Differentiability Euler, Leonhard

At an elementary level, one of the dogmas taught to almost every chemist is that in thermodynamics only differences bctwmi thermodjmamic potentials at various state points matter. This is essentiallj a consequence of the discussion in Section 1.3 where we emphasized that exact differentials exist for thermodynamic potentials such as 14, S, T, Q, or fl. These potentials therefore satisfy Eq. (1.18). However, one is frequently confronted with the problem of calculating absolute values of thennodynamic potentials theoretically. An example is the determination of phase equilibria, which is one of the key issues in this book cliapter. In this context a theorem associated with the Swiss mathematician Leonhard Euler is quite useful. We elaborate on Euler s theorem in Appendix A.3 where we also introduce the notion of homogeneous functions of degree k. 

This is a second-order differential equation, but slightly less complicated than the Schrbdinger equation tackled in the main part of the appendix. It is also a problem considered by Leonhard Euler when complex exponentials were emerging in the world of mathematics. 

Lagrange, Comte Joseph Louis (1736-1813) An Italian-born French mathematician and astronomer noted for his work in mechanics, harmonics, and in the calculus of variations. He also established the theory of differential equations. He succeeded Swiss mathematician and physicist Leonhard Euler (1707-83) as the director of mathematics at the Prussian Academy of Sciences in Berlin, during which time he published his work in MicaniqueAnalytique(n88), that covered every area of pure mathematics. 

Leonhard Euler (1707-1783) was not interested in numerical integration of ordinary differential equations, but he was interested in initial value problems. Incidentally, Euler is also responsible for what, according to Richard Feynman, is the most remarkable equation ever e + 1 = 0. 

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