Introduction to Differentiable Manifolds

This book gives an introduction to the basic concepts which are used indifferential topology differential geometry and differential equations. Acertain number o... » 

This book gives an introduction to the basic concepts which are used indifferential topology differential geometry and differential equations. Acertain number of concepts are essential for all three of these areas and areso basic and elementary that it is worthwhile to collect them together so thatmore advanced expositions can be given without having to start from the verybeginning. The concepts are concerned with the general basic theory ofdifferential manifolds. As a result this book can be viewed as a prerequisiteto Fundamentals of Differential Geometry. Since this book is intended as a textto follow advanced calculus manifolds are assumed finite dimensional. In thenew edition of this book the author has made numerous corrections to the textand he has added a chapter on applications of Stokes Theorem. TOCForeword.Acknowledgments. Differential Calculus. Manifolds. Vector Bundles. VectorFields and Differential Equations. Operations on Vector Fields andDifferential Forms. The Theorem of Frobenius. Metrics. Integration ofDifferential Forms. Stokes Theorem. Applications of Stokes Theorem. «