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The study of two-dimensional analytic geometry has gone in and out of fashion several times over the past century, however this classic field of mathematics has once again become popular due to the growing power of personal computers and the availability of powerful mathematical software systems, such as Mathematica, that can provide an interactive environment for studying the field. By combining the power of Mathematica with an analytic geometry software system called Descarta2D, the author has succeeded in meshing an ancient field of study with modern computational tools, the result being a simple, yet powerful, approach to studying analytic geometry. Students, engineers and mathematicians alike who are interested in analytic geometry can use this book and software for the study, research or just plain enjoyment of analytic geometry. Mathematica provides an attractive environment for studying analytic geometry. Mathematica supports both numeric and symbolic computations meaning that geometry problems can be solved for special cases using numbers, as well as general cases producing formulas. Mathematica also has good facilities for producing graphical plots which are useful for visualizing the graphs of two-dimensional geometry. * A classic study in analytic geometry, complete with in-line Mathematica dialogs illustrating every concept as it is introduced * Excellent theoretical presentation *Fully explained examples of all key concepts * Interactive Mathematica notebooks for the entire book * Provides a complete computer-based environment for study of analytic geometry * All chapters and reference material are provided on CD-ROM in addition to being printedin the book * Complete software system: Descarta2D * A software system, including source code, for the underlying computer implementation, called Descarta2D is provided * Part VII of the book is a listing of the (30) Mathematica files supporting Descarta2D; the source code is also supplied on CD-ROM * Explorations * More than 120 challenging problems in analytic geometry are posed; Complete solutions are provided both as interactive Mathematica notebooks on CD-ROM and as printed material in the book * Mathematica and Descarta2D Hints expand the reader's knowledge and understanding of Descarta2D and Mathematica * Sortware developed with Mathematica 3.0 and is compatible with Mathematica 4.0 * Detailed reference manual * Complete documentation for Descarta2D * Fully integrated into the Mathematica Help Browser
The two volume set LNCS 6443 and LNCS 6444 constitutes the proceedings of the 17th International Conference on Neural Information Processing, ICONIP 2010, held in Sydney, Australia, in November 2010. The 146 regular session papers presented were carefully reviewed and selected from 470 submissions. The papers of part I are organized in topical sections on neurodynamics, computational neuroscience and cognitive science, data and text processing, adaptive algorithms, bio-inspired algorithms, and hierarchical methods. The second volume is structured in topical sections on brain computer interface, kernel methods, computational advance in bioinformatics, self-organizing maps and their applications, machine learning applications to image analysis, and applications.
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus. This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes. This book will prove useful to undergraduate trigonometric students.
This is a new release of the original 1938 edition.
Excerpt from Introduction to Analytic Geometry In preparing this volume the authors have endeavored to write a drill book for beginners which presents, in a manner conforming with modern ideas, the fundamental concepts of the subject. The subject-matter is slightly more than the minimum required for the calculus, but only as much more as is necessary to permit of some choice on the part of the teacher. It is believed that the text is complete for students finishing their study of mathematics with a course in Analytic Geometry. The authors have intentionally avoided giving the book the form of a treatise on conic sections. Conic sections naturally appear, but chiefly as illustrative of general analytic methods. Attention is called to the method of treatment. The subject is developed after the Euclidean method of definition and theorem, without, however, adhering to formal presentation. The advantage is obvious, for the student is made sure of the exact nature of each acquisition. Again, each method is summarized in a rule stated in consecutive steps. This is a gain in clearness. Many illustrative examples are worked out in the text. Emphasis has everywhere been put upon the analytic side, that is, the student is taught to start from the equation. He is shown how to work with the figure as a guide, but is warned not to use it in any other way. Chapter III may be referred to in this connection. 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.
The study of analytic geometry has long been a foundational component of mathematical education, and this classic text by Charles Herschel Sisam and Virgil Snyder remains one of the most thorough and lucid treatments of the subject available. In clear and accessible prose, the authors offer a detailed exploration of the key concepts and techniques that underlie analytic geometry, including vectors, planes, and points, as well as the applications of these principles in fields ranging from physics and engineering to economics and computer science. An essential reference for students, teachers, and anyone interested in the beauty and power of mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
In this classic textbook, Riggs provides a comprehensive overview of analytic geometry, covering topics such as the straight line, circle, parabola, and hyperbola. Written in a clear and accessible style, Riggs's book is an essential resource for anyone studying math or science at the college level. This book is perfect for students or instructors looking for a thorough introduction to this important mathematical field. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.