"This book presents in an elegant way, the essentials of two and three dimensions of analytical geometry with plenty of examples to illustrate the basic ideas and to bequeath to the students numerous techniques of problem-solving. The exercises provide ample problems to supplement steady progress and to broaden the intuition of generalization. The overall approach is systematic, rigorous and least dependent on Euclidean propositions."--BOOK JACKET.
Author: P.K. Jain
Publisher: New Age International
Release Date: 2005-01-01
The Book Is Intended To Serve As A Textbook For B.A. / B.Sc. Hons. And Pass Course Students Of Indian Universities And Abroad. It Is Also Meant For The Engineering Students And Other Professional Competitive Examinations Such As Ias, Ies, Pcs Etc.The Text Starts With The Introduction Of Coordinates Of A Point In A Space, Distance Formula, Projection, Direction Cosines, Locus And Followed By The Study Of The Plane, Straight Line, Sphere, Cone, Cylinder, Central Conicoids And Paraboloids. An Appendix Has Been Given On General Equation Of Second Degree. The Salient Features Of The Book Are: * Presentation Of The Subject In Natural Way * Description Of The Concepts With Justification * Grading Of Exercises * Exercises (Solved And Unsolved) After Each Section And Miscellaneous Set Of Exercises At The End Of Each Chapter. * Notes And Remarks At Proper Places
This volume discusses the classical subjects of Euclidean, affine and projective geometry in two and three dimensions, including the classification of conics and quadrics, and geometric transformations. These subjects are important both for the mathematical grounding of the student and for applications to various other subjects. They may be studied in the first year or as a second course in geometry.The material is presented in a geometric way, and it aims to develop the geometric intuition and thinking of the student, as well as his ability to understand and give mathematical proofs. Linear algebra is not a prerequisite, and is kept to a bare minimum.The book includes a few methodological novelties, and a large number of exercises and problems with solutions. It also has an appendix about the use of the computer program MAPLEV in solving problems of analytical and projective geometry, with examples.
Author: D. V. Kletenik
Release Date: 2016-06-06
A Collection of Problems in Analytical Geometry, Part II: Three-Dimensional Analytical Geometry is a collection of problems dealing with analytical geometry in the field of theoretical mechanics. The book discusses rectangular Cartesian coordinates in three-dimensional space and the division of an interval in a given ratio. The sample questions concern problems dealing with isosceles triangles, vertices, and center of gravity of equal masses. The book defines the concept of a vector and then lists problems concerning the triangle law and the scalar product of two vectors. Other problems focus on the equations of a surface and a curve and on questions related to the intersection of three surfaces. The text lists other problems such as the equation of a plane, the direction-vector of a straight line, and miscellaneous problems pertaining to the equations of a plane, of a straight line, and of a sphere in a direction-vector. The selection is useful for professors in analytical geometry and for other courses in physic-mathematics and general engineering.
Author: James T. Smith
Publisher: John Wiley & Sons
Release Date: 2000-01-10
A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: Ample exercises designed to promote effective problem-solvingstrategies Insight into novel uses of Euclidean geometry More than 300 figures accompanying definitions and proofs A comprehensive and annotated bibliography Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.