The General Stokes Theorem

  • Satish Shirali
  • Harkrishan Lal Vasudeva


The most important formula of analysis is the fundamental theorem of calculus. The formulas of Green, Gauss and Stokes are an extension of this theorem. They also constitute the extensively used part of the machinery of integral calculus. A far reaching generalisation of the above said theorems is the Stokes Theorem. In order to prove the theorem in its general form, we need to develop a good deal of material, known as differential forms. Much care has been taken to give clear definitions, examples and transparent proofs to tehnical challenging results. Differential forms also provide better insight into vector calculus, as is illustrated by the material covered in Section 8-8. A less formal and more intuitive introduction to the material covered in this chapter is available in Crowin and Szczarba [8], Lang [18] and Protter and Morrey [20].


Vector Field Open Subset Differential Form Standard Representation Divergence Theorem 
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  1. 20.
    Protter, MH, Morrey, CB. A First Course in Real Analysis, 2nd ed. Springer Verlag, New York, 1991.Google Scholar
  2. 18.
    Lang, S. Undergraduate Analysis, 2nd ed. Springer Verlag, New York, 1997.Google Scholar
  3. 8.
    Corwin, LJ, Szczarba, RH, Multivariable Calculus. Marcel Dekker Inc, New York and Basel, 1982.Google Scholar
  4. 21.
    Pugh, CC. Real Mathematical Analysis. Springer Verlag, New York, 2002.Google Scholar
  5. 23.
    Shirali, S, Vasudeva, HL. Mathematical Analysis. Narosa Publishing House, New Delhi, 2006.Google Scholar

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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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