Synopses & Reviews
Concise and user-friendly, this college-level text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theory. The introductory approach bridges the gap between mere manipulation and a genuine understanding of an important aspect of both pure and applied mathematics.
Beginning with a consideration of coordinate transformations and mappings, the treatment examines loci in three-space, transformation of coordinates in space and differentiation, tensor algebra and analysis, and vector analysis and algebra. Additional topics include differentiation of vectors and tensors, scalar and vector fields, and integration of vectors. The concluding chapter employs tensor theory to develop the differential equations of geodesics on a surface in several different ways to illustrate further differential geometry.
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Assuming only a knowledge of basic calculus, this text presents an elementary and gradual development of tensor theory. From this treatment, the traditional material of courses on vector analysis is deduced as a particular case. In addition, the book forms an introduction to metric differential geometry. 1962 edition.
Table of Contents
1. Coordinate Transformations and Mappings 2. Loci in Three-Space 3. Transformation of Coordinates in Space; Differentiation 4. Tensor Algebra 5. Tensor Analysis 6. Vector Analysis 7. Vector Algebra 8. Differentiation of Vectors 9. Differentiation of Tensors 10. Scalar and Vector Fields 11. Integration of Vectors 12. Geodesic and Union Curves Index