The Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial) are discussed.
Contains more than 1400 curves, almost three times as many as in the 1987 edition. The curves are normalized in appearance to aid making comparisons among materials. All diagrams include metric units, and many also include U.S. customary units
Contains more than 500 fatigue curves for industrial ferrous and nonferrous alloys. Also includes an explanation of fatigue testing and interpretation of test results. Each curve is presented independently and includes an explanation of its particular importance.
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
The most comprehensive collection of time-temperature diagrams for irons and steels ever collected. Between this volume and its companion, Atlas of Time Temperature Diagrams for Nonferrous Alloys, you'll find the most comprehensive collection of time-temperature diagrams ever collected. Containing both commonly used curves and out-of-print and difficult-to-find data, these Atlases represent an outstanding worldwide effort, with contributions from experts in 14 countries. Time-temperature diagrams show how metals respond to heating and cooling, allowing you to predict the behavior and know beforehand the sequence of heating and cooling steps to develop the desired properties. These collections are a valuable resource for any materials engineer Both Collections Include: Easy-to-Read Diagrams Isothermal transformation Continuous cooling transformation Time-temperature precipitation Time-temperature embrittlement Time-temperature ordering Materials Included in the Irons and Steels Volume: Low-carbon High Strength Low Alloy Stainless (Maraging, austenitic, ferritic, duplex) Chromium, molybdenum, vanadium, silicon Structural Quenched and tempered Spring and Rail High-temperature creep-resistant Tool and die Eutectoid, hypereutectoid carbon Deep hardening Titanium bearing Irons: Gray cast, malleable, white, white cast, ductile.
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
This book is a reference for librarians, mathematicians, and statisticians involved in college and research level mathematics and statistics in the 21st century. We are in a time of transition in scholarly communications in mathematics, practices which have changed little for a hundred years are giving way to new modes of accessing information. Where journals, books, indexes and catalogs were once the physical representation of a good mathematics library, shelves have given way to computers, and users are often accessing information from remote places. Part I is a historical survey of the past 15 years tracking this huge transition in scholarly communications in mathematics. Part II of the book is the bibliography of resources recommended to support the disciplines of mathematics and statistics. These are grouped by type of material. Publication dates range from the 1800's onwards. Hundreds of electronic resources-some online, both dynamic and static, some in fixed media, are listed among the paper resources. Amazingly a majority of listed electronic resources are free.
Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
