• 096229 - MATHEMATICAL AND NUMERICAL METHODS IN ENGINEERING [1]

Program of the course.

Differential calculus for functions of several real variables. Series of functions. Transport equation. Traffic flow models. Method of characteristics. Rankine-Hugoniot relation. Shock and rarefaction waves. Entropy condition. Heat equation. Well-posed problems. Separation of variables. Maximum principles. Fundamental solution.Duhamel principle. Harmonic functions. Mean value properties. Maximum principles. Poisson’s formula for the disk. Newtonian potentials. Wave equation. Well-posed problems and separation of variables. D’Alembert formula. Lebesgue integral. Hilbert spaces. Projection theorem and Riesz representation theorem.

Evaluation procedures.

The exam in Mathematical Methods is written and concerns both in questions about the theory and in exercises about the topics listed above. Students should show knowledge and understanding of such topics as concerns the theory questions, and applied knowledge as regards the capability of solving the proposed exercises. The students' classworks should show autonomy and communication skills as well.

We remind the students, as mentioned in the examination procedures of the course as a whole, that it is possible to take the exam in one modulus (Mathematical or Numerical Methods) in one of the five examination dates and the exam in the other modulus in another examination date, provided such dates are in the same academic year. The partecipation to the written exam in one of the two moduli automatically discards any previous grade obtained for that modulus, even if the student chooses to withdraw.

The exam will be held in written form. It will contain exercises on the topics covered by the course, and questions about the theory.

The final grade is the (rounded up) arithmetic mean of the grades obtained in the two moduli. To have the votation “30 cum laude” one should obtain 30 with laude in both the subparts. In case of a votatin of 30 with laude in only one of the two subparts, this gives a contribution of 30 in the arithmetic mean.