
Course unit
CALCULUS OF VARIATIONS
SCP3050978, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/05 
Mathematical Analysis 
8.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

The Analysis 1 and 2 and the Real Analysis courses 
Target skills and knowledge:

The classical formalism of the calculus of variations in its hystorical development, with applications and motivations to geometry and physics. The development of the modern theory of the calculus of variations in the setting of Sobolev spaces. 
Examination methods:

Homeworks and oral exam 
Assessment criteria:

The teacher will ascertain the student's proficiency in the course's main subjects 
Course unit contents:

Introduction to the classical formalism of the Calculus of Variations: indirect methods, first variation, EulerLagrange equations, applications.
First direct methods, working in spaces of Lipschitz functions, via a priori gradient estimates.
Modern direct methods: introduction to Sobolev spaces and their use in minimization problems. Tonelli's theorem and the XX problem of Hilbert.
Introduction to currents.
Introduction to optimal transportation
Plateau problem 
Planned learning activities and teaching methods:

Blackboard lessons 
Additional notes about suggested reading:

The reference material will be communicated during the course. 
Textbooks (and optional supplementary readings) 


