Differential and integral calculus for functions of several variables. Curves and surfaces. Differential forms. The divergence theorem. Stokes’ formula. Series and sequences of functions. Power series. Differential equations
Knowledge acquired:
To give the base instruments for the differential and integral calculus in several variables, and for the study of differential equations and differential forms
Competence acquired: Knowledge of fundamental issues of calculus in several variables: limits, continuity, differentiability, multiple integrals Basic knowledge of the theory of differential equations and differential forms.
Skills acquired (at the end of the course):
At the end of the course the student learns how to apply the tools of calculus to the study of functions of several real variables, the research of maxima and minima, function approximation, evaluations of areas and volumes. Moreover he/she is able to solve several kinds of differential equations and problems involving the theory of differential forms.
Prerequisites
Courses required: Mathematical Analysis I
Teaching Methods
CFU: 9
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Contact hours for: Lectures (hours): 80
Intermediate examinations: 9
Further information
For up-to-date information about office hours and supplementary material please look at the web pages of the teachers.
Type of Assessment
Written test followed by an oral test
Course program
Differential and integral calculus for functions of several variables. Continuity, derivability and differentiability. Taylor’s formula. Multiple integrals. Fubini’s theorem. Curves and surfaces. Maxima and minima with boundary conditions. Dini’s theorem. Differential forms. Closed and exact forms. The Divergence theorem. Stokes’ formula. Series and sequences of functions. Convergence and uniform convergence. Power series. Differential equations. Cauchy problem. Integration methods for special classes of differential equations. Linear differential equations and systems.