GAUSS 12.0

Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy. ...

Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. ...

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light.

This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with nonrandom predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered include inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and nonoptimal properties of Gauss-Markov, Bayes, and shrinkage estimators under the assumption of normality, the optimal properties of F-tests, and the analysis of covariance and missing observations. ...

This hardcover edition of A Survey of Minimal Surfaces is divided into twelve sections discussing parametric surfaces, non-parametric surfaces, surfaces that minimize area, isothermal parameters on surfaces, Bernstein's theorem, minimal surfaces with boundary, the Gauss map of parametric surfaces in E3, non-parametric minimal surfaces in E3, application of parametric surfaces to non-parametric problems, and parametric surfaces in En. For this edition, Robert Osserman, Professor of Mathematics at Stanford University, has substantially expanded his original work

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem....

Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann. ...

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19th century.

Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

Provides students and practicing engineers with tools that can be used for the solution of parameter estimation problems. The emphasis is on chemical engineering applications and on systems described by nonlinear algebraic and ordinary differential equations. The Gauss- Newton method is featured, but shortcut methods are also presented. Englezos (University of British Columbia) and Kalogerakis (Technical University of Crete) describe how to formulate and solve parameter estimation problems, compute the statistical properties of the parameters, perform model adequacy tests, and design experiments for parameter estimation or model discrimination. The CD-ROM contains Fortran programs for solving estimation problems.

Media Magician for Mac helps manage/backup/combine/convert your camcorder footages and videos for better editing in FCP/ FCE/ Avid Studio/ iMovie/ Adobe Premere/ Adobe After Effect/ Apple Aperture, playback on iPad/ iPhone/ Apple TV/ Android Tablets, and sharing on YouTube. The simple editing functionalities help you frame-by-frame trim, join, cut, delete clips on timeline; add 3D and gauss blur effects, etc. You can flip video horizontally, vertically, clockwise, or counter-clockwise as well. Volume can also be enlarged or reduces for output.

Germany in the early 19th century. "Die Vermessung der Welt" follows the two brilliant and eccentric scientists Alexander von Humboldt and Carl Friedrich Gauss on their life paths.

By the 17th century, Europe had taken over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss.

In this second volume of Translation and Commentary I begin development of that part of Lie's work that has the greatest scientific import-the relation between group theory and differential equations. To have a perspective on this work, it is useful to think of analogies between the history of analysis and geometry. For analysis, one sees relatively clearly the outline of the historical development. First, Newton and Leibniz, then the completion of their "revolution" in the 18-th century by Euler, Lagrange, etc., then the magnificent progress through the 190th century-Gauss, Abel, Cauchy, Riemann, Weirstrass, Hilbert. ...