Differentiable Manifolds

This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. The basic objective of the theory of differentiable manifolds is to extend the application of the calculus of Rn spaces to sets that do not possess the structure of a normed vector space. The differentiability of a function from Rn to Rm means that around each interior point of its domain, the function can be approximated by a linear transformation.
Basic concepts, such as differentiable manifolds, differentiable mappings, tangent vectors, vector fields, and differential forms, are briefly introduced in the first three chapters. Chapter 4 gives a concise introduction to differential geometry needed in subsequent chapters. Chapters 5 and 6 provide interesting applications to differential geometry and general relativity. Lie groups and Hamiltonian mechanics are closely examined in the last two chapters. Included throughout the book are a collection of exercises of varying degrees of difficulty.
Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics.