Introduction to Multidimensional Calculus

  • Reinhard HentschkeEmail author
  • Christian Hölbling
Part of the Undergraduate Lecture Notes in Physics book series (ULNP)


Generalizing from flat to arbitrary spacetime, we develop the basic formalism of differential geometry, which is the mathematical foundation of the general theory of relativity. Vectors, tensors and the important concept of the covariant derivative are introduced. The latter allows us to compare vectors and tensors at different points. The generalization of symmetry transformations with Killing fields is also introduced.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany

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