Dominique Tournès

Diagrams in the theory of differential equations (eighteenth to nineteenth centuries)

Diagrams have played an important role throughout the entire history of differential equations. Geometrical intuition, visual thinking, experimentation on diagrams, conceptions of algorithms and instruments to construct these diagrams, heuristic proofs based on diagrams, have interacted with the development of analytical abstract theories. We aim to analyze these interactions during the two centuries the classical theory of differential equations was developed. They are intimately connected to the difficulties faced in defining what the solution of a differential equation is and in describing the global behavior of such a solution.

The method of Cholesky for linear systems

This chapter is devoted to the method of Cholesky for solving systems of linear equations with a symmetric (and positive definite) matrix. In Section 4.1, we will introduce the method of least squares which is used for treating data generated by a topographical survey. These data have to be adjusted as explained in Section 4.2. Then, a system of linear equations is obtained. Its solution can be obtained by various methods which were in use before Cholesky’s discovery. They will be reviewed in Section 4.3. Section 4.4 is devoted to the manuscript of Cholesky. Then, it will be analyzed in Section 4.5. In Section 4.6, we will discuss other methods for linear systems which were introduced after Cholesky’s. Finally, its diffusion in the scientific community will be the subject of Section 4.7.

Cholesky’s family

This chapter gathers the information we were able to find on the family (past and present) of Cholesky. Most of it is due to the extensive research of Raymond Nuvet, the vice–mayor of Montguyon, in the municipal archives of all the villages around.

An unpublished book by Cholesky

The Ecole Speciale des Travaux Publics (ESTP), the innovative establishment discussed extensively in the previous chapter, asked Cholesky to write four correspondence courses: Topographie generale (General Topography), Leves d’etudesa la planchette (Advanced Plane Table Surveying), Calcul graphique des contenances (Graphical Calculation of Capacities), Notions de cosmographie et d’astronomie de position (Notions of Cosmography and Positional Astronomy).

Léon Eyrolles and his superior school

Since Cholesky was involved in the school founded by Eyrolles, let us now spend some time on this man and his activities.

Biography of Cholesky

Andre–Louis Cholesky was born on Friday 15 October 1875, at 1:00 pm, in Montguyon, a village in the district of Jonzac (department of Charente–Inferieure, named Charente–Maritime since 1942), about 60 km northeast of Bordeaux and 65 km southwest of Angouleme, which counted around 1,500 inhabitants at that time.