Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the... subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com

The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary... introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss-Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The only prerequisites are one year of undergraduate calculus and linear algebra.

Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED... SECOND EDITION, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text. *Fortieth anniversary of publication! Over 36,000 copies sold worldwide*Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study*Extensive update of appendices on Mathematica and Maple software packages *Thorough streamlining of second edition's numbering system*Fuller information on solutions to odd-numbered problems*Additional exercises and hints guide students in using the latest computer modeling tools

This is a revised edition of the 1999 text on the electronic structure and properties of solids, similar in spirit to the well-known 1980 text... Electronic Structure and the Properties of Solids. The revisions include an added chapter on glasses, and rewritten sections on spin–orbit coupling, magnetic alloys, and actinides. The text covers covalent semiconductors, ionic insulators, simple metals, and transition-metal and f-shell-metal systems. It focuses on the most important aspects of each system, making what approximations are necessary in order to proceed analytically and obtain formulae for the properties. Such back-of-the-envelope formulae, which display the dependence of any property on the parameters of the system, are characteristic of Harrison’s approach to electronic structure, as is his simple presentation and his provision of all the needed parameters. In spite of the diversity of systems and materials, the approach is systematic and coherent, combining the tight-binding (or atomic) picture with the pseudopotential (or free-electron) picture. This provides parameters — the empty-core radii as well as the covalent energies — and conceptual bases for estimating the various properties of all these systems. Extensive tables of parameters and properties are included. The book has been written as a text, with problems at the end of each chapter, and others can readily be generated by asking for estimates of different properties, or different materials, than those treated in the text. In fact, the ease of generating interesting problems reflects the extraordinary utility and simplicity of the methods introduced. Developments since the 1980 publication have made the theory simpler and much more accurate, besides allowing much wider application.

The study of fluid dynamics is a central theme in modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital... role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics that is suitable for all undergraduates coming to the subject for the first time. Students need only a basic knowledge of vector calculus, complex analysis, and simple methods of solving differential equations. Numerous exercises (with hints and answers) illustrate the main ideas and serve to organize the reader's understanding. The wide range of topics discussed include inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flows, along with historical information and many references to important experiments. This is a comprehensive and absorbing introduction to the mathematical study of fluid behavior.

This edition retains the basic approach and style that has appealed to readers for over fifty years. The first half focuses on fundamental physical and... analytical principles. The second half covers applications of those principles to flow in pipes and open channels, lift and drag, fluid machinery, and compressible flow. The final chapter is an introduction to an array of fluid measurements and the instruments for making them.

An Aspen Food Science Text Series Book. Following the success of the previous editions, this popular introductory text continues to provide thorough,... up-to-date information covering a broad range of topics in food science, with emphasis on food processing and handling and the methodology of specific foods. Presenting a multitude of easy-to-understand figures, tables, illustrated concepts and methods, this text maintains the strengths of the previous edition while adding new information. The book opens with a revised chapter on what food science actually is, detailing the progression of food science from beginning to future. Succeeding chapters include the latest information on food chemistry and dietary recommendations, food borne diseases and microbial activity. A complete revision of HACCP is outlined, accompanied by numerous examples of flow charts and applications, as well as major additions on food labeling. Extensive updates have been made on processing methods and handling of foods, such as new procedures on: candy making; coffee and tea production; beer and wine production; soft drinks; ultra high temperature processing; aseptic packaging; aquaculture and surimi; and UHT and low temperature pasteurization of milk. In addition, there is a completely new section which includes safety and sanitation as well as laboratory exercises in sensory, microbiological, chemical quality test, and processing methods for a variety of the foods described in previous chapters.

This nicely written manuscript takes a gentler approach than other functional analysis graduate texts, and includes an improved approach along with a... better choice of topics. The concise treatment makes this ideal for a one-semester course. The exercises in this manuscript are numerous and of a very high quality. Interesting historical tidbits are scattered throughout the text, many of which will be new to most readers. The main prerequisites are basic undergraduate courses in real analysis, linear algebra, and point set topology.

This nicely written manuscript takes a gentler approach than other functional analysis graduate texts, and includes an improved approach along with a... better choice of topics. The concise treatment makes this ideal for a one-semester course. The exercises in this manuscript are numerous and of a very high quality. Interesting historical tidbits are scattered throughout the text, many of which will be new to most readers. The main prerequisites are basic undergraduate courses in real analysis, linear algebra, and point set topology.

Although extensively revised, this new edition continues in the fine tradition of its predecessor. Major changes include: a notation that formalizes the... distinction between equality and congruence and between line, ray and line segment; a completely rewritten chapter on mathematical logic with inclusion of truth tables and the logical basis for the discovery of non-Euclidean geometries; expanded coverage of analytic geometry with more theorems discussed and proved with coordinate geometry; two distinct chapters on parallel lines and parallelograms; a condensed chapter on numerical trigonometry; more problems; expansion of the section on surface areas and volume; and additional review exercises at the end of each chapter. Concise and logical, it will serve as an excellent review of high school geometry.