title: The Geometry of Physics: An Introduction
author:  Theodore Frankel 
description: ' ... extremely helpful for students in physics and engineering ... recommended to a wide audience ...' European Mathematical Society<br /><br />'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt fr Mathematik und ihre Grenzgebiete
zlib_text: # Part I  
  General
  
  
  © Springer International Publishing Switzerland 2015
  
  Gui-Qiang G. Chen, Michael Grinfeld and R. J. Knops (eds.)Differential
  Geometry and Continuum MechanicsSpringer Proceedings in Mathematics &
  Statistics13710.1007/978-3-319-18573-6_1
  
  # 1\. Compensated Compactness with More Geometry
  
  Luc Tartar1
  
  (1)
  
  University Professor of Mathematics Emeritus, Carnegie Mellon University,
  Pittsburgh, PA, USA
  
  Luc Tartar
  
  Email: [luctartar@gmail.com](mailto:luctartar@gmail.com)
  
  The theory of compensated compactness, partly developed in collaboration with
  François Murat, proved useful for attacking questions in the nonlinear PDE
  (partial differential equations) of continuum mechanics and physics. Many
  years ago, I believed an improvement could be achieved that included more
  geometrical ideas. I can only conjecture what should be done, but I consider
  it useful to present an historical perspective, in order to place ideas in
  their context, and indicate where geometry may be approp