Differential Geometry

Reactive Publishing

Differential Geometry: Curves, Surfaces, and Their Applications in Engineering Design and Physics provides a clear and rigorous introduction to the fundamental concepts of differential geometry, with a strong emphasis on their practical applications in engineering and physics.

The book explores the core theory of curves and surfaces in Euclidean space, including curvature, torsion, geodesics, manifolds, and tensor analysis. It then demonstrates how these mathematical tools are applied to real-world problems in engineering design, computer-aided modeling, structural analysis, and physical systems.

Readers will find detailed coverage of:

• Parametric curves and surfaces
• Frenet-Serret formulas and fundamental forms
• Gaussian and mean curvature
• Applications in CAD/CAM, robotics, and mechanical design
• Differential geometry methods in general relativity and classical physics

Written for advanced undergraduates, graduate students, and practicing engineers and physicists, this book bridges pure mathematics with applied fields. It balances theoretical foundations with concrete examples and problem-solving approaches used in technical design and scientific research.

This work serves as both a learning resource and a reference for those seeking to understand the geometric principles underlying modern engineering and physical modeling.