Differential Geometry of Manifolds

Analysis of Multivariable Functions Functions from Rn to Rm Continuity, Limits, and Differentiability Differentiation Rules: Functions of Class Cr Inverse and Implicit Function Theorems Coordinates, Frames, and Tensor Notation Curvilinear Coordinates Moving Frames in Physics Moving Frames and Matrix Functions Tensor Notation Differentiable Manifolds Definitions and Examples Differentiable Maps between Manifolds Tangent Spaces and Differentials Immersions, Submersions, and Submanifolds Chapter Summary Analysis on Manifolds Vector Bundles on Manifolds Vector Fields on Manifolds Differential Form. Read more... Abstract: Analysis of Multivariable Functions Functions from Rn to Rm Continuity, Limits, and Differentiability Differentiation Rules: Functions of Class Cr Inverse and Implicit Function Theorems Coordinates, Frames, and Tensor Notation Curvilinear Coordinates Moving Frames in Physics Moving Frames and Matrix Functions Tensor Notation Differentiable Manifolds Definitions and Examples Differentiable Maps between Manifolds Tangent Spaces and Differentials Immersions, Submersions, and Submanifolds Chapter Summary Analysis on Manifolds Vector Bundles on Manifolds Vector Fields on Manifolds Differential Form From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices Content: Front Title Page Copyright Contents Preface Acknowledgments 1. Analysis of Multivariable Functions 2. Coordinates, Frames, and Tensor Notation 3. Differentiable Manifolds 4. Analysis on Manifolds 5. Introduction to Riemannian Geometry 6. Applications of Manifolds to Physics Appendix A Appendix B Appendix C Bibliography Back