corso|33498

GENERAL OBJECTIVES The student must be able to study and use - curves and surfaces, - partial and directional derivatives of functions of several variables - two-dimensional and three-dimensional domains, - curvilinear coordinates (polar, spherical, cylindrical), - multiple, surface and line integrals, - vector fields and differential forms; line integrals and circulations; irrotational fields; conservative fields and their potentials, - the various differential operators and apply the Divergence and Curl Theorems to the calculation of flows, - power, Taylor and Fourier series.   SPECIFIC OBJECTIVES: KNOWLEDGE AND UNDERSTANDING. The course will provide in-depth knowledge and understanding of the fundamental concepts and tools of Analysis in several variables, in particular the use of differentiation and integration in several variables; curves and surfaces; differential operators, such as the gradient, divergence, curl, Laplacian; sequences and series of functions, with particular attention to Taylor and Fourier series. APPLYING KNOWLEDGE AND UDERSTANDING. The student will be able to apply the tools learned in this course to practical problems, which arise from Physics and Engineering, such as the study of Partial Differential Equations, the study of vector fields, the calculation of centers of mass, moments of inertia, work of conservative and non- conservative forces, the applications of Gauss’ and Stokes’ Theorems and the study of Maxwell's Equations. CRITICAL AND JUDGMENT SKILLS. The course will allow the student to choose, given a physical or engineering problem, the best resolution methodology, through a deep understanding of the requirements and constraints imposed by the context. COMMUNICATION SKILLS. At the end of the course the student will be able to illustrate the importance of the tools learned in the lessons, in order to apply them to problems of Physics and Engineering, such as the reconstruction of signals, the study of problems of fluid dynamics, electromagnetism, hydrodynamics and in general problems that involve the use of the tools of differential and integral calculus in several variables. LEARNING ABILITY. The student will develop independent study skills, for what concerns the theoretical study of the topics covered by the course and their application to concrete problems in Physics and Engineering.