
This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem,... more...
Page: 371-380 results of 1704