ECTS - University of Pisa
Scheda programma d'esame
LINEAR ALGEBRA AND MATHEMATICAL ANALYSIS II
STEFANO GALATOLO
Academic year2016/17
CourseELECTRONIC ENGINEERING
Code591AA
Credits12
PeriodSemester 1 & 2
LanguageItalian

ModulesAreaTypeHoursTeacher(s)
ALGEBRA LINEAREMAT/03LEZIONI60
STEFANO GALATOLO unimap
ANALISI MATEMATICAMAT/05LEZIONI60
STEFANO GALATOLO unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The student who successfully completes the course will have a working knowledge of the main tools in linear algebra (linear systems, matrices, eigenvalues, analytic geometry) and in the differential and integral calculus for functions of several real variables (max/min problems, integrals in 2d and 3d, integrals over curves and surfaces).
Assessment criteria of knowledge
In the multiple choice test (30 minutes, 16 questions) the student must demonstrate his/her knowledge of the basic course contents and prerequisites. In the written exam (3 hours, 4 problems), the student must demonstrate his/her ability to approach and solve standard problems requiring the tools presented in the course. Solutions are presented in written form. Correctness and clarity of solutions will be assessed. During the oral exam the student's ability to explain correctly the main topics presented during the course at the board will be assessed.

Methods:

  • Final oral exam
  • Final written exam
Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • individual study

Attendance: Advised

Teaching methods:

  • Lectures
Syllabus
Vector spaces, linear dependence, generators and bases, dimension, subspaces. Linear systems and affine subspaces. Parametric and Cartesian equations of an affine subspace. Linear maps and matrices, kernel and image, change of basis. Determinants, Binet's theorem, inverse matrix, rank. Eigenvalues and eigenvectors. Diagonalization of symmetric and Hermitian matrices. Differential calculus in several variables. Limits, continuity, partial and directional derivatives, differential, gradient. Jacobian matrix. Higher order derivatives. Taylor's formula. Extrema with and without constraints. Integral calculus in several variables. Riemann integration. Reduction formula. Change of variable formula. Area and volume computation. Generalized integrals. Vector calculus. Parametric curves and curvilinear integrals. Vector fields and linear differential forms. Integration on closed paths. Conservative fields and exact forms. Surface integrals. Gauss-Green and Stokes theorems.
Bibliography
Students are highly recommended to read the course notes prepared by the teacher (a printout of the lectures) which can be easily downloaded from the teacher's home page. For the analysis part, also the following textbook are suggested: Bramanti, Pagani, Salsa, Analisi II, Zanichelli Barutello, Conti, Ferrario, Terracini, Verzini, Analisi II, Apogeo Students are also highly recommended to work on the suggested exercises. For the mathematical analysis section of the course, theory and exercises can be found in the following textbooks: M.Ghisi, M.Gobbino - Schede di Analisi Matematica - Edizioni Esculapio M.Ghisi, M.Gobbino - Esercizi di Analisi Matematica II (Parte A) - Edizioni Esculapio Further bibliography, especially for the linear algebra section, will be indicated.
Updated: 14/11/2016 17:27