Differential Geometry - (De Gruyter Textbook) by Muhittin E Aydin & Svetlin G Georgiev (Paperback)
About this item
Highlights
- This textbook offers a different approach to classical textbooks in Differential Geometry.
- About the Author: Muhittin Evren Aydin a mathematician who works on various aspects of mathematics.
- 290 Pages
- Mathematics, Geometry
- Series Name: de Gruyter Textbook
Description
About the Book
This graduate textbook introduces two and three-dimensional curves and surfaces deduced from the Frenet equations. It presents the fundamental theory of tangent planes and normal surfaces by using differentiable maps and differentials. The book alsoBook Synopsis
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.
About the Author
Muhittin Evren Aydin a mathematician who works on various aspects of mathematics. Currently he focuses on differential geometry, Riemannian geometry, fractional calculus, microeconomics, and applications of differential geometry.
Svetlin G. Georgiev is a mathematician who works on various aspects of mathematics. Currently he focuses on ordinary and partial differential equations, differential geometry, dynamic geometry on time scales, integral equations on time scales, theory of distributions and harmonic analysis.