Geometry of Curves and Surfaces with Maple
Vladimir Rovenski, Technion & University of Haifa, Israel
0-8176-4074-6 * 2000 * $49.95 tent. * Hardcover * 310 pages * 391 Illustrations

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 geometrical images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry.

Well-illustrated with more than 350 figures--reproduceable 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 Birkhäuser web site.

Aimed at a broad audience of students, instructors of mathematics, computer scientists and engineers who have a 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, 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.

Click chapter titles to see extracts from each chapter.



Maple V: A Quick Reference

Part I. Functions and Graphs with MAPLE

Chapter 1. Graphs of Tabular and Continuous Functions

Chapter 2. Graphs of Composed Functions

Chapter 3. Interpolation of Functions

Chapter 4. Approximation of Functions

Part II. Curves with MAPLE

Chapter 5. Plane Curves in Rectangular Coordinates

Chapter 6. Curves in Polar Coordinates

Chapter 7. Asymptotes of Curves

Chapter 8. Space Curves

Chapter 9. Tangent Lines to a Curve

Chapter 10. Singular Points of Curves

Chapter 11. Length and Center of Mass of a Curve

Chapter 12. Curvature and Torsion of Curves

Chapter 13. Fractal Curves and Dimension

Chapter 14. Spline Curves

Chapter 15. Non-Euclidean Geometry on the Half-Plane

Chapter 16. Convex Hulls

Part III. Polyhedra with MAPLE

Chapter 17. Regular Polyhedra

Chapter 18. Semi-Regular Polyhedra

Part IV. Surfaces with MAPLE

Chapter 19. Surfaces in Space

Chapter 20. Some Classes of Surfaces

Chapter 21. Some Other Classes of Surfaces