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-Born in Potsdam, Prussia (now Germany)
-Family: Jewish, Wealthy
Father- Banker
Eldest Brother- Physicist
Early Education:
-Taught by uncle
-Gymnasium (Year one
allowed to graduate to
University) (Only 12 yrs. old)
University of Berlin: Spring 1821
Jacobi researches Classics, Philosophy, and focuses in Mathematics
-begins research solving quintic equations by radicals (1821)
-studies Lagrange b/c of poor standards at University
http://en.wikipedia.org/wiki/Joseph-Louis_Lagrange
-1823-24 Jacobi passed examinations to teach mathematics
-Can teach at prestigious Gymnasium in Berlin (Joachimsthal) but submits for doctoral dissertation to University of Berlin
-Habilitation Thesis (provides for him to teach= on iterated functions)
-Berlin Academy of Sciences in 1825 doesn't publish
-1825- converts to catholicism
http://www.cathnewsusa.com/2011/05/jewish-catholic-dialogue-discusses-sources-of-authority/
-transferred to the University of Königsberg in 1826 (works with Neumann and Bessel)
-Develops Theory of Elliptic Functions based on four theta functions (alongside Niels Henrick Abel of Norway) (gains Legendre's interest)
-determines that the quotients of the theta functions yields the three Jacobian Elliptic Functions: sn z, cn z, and dn z (pub. 1829)
-1932= Hyperelliptic functions obtained by inverting Hyperelliptic integrals= develops Abelian Functions (complex functions of several variables)
Elliptic functions
Hamilton-Jacobi equation- created as a result of work with differential ens. and dynamics
Use: Study of Quantum and rational mechanics and their presentation
Figure 4: Differential of the action function as a function of variations and in the endpoint of an extremal world line.
-Concerning the Structure and Properties of Determinants (research in partial differential equations of the first order and how they could be applied to the differential equations of dynamics)
Use: Theory of Determinants and Invention of Functional Determinant for analytical Investigations
Further Contributions:
-proved if single-valued function of one variable is doubly periodic then the ratio of the periods is imaginary
-Jacobi Triple Product Formula (properties of theta functions)
Functional Determinant
-January 1851- catches influenza
-Dies 18th of Feb, 1851 after contracting Smallpox with little recovery period between illnesses in Berlin, Germany
http://www.usna.edu/Users/math/meh/jacobi.html
Biography in Encyclopaedia Britannica. http://www.britannica.com/eb/article-9043197/Carl-Jacobi
"Carl Gustav Jacob Jacobi." Jacobi Biography. Web. 25 May 2015. http://www-history.mcs.st-and.ac.uk/Biographies/Jacobi.html
D Stander, Makers of modern mathematics : Carl Gustave Jacob Jacobi, Bull. Inst. Math. Appl. 24(1-2) (1988), 27-28.
J McCleary, On Jacobi's remarkable curve theorem, Historia Math. 21 (3) (1994), 377-385.
S S Demidov, On the history of the theory of first-order partial differential equations : C G J Jacobi's 'first method' (Russian), Istor.-Mat. Issled. 26 (1982), 137-153.
T Hawkins, Jacobi and the birth of Lie's theory of groups, in S S Demidov et al. (eds), Amphora : Festschrift for Hans Wussing on the occasion of his 65th birthday (Basel- Boston- Berlin, 1992), 289-313.