Wonderfully detailed
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To me, any excellent book on mathematics or mathematical physics spells out all the difficult calculations in glorious detail. This is one of those books.
Starting from Euclidian geometry in three dimensions, the book takes the reader on a safe journey to the higher mathematics of tensors and differential forms, and their use in variational problems in physical field theories, primarily vector field theories and metric field theories (gravity).
The highlight is a proof that the equations of General Relativity (including a cosmological constant term) is the only second order (in the metric) equations of motion obtainable from a Lagrangian of second order (in the metric). Wonderfully clarifying!
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Challenging, thorough introduction
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This book covers thoroughly the basics of tensor analysis, differential forms and variational calculus. The problems at the end of each chapter are a good blend of straight mechanical computation through to challenging, abstract exercises.
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United States | 
United Kingdom | 
Canada