ANALYSIS II
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- WALTER BOSCHERI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/05
Training objectives
- The course aims to introduce students to the study of the calculus with functions of several variables. Moreover, the course will provide essential implements to apply partial derivatives to the study of functions of several variables, finding largest and smallest values of a function, to obtain qualitative information about the shape of the graph, to calculate the volume under a surface. Moreover, the course will provide some of the basic elements of differential equations and Fourier Series.
At the end of the course, the student should get the ability to solve maximum and minimum problems for functions of several variables, to obtain the equation of the tangent plane, to calculate double and triple integrals, to solve some classes of differential equations, to develop a function in Fourier Series. Prerequisites
- The student must be acquainted with calculus for functions of a real variable.
Course programme
- The course includes 48 hours of lectures and exercises.
Differential calculus
1) partial derivatives
2) differentiable functions
3) higher derivatives
4) maximum and minimum points
5) constrained minimization
Integrals in R^n
1) double integrals
2) double integrales with change of coordinates
3) triple integrals
4) change of variables in triple integrals
Curves and surfaces
1) line integrals
2) scalar and vectorial fields
3) surfaces and surface integrals
Vectorial differential calculus
1) gradient, divergence, rotor
2) Green theorem
3) divergence theorem
4) Stokes theorem
Differential equations
1) introduction and classification
2) first order equations
3) second order equations
4) linear equations with constant coefficients
5) introduction to numerical methods for ODEs
Recalls on series and continuous functions:
1) Series and continuous functions
3) Complex numbers
Series and sequences of functions
1) introduction
2) power series
3) Fourier series Didactic methods
- Lectures on the topics of the course program.
Exercises performed by the teacher at the blackboard. Learning assessment procedures
- The exam is written. Usage of text books and personal notes as well as calculator are allowed.
It will also be possible to carry out two intermediate exams, the first part at the beginning of November, the second one before Christmas.
All detailed information about the exam can be found on the course googleclassroom page. Reference texts
- R. Adams, Calcolo Differenziale 2, Casa Editrice Ambrosiana, 2014.
Other references:
M. Bramanti, C. D. Pagani, S. Salsa. Matematica. Calcolo infinitesimale e algebra lineare.
Zanichelli, Edizione 2, 2004.
Teacher's notes
N. Fusco, P. Marcellini, C. Sbordone. Lezioni di analisi matematica due.
Zanichelli, 2020.
S. Salsa, A. Squellati. Esercizi di matematica, volume 2, Zanichelli (2002).
