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内容説明
This book emerged from courses taught at the University College of Dublin， Carnegie-Mellon University and mostly at Simon Fraser University. This is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra in Chapters 1 and 2. Differential manifold is introduced in Chapter 3. Tensor analysis， differential forms， connection forms， and curvature tensor are discussed in Chapter 4. Chapters 5， 6 and 7 investigate in great detail Riemannian and pseudo-Riemannian manifolds. Throughout the book， examples and problems are furnished from the theory of relativity and continuum mechanics. The extensive presentation of mathematical tools， examples and problems make this book a unique text for the pursuit of both the mathematical relativity theory and continuum mechanics.