Geometry of Curves and Surfaces with MAPLE PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Geometry of Curves and Surfaces with MAPLE PDF full book. Access full book title Geometry of Curves and Surfaces with MAPLE by Vladimir Rovenski. Download full books in PDF and EPUB format.
Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 1461221285
Category : Mathematics
Languages : en
Pages : 310
Get Book Here
Book Description
This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.
Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 1461221285
Category : Mathematics
Languages : en
Pages : 310
Get Book Here
Book Description
This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.
Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 0387712771
Category : Mathematics
Languages : en
Pages : 463
Get Book Here
Book Description
This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.
Author: John Oprea
Publisher: MAA
ISBN: 9780883857489
Category : Mathematics
Languages : en
Pages : 508
Get Book Here
Book Description
This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Author: mary Gray
Publisher: CRC Press
ISBN: 9780849371646
Category : Mathematics
Languages : en
Pages : 1094
Get Book Here
Book Description
The Second Edition combines a traditional approach with the symbolic manipulation abilities of Mathematica to explain and develop the classical theory of curves and surfaces. You will learn to reproduce and study interesting curves and surfaces - many more than are included in typical texts - using computer methods. By plotting geometric objects and studying the printed result, teachers and students can understand concepts geometrically and see the effect of changes in parameters. Modern Differential Geometry of Curves and Surfaces with Mathematica explains how to define and compute standard geometric functions, for example the curvature of curves, and presents a dialect of Mathematica for constructing new curves and surfaces from old. The book also explores how to apply techniques from analysis. Although the book makes extensive use of Mathematica, readers without access to that program can perform the calculations in the text by hand. While single- and multi-variable calculus, some linear algebra, and a few concepts of point set topology are needed to understand the theory, no computer or Mathematica skills are required to understand the concepts presented in the text. In fact, it serves as an excellent introduction to Mathematica, and includes fully documented programs written for use with Mathematica. Ideal for both classroom use and self-study, Modern Differential Geometry of Curves and Surfaces with Mathematica has been tested extensively in the classroom and used in professional short courses throughout the world.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Elsa Abbena
Publisher: CRC Press
ISBN: 1351992201
Category : Mathematics
Languages : en
Pages : 1024
Get Book Here
Book Description
Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.
Author: Victor Andreevich Toponogov
Publisher: Springer Science & Business Media
ISBN: 0817644024
Category : Mathematics
Languages : en
Pages : 215
Get Book Here
Book Description
Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 038771278X
Category : Mathematics
Languages : en
Pages : 463
Get Book Here
Book Description
This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.
Author: David Salomon
Publisher: Springer Science & Business Media
ISBN: 0387284524
Category : Computers
Languages : en
Pages : 466
Get Book Here
Book Description
Requires only a basic knowledge of mathematics and is geared toward the general educated specialists. Includes a gallery of color images and Mathematica code listings.
Author: Thomas F. Banchoff
Publisher: CRC Press
ISBN: 100059775X
Category : Mathematics
Languages : en
Pages : 371
Get Book Here
Book Description
Through two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player. The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research. At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises. This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.
