History - IV
A.D Era - 18th Century
a. Carl Gustav Jacobi (1804 - 1851 A.D)
-> Important research about partial differential equations of the first order and applied to dynamics.
-> He proved that a single - valued function of one variable is doubly periodic then the period ratios is imaginary.
-> "The spherical image of the normal directions along a closed differentiable curve in space divides the unit sphere into regions of equal area".
b. Karl Weierstrass (1815 - 1897 A.D)
-> Define the Limit.
-> Developed the technique of analytic continuation.
-> Along with Reimann published Abelian function theory.
c. Bernhard Riemann (1826 - 1866 A.D)
-> Real Analysis.
-> Riemann Integral.
-> Riemann - Liouville differ integral.
d. Srinivasa Ramanujan (1887 - 1920 A.D)
-> Hardy Number (1729).
-> 1911, brilliant work on Bernoulli numbers in the Journal of the Indian mathematical society.
A.D Era - 19th Century
a. Alang Turing (1912 - 1954 A.D)
-> Universal Turing Machine and Tuning Machine.
-> The Bombe Machine.
-> Two mathematical approaches to code - breaking for Code and Cypher School.
b. Abraham Robinson (1918 - 1974 A.D)
-> Non - standard analysis.
-> He found a model competition known as "closure" for the axioms of differential fields.