00020 - Higher Analysis

Learning outcomes

The purpose of this course is to acquaint the student with techniques in higher analysis allowing him to pursue further studiies in his future career.

Course contents

This course is an introduction to the theory of Partial Differential Equations (PDEs) for students majoring in both pure and applied mathematics.
Basically the course has two parts:
1- Introduction to distribution theory and their Fourier transform.
2- Fundamental solutions of some classical PDEs; wave, heat equation, Laplace equation, Cauchy-Riemann and Schroedinger equation. Some classical integration
methods will also be covered for these equations as well as for their boundary value problems. Furthermore vector fields and the first concepts in the theory of the Cauchy problem will also be treated pending time availability.

Readings/Bibliography

1- L. Hoermander, Linear Partial Differential Operators, Springer 1963.
2- F. Treves, Basic Linear Differential Equations, Dover.

Further readings, complementary readings or whatever the students may possibly need will be given in class.

Teaching methods

The general theory is supported 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 dicipline.

Assessment methods

1- Homework at pre-determined time intervals.

2- Problems solved in class by the teacher as well as by the students.

3- Written and oral exam. The latter always starts from the exposition of some (relevant) topic chosen by the student. 

Teaching tools

Both class tests and homework.

Office hours

See the website of Antonio Bove