Differential Geometry and Its Visualization

Download or read book Differential Geometry and Its Visualization written by Eberhard Malkowsky and published by CRC Press. This book was released on 2023-08-30 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Its Visualization is suitable for graduate level courses in differential geometry, serving both students and teachers. It can also be used as a supplementary reference for research in mathematics and the natural and engineering sciences. Differential geometry is the study of geometric objects and their properties using the methods of mathematical analysis. The classical theory of curves and surfaces in three-dimensional Euclidean space is presented in the first three chapters. The abstract and modern topics of tensor algebra, Riemannian spaces and tensor analysis are studied in the last two chapters. A great number of illustrating examples, visualizations and genuine figures created by the authors’ own software are included to support the understanding of the presented concepts and results, and to develop an adequate perception of the shapes of geometric objects, their properties and the relations between them. Features Extensive, full colour visualisations. Numerous exercises. Self-contained and comprehensive treatment of the topic.