Differential Geometry and Its Applications (Second Edition)

Author: John Oprea
Publisher:
Publish Date: 2005-05-01
Features: This book is an excellent textbook on differential geometry, covering a broad range of topics. It not only includes classic theories in the field but also introduces algebraic systems and Maple, as well as the practical applications of differential geometry in modern life. The book primarily introduces variational methods, optimal control theory, and differential geometry, helping readers understand various phenomena in life, such as the formation of soap films and the motion of particles on surfaces. Specific content includes mean curvature, completeness, and the Gauss-Bonnet theorem, minimal surfaces, variational methods, and geometry. Additionally, the book contains numerous exercises with corresponding hints and solutions, along with a series of examples, definitions, and notes. It can serve as a differential geometry textbook for higher education majors in teaching fields and other science and engineering disciplines. For professionals, the book also holds reference value.