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76297 - Higher Analysis 1

Academic Year 2020/2021

                
                        Docente:
                        Alberto Parmeggiani
                    
                        Credits:
                        6
                    
                        SSD:
                        MAT/05
                    
                        Language:
                        Italian
                    
                        Teaching Mode:
                        Traditional lectures
                        
                            Campus:
                            Bologna
                        
                            Corso:
                            Second cycle degree programme (LM) in
                            Mathematics (cod. 8208)

                            Teaching resources on Virtuale

Learning outcomes

The purpose of this course is to acquaint the student with the modern theory of distributions (generalized functions), fundamental to understand problems and techniques coming form the modern theory of PDEs.

Course contents

The course should be an introduction to the theory of Partial Differential Equations (PDEs) for students majoring in both pure and applied mathematics. The first semester is devoted to distribution theory and the theory of Fourier transform in distribution category, along with the method of the characteristics for solving first order partial differential equations.

Readings/Bibliography

L. Hörmander: Linear Partial Differential Operators, Springer (1969 Edition).
F. Treves: Basic Linear Differential Equations, Dover.
J. Chazarain - A. Piriou: Introduction to the Theory of Linear Partial Differential Equations, North Holland.
C. Zuily: Eléments de distributions et d'équations aux dérivées partielles. Dunod.
F.G. Friedlander. Introduction to the theory of distributions. Second edition. With additional material by M. Joshi. Cambridge University Press, Cambridge, 1998.

Teaching methods

The general theory is completed by a number of problems as well as applications. This should provide the students with an applied math major of a sufficient background in their discipline.

Assessment methods

Homeworks.
Problems solved in class by the teacher as well as by the studen
The final exam consists of a written and oral exam, to be taken withing the same session. In the written exam, related to the arguments developed during the course (2 hours; no notes or electronic devices are allowed) the student will receive an evaluation: insufficient/sufficient/good/excellent, and a score in thirtieths. In case of the rating "insufficient" the student will have to repeat the written exam, in case of rating at least "sufficient", the student will be able to proceed to the oral exam. The latter always starts from the exposition of some (relevant) topic chosen by the student. A sufficient written exam will be held valid within the session.

Office hours

See the website of Alberto Parmeggiani