This concise text on geometry with applications in a variety of disciplines is devoted to three main geometrical topics: curves, surfaces, and polyhedra. It presents elementary methods for analytical modeling and their visualization,as well as demonstrating the potential of symbolic computational tools to support the development of analytical solutions. The author systematically examines powerful tools including 2D and 3D animation of geometric images, transformations, shadows and colors, and then further studies more complex geometrical modeling problems related to analysis and differential equations. 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. The book is also well-illustrated, with over 300 figures reproducible using Matlab programs. This text greatly extends the author's previous title, 'Geometry of Curves and Surfaces with Maple' (Birkhauser, 2000), and has a different focus. In addition to being applications-driven and motivated by numerous examples and exercises from real-world fields suchas physics, engineering, biology, computer science, and IT, the book also contains more than 60 percent new material, including new sections with a geometric view of dynamical systems and PDEs, fractals, and surfaces-splines. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines, engineers, computer scientists, and instructors of applied mathematics. Covers basic Matlab as well as complex geometrical modeling problems related to analysis and differential equations Integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format Provides over 150 stimulating exercises and problems and over 300 figures reproducible using Matlab programs Is applications-driven and motivated by numerous examples and exercises from a variety of real-world fields such as physics, engineering, biology, computer science, and IT Systematic and rigorous presentation INDICE: Preface.- Part 1: Preliminaries.- Basic Matlab. Analytic Geometry.- Geometric View on Linear Algebra.- Part 2: Curves and Surfaces.- Plane Curves.- Space Curves.- Surfaces.- Curve and Surface Fitting.- Polyhedra and HigherDimensional Objects.- Part 3: Selected Themes.- Computational Geometry.- Geometrical Splines.- Non-Euclidean Geometries.- Applications of Differential Equations (in Physics, Mechanics, Biology and Engineering).- Geometry of DynamicalSystems.- Visualizing Solutions of PDEs.- Explorations (solution worksheets).- References.- Index.
- ISBN: 978-0-387-71277-2
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 292
- Fecha Publicación: 01/12/2009
- Nº Volúmenes: 1
- Idioma: Inglés