The module is a completion of the Mathematical Analysis I course and it aims to provide more mathematical skills and application elements useful for a Civil Engineer.
The course aims at providing the student with basic operative knowledge on differential and integral calculus for functions of two and three real variables, with some attention to mathematical rigour. Some of the founding elements of mathematical modeling are developed in the second half of the course, such as the elementary theory of ordinary differential equations and systems.
60 hours of lectures.
Parametric curves in plane and in space: closed, simple, regular curves, length of a curve, line integrals of real valued function. Irrotational and conservative fields, simply connected domains, line integrals of a vector field. Double integrals on finite unions of normal domains, reduction formulas, change of variables. Triple integrals, reduction formulas for domains which are normal to a plane or a line, change of variables, cylindrical and spherical coordinates. Parametric surfaces in space, surface integrals of scalar functions, flows of vector fields through surfaces. Gauss-Green formulas. Divergence theorem in plane and in space. Stokes' theorem. Local and global existence and uniqueness theorems for differential equations and systems. Partial and complete linearization of differential systems. Linear differential (homogeneous and non-homogeneous) systems with constant coefficients. Bernoulli and Euler ordinary differential equations.
For the theory
For the exercise
In addition during the lectures will be distributed sheets with texts of exercises to do for a personal assessment of the level of preparation. Other recommended reading will be inserted in aulaweb DICCA, where the course is present.
ANNA ROSSI (President)
MARCO BARONTI
MAURIZIO CHICCO
MANUEL MONTEVERDE
MARIA EZIA SERPICO
MATHEMATICAL ANALYSIS II
The exam consists of a written and an oral test. The written test is based on the resolution of problems similar to those carried out during the course. In such a test is proven the ability to perform problems relating to multiple integration, to the integration on curves and surfaces of scalar functions, to the issues related to vector fields and to the systems of linear differential equations. In the oral exam is assessed the understanding of the concepts and reasoning skills acquired by the students. For each written test is allowed to use texts, notes and calculator. The tests are individual. The oral exam will be supported in the same session of the written examination. With regard to the determination of the final grade, the Commission will assess the outcome of both tests. To take part in the written test are required to:
