Applications

Mathematics has two sides, the theoretical and the practical. The one attracting general attention is the practical side. The theoretical side is usually considered to be incomprehensible except to specialists. This dichotomy of the subject is as old as the subject itself. The mechanical inventions of Archimedes, for instance, his water screw and his water-driven model of the planetary system, made him famous, but he preferred theory. The historian Plutarch says that although his inventions had given him the reputation of superhuman wisdom, Archimedes did not want to write about these things but kept to the abstract world of mathematics. Gauss, who did a great deal of applied mathematics, took the same position. But if we leave the great innovators we shall find that the overwhelming majority of people who have devoted some of their time and energy to the subject have used it as a tool to get interesting numerical results and to understand more or less complex situations. Mathematics is used both for numerical calculation and the construction of models. We shall give a review of the history and practice of numerical analysis, look into some difference schemes, and construct a model of the vocal tract explaining how vowels are produced.