This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as book form will allow.
0. Fundamental Not(at)ions.- I. Real Vector Spaces.- II. Affine Spaces.- III. Dual Spaces.- IV. Metric Vector Spaces.- V. Tensors and Multilinear Forms.- VI Topological Vector Spaces.- VII. Differentiation and Manifolds.- VIII. Connections and Covariant Differentiation.- IX. Geodesics.- X. Curvature.- XI. Special Relativity.- XII. General Relativity.- Index of Notations.
Series: Graduate Texts in Mathematics
Number Of Pages: 434
Published: June 2010
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5
Weight (kg): 0.77
Edition Number: 2
Edition Type: Revised