Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. It introduces manifolds in a both streamlined and mathematically rigorous way while keeping a view toward applications, particularly in physics.

The author takes a practical approach, containing extensive exercises and focusing on applications, including the Hamiltonian formulations of mechanics, electromagnetism, string theory.

The Second Edition of this successful textbook offers several notable points of revision.

New to the Second Edition:

  • New problems have been added and the level of challenge has been changed to the exercises
  • Each section corresponds to a 60-minute lecture period, making it more user-friendly for lecturers
  • Includes new sections which provide more comprehensive coverage of topics
  • Features a new chapter on Multilinear Algebra

chapter Chapter 1|37 pages

Analysis of Multivariable Functions

chapter Chapter 2|25 pages

Variable Frames

chapter Chapter 3|54 pages

Differentiable Manifolds

chapter Chapter 4|59 pages

Multilinear Algebra

chapter Chapter 5|72 pages

Analysis on Manifolds

chapter Chapter 6|55 pages

Introduction to Riemannian Geometry

chapter Chapter 7|56 pages

Applications of Manifolds to Physics