Differential Geometry

This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis. Chapter I Operations with Vectors.

Chapter II Plane Curves.

Chapter III Space Curves.

Chapter IV The Basic Elements of Surface Theory.

Chapter V Some Special Surfaces.

Chapter VI The Partial Differential Equations of SurfaceTheory.

Chapter VII Inner Differential Geometry in the Small from theExtrinsic Point of View.

Chapter VIII Differential Geometry in the Large.

Chapter IX Intrinsic Diferential Geometry of Manifolds.Relativity.

Chapter X The Wedge Product and the Exterior Derivative ofDifferential Forms, with Applications to Surface Theory.

Appendix A Tensor Algebra in Affine, Euclidean, and MinkowskiSpaces.

Appendix B Differential Equations.

Bibliography.

Index.

James J Stoker was an American applied mathematician and engineer. He was director of the Courant Institute of Mathematical Sciences and is considered one of the founders of the institute, Courant and Friedrichs being the others. Stoker is known for his work in differential geometry and theory of water waves.