Differential Geometry: Frenet Equations and Differentiable Maps

Differential Geometry: Frenet Equations and Differentiable Maps (De Gruyter Textbook)
Author: Muhittin E. Aydin (Author), Svetlin G. Georgiev (Author)
Publisher finelybook 出版社: De Gruyter
Edition 版次: 1st
Publication Date 出版日期: 2024-11-04
Language: English
Print length 页数: 370 pages
ISBN-10: 3111500896
ISBN-13: 9783111500898

Book Description

This textbook offers a different approach to classical textbooks in Differential Geometry. It includes practical examples and over 300 advanced problems designed for graduate students in various fields, such as fluid mechanics, gravitational fields, nuclear physics, electromagnetism, solid-state physics, and thermodynamics. Additionally, it contains problems tailored for students specializing in chemical, civil, and electrical engineering and electronics. The book provides fully detailed solutions to each problem and includes many illustrations to help visualize theoretical concepts.

The book introduces Frenet equations for plane and space curves, presents the basic theory of surfaces, and introduces differentiable maps and differentials on the surface. It also provides the first and second fundamental forms of surfaces, minimal surfaces, and geodesics. Furthermore, it contains a detailed analysis of covariant derivatives and manifolds.

The book covers many classical results, such as the Lancret Theorem, Shell Theorem, Joachimsthal Theorem, and Meusnier Theorem, as well as the fundamental theorems of plane curves, space curves, surfaces, and manifolds.