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The study of how continuous mathematical structures (Functions) vary around the Neighborhood of a point on a Surface. Analysis includes Calculus, Differential Equations, etc.
See also Analysis Situs, Calculus, Complex Analysis, Functional Analysis, Nonstandard Analysis, Real Analysis
References
 
Bottazzini, U.  The ``Higher Calculus'': A History of Real and Complex Analysis from Euler to Weierstraß.
  New York: Springer-Verlag, 1986.
 
Bressoud, D. M.  A Radical Approach to Real Analysis.  Washington, DC: Math. Assoc. Amer., 1994.
 
Ehrlich, P.  Real Numbers, Generalization of the Reals, & Theories of Continua.  Norwell, MA: Kluwer, 1994.
 
Hairer, E. and Wanner, G.  Analysis by Its History.  New York: Springer-Verlag, 1996.
 
Royden, H. L.  Real Analysis, 3rd ed.  New York: Macmillan, 1988.
 
Wheeden, R. L. and Zygmund, A.  Measure and Integral: An Introduction to Real Analysis.  New York: Dekker, 1977.
  
 
Whittaker, E. T. and Watson, G. N.  A Course in Modern Analysis, 4th ed.  Cambridge, England: Cambridge University
  Press, 1990.
 
 Analysis