Transformation of Integrals



So far we have presumed a minimal knowledge of linear algebra on the part of the reader. However in this chapter, we shall use basic properties of determinants and the fact that any invertible matrix is a product of ‘elementary’ matrices.

The transformation formula that justifies the so called ‘substitution’ or ‘change of variables’ rule for evaluating a Riemann integral is fairly easy to establish in ℝ. In higher dimensions however, the corresponding formula is far more difficult to prove. This is the task we take up in this chapter.


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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research (Mohali)PanchkulaIndia
  2. 2.Indian Institute of Science Education and Research (Mohali)ChandigarhIndia

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