ECTS - University of Pisa
Scheda programma d'esame
MATHEMATICAL ANALYSIS II
MARINA GHISI
Academic year2016/17
CourseMECHANICAL ENGINEERING
Code190AA
Credits6
PeriodSemester 1
LanguageItalian

ModulesAreaTypeHoursTeacher(s)
ANALISI MATEMATICAMAT/05LEZIONI60
MARINA GHISI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The students will develop a working knowledge of the main tools of differential and integral calculus in several variables. The students who successfully complete the course for example will be able to find extremals with and without constraints, to compute 2 and 3 dimensional integrals and to use in the appropriate way Gauss-Green and Stokes theorems.
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 the form of a short essay. Correctness and clarity of the essay 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
DIFFERENTIAL CALCULUS IN SEVERAL VARIABLES. Limits of functions. Continuity. Partial derivatives and directional derivatives. Differentiable functions and differential. Tangent hyperplane. Gradient. Sufficient conditions for the differentiability. Jacobian matrix. Differentiation of a composition of functions. Higher order derivatives. Taylor's formula. Extremals with and without constraints. INTEGRAL CALCULUS IN SEVERAL VARIABLES. Reduction formula. Change of variable formula. Area and volume computation. Generalized integrals. VECTOR FIELDS. Parametric curves. Lenght of a curve. Curvilinear integral. Vector fields and linear differential forms. Integration on closed paths. Conservative fields and exact forms. Surface integral of functions. Gauss-Green and Stokes theorems.
Bibliography
Recommended reading includes the following works M. Ghisi, M. Gobbino; Esercizi di Analisi Matematica II, parte A; Ed. Esculapio. M. Ghisi, M. Gobbino; Schede di Analisi Matematica; Ed. Esculapio. Further bibliography will be indicated.
Updated: 14/11/2016 17:27