Description
Scientific Publishers Differental Geometry by Poonam Kumari
The book is intended to serve as a textbook for the undergraduate students in Mathematics. It is also useful for the postgraduate students. The book deals with the local theory of curves and surfaces in three dimensional Euclidean space. The subject is presented in a simple manner using the methods of differential calculus, integral calculus and vector algebra. Chapter 1 begins with the theory of curves in three dimensional Euclidean space. The curves are represented in a parametric form as a function of one variable.The geometric properties and various quantities associated with the curves such as the unit tangent vector, curvature and torsion are expressed via derivatives. The subsequent chapters discuss representation of a surface in various forms; concepts of characteristics, envelopes, and developable surfaces; fundamental magnitudes and their properties; normal curvature; principal curvature and principal directions; geodesics and their properties. A large number of solved examples followed by a carefully selected set of exercises are given at the end of each section.