Excerpt from Ray's Algebra, Vol. 2: An Analytical Treatise, Designed for High Schools and Colleges On some subjects it was necessary to be brief, to bring the work within suitable limits. For example, what is here given of the Theory of Equations, is to be regarded merely as an outline of the more practical and interesting parts of the subject, which alone is suficient for a distinct treatise, as may' be seen by refer ring to the works of Young or Hymera in English, or of defourcy er Reynaud in French. Some topics and exercises deemed both useful and interesting. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Republished version of the Ray's Arithmetic from the late 1870's and early 1880's. Includes the following books: (some in hardback and some in paperback) Primary Arithmetic, Intellectual Arithmetic, Practical Arithmetic, Key to the Primary/Intellectual/Practical, Test Examples in Arithmetic, Higher Arithmetic, Key to Higher Arithmetic, Parent Teacher Guide (by Ruth Beechick).

To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.

In 19th century America, Joseph Ray was the McGuffey of arithmetic. His textbooks, used throughout the United States, laid the mathematical foundations for the generations of inventors, engineers and businessmen who would make the nation a world power.

Guides your scheduling and planning through the Ray's Arithmetic books. Shows where you can adapt to the needs of slower or advanced students, making selective use of basic portions that are important for all students and higher-level portions that challenge the best students. Provides a test for each unit. Describes games and activities which add variety to your teaching.

This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.

This is the second edition of the standard text on design theory. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.