Mathematical Analysis Complements

The main objective of the course is to provide students with the basic elements of the Theory of Lebesgue Spaces, on issues of theory of topological linear spaces and on the existence and regularity of functional minima. The course aims to provide students with the following skills: 

1) Knowledge and understanding: Knowledge of fundamental results and methods of Real Analysis. Ability to read, understand and study in depth a topic of mathematical literature and propose it again in a clear and accurate way. Ability to understand problems and extract their substantial elements. 

2) Ability to apply knowledge and understanding: Ability to construct or solve examples or exercises and to tackle new theoretical problems, searching for the most suitable techniques and applying them appropriately. 

3) Autonomy of judgment (making judgments): Being able to produce proposals aimed at correctly interpreting complex problems in the context of Lebesgue Spaces. Be able to independently formulate relevant judgments on the applicability of theorems related to topological linear spaces. 

4) Communication skills: Ability to present arguments, problems, ideas and solutions, both one's own and others', in mathematical terms and their conclusions, with clarity and accuracy and in ways appropriate to the listeners to whom one is addressing, both in oral and written form. Ability to clearly motivate the choice of strategies, methods and contents, as well as the computational tools adopted. 

5) Learning skills: Read and study in depth a topic of the literature in the field of linear transformations and continuous transformations. Approach in an autonomous way the systematic study of topics of Lebesgue Spaces not previously explored.

To take the final exam, you must have booked on the SmartEdu portal. For any technical issues with your booking, please contact the Academic Office.

Frontal lessons. 

The lessons are integrated with exercises relevant to the topics covered and will be held in frontal mode. It is also specified that 35 hours of lessons are planned (typically, these are theory) and 12 hours of other activities (typically, these are exercises). 

If the teaching is taught in mixed mode or remotely, the necessary changes may be introduced with respect to what was previously declared, in order to respect the planned program and reported in the Syllabus. Students with disabilities and/or DSA must contact the teacher, the CInAP representative of the DMI and the CInAP well in advance of the exam date to communicate that they intend to take the exam using the appropriate compensatory measures (which will be indicated by the CInAP).

In order to consciously follow the course, it is necessary to know the contents of the classic courses of Mathematical Analysis I and II. In order to take the exam, it is mandatory to have already passed the exam of Mathematical Analysis II (see Regolamento del Corso di Studi).

[1] H. Cartan, Differential calculus on normed spaces: a course in Analysis, 2017.

[2] E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, 2005.

[3] G. Buttazzo, M. Giaquinta, S. Hildebrandt, One-dimensional Variational Problems. An Introduction, Oxford University Press, 1998.

At the end of the lessons there will be a final oral exam.

To take the final exam, you must have booked on the SmartEdu portal. For any technical issues regarding your booking, please contact the Academic Office.