Differential Geometry of Manifolds

Description

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 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