Introduction to integral calculus in one or more variables. The notion of differential equation and some applications. Elements of statistics.
teacher profile teaching materials
The notion of area. Riemann sums and definite integral. The fundamental theorem of calculus. Integration techniques: integral by subbstitution and by parts; integral of rational functions. Area enclosed by curves. The mean value of a function. Improper integrals.
Length of a curve and curvilinear integral.
ORDINARY DIFFERENTIAL EQUATIONS
Separable differential equations. Linear first order differential equations. Second order differential equations with constant coefficients. Vectorial fields. The theorem of existence and uniqueness. The Euler method.
INTEGRALS IN TWO OR MORE VARIABLES
The notion of volume. Integrals in planar domains and in the three-dimensional space. Surface area and integral on a surface.
Change of variables. The divergence theorem, Green's theorem and Stokes' theorem.
PARTIAL DIFFERENTIAL EQUATIONS
The wave and heat equations on an interval.
- P. Marcellini, C. Sbordone, Calcolo.
- P. Marcellini, C. Sbordone, Esercitazioni di Analisi Matematica I, prima parte e seconda parte.
Programme
INTEGRATION IN ONE VARIABLEThe notion of area. Riemann sums and definite integral. The fundamental theorem of calculus. Integration techniques: integral by subbstitution and by parts; integral of rational functions. Area enclosed by curves. The mean value of a function. Improper integrals.
Length of a curve and curvilinear integral.
ORDINARY DIFFERENTIAL EQUATIONS
Separable differential equations. Linear first order differential equations. Second order differential equations with constant coefficients. Vectorial fields. The theorem of existence and uniqueness. The Euler method.
INTEGRALS IN TWO OR MORE VARIABLES
The notion of volume. Integrals in planar domains and in the three-dimensional space. Surface area and integral on a surface.
Change of variables. The divergence theorem, Green's theorem and Stokes' theorem.
PARTIAL DIFFERENTIAL EQUATIONS
The wave and heat equations on an interval.
Core Documentation
- D. Benedetto, M. Degli Espositi, C. Maffei, Matematica per le scienze della vita.- P. Marcellini, C. Sbordone, Calcolo.
- P. Marcellini, C. Sbordone, Esercitazioni di Analisi Matematica I, prima parte e seconda parte.
Type of delivery of the course
Blackboard lectures in presenceType of evaluation
Written test and oral exam on the whole program of the course teacher profile teaching materials
2. Paolo Marcellini, Carlo Sbordone; Calcolo; Liguori Editore
3. James Stewart; Calculus - Early trascendentals; Ed. Thomson
Programme
Area and distance; Integrals; Fundamental Theorem of Calculus; Techniques of integration; Approximation of integrals; Arc length; Area of a surface of revolution; Volume of a solid of revolution; Multiple integrals; changes of variables; Surface integrals; Divergence, Greens' and Stokes' Theorems; Ordinary and Partial differential equationsCore Documentation
1. D.Benedetto, M.Degli Esposti, C.Maffei; Matematica per le scienze della vita; Casa Editrice Ambrosiana2. Paolo Marcellini, Carlo Sbordone; Calcolo; Liguori Editore
3. James Stewart; Calculus - Early trascendentals; Ed. Thomson
Reference Bibliography
1. D.Benedetto, M.Degli Esposti, C.Maffei; Matematica per le scienze della vita; Casa Editrice Ambrosiana 2. Paolo Marcellini, Carlo Sbordone; Calcolo; Liguori Editore 3. James Stewart; Calculus - Early trascendentals; Ed. ThomsonType of delivery of the course
The lessons are partially in-class; some of the students can attend online via TeamsAttendance
Attendance is mandatoryType of evaluation
The exam consists of a written test and an oral session