# MATHEMATICAL ANALYSIS II

Academic year and teacher

If you can't find the course description that you're looking for in the above list,
please see the following instructions >>

- Versione italiana
- Academic year
- 2021/2022
- Teacher
- FAUSTO SEGALA
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/05

#### Training objectives

- The aim of the course for second-year students in physics is to give the basic knowledges related to differential and integral calculus for functions of several variables.

After passing the analysis II exam,the student will be able to solve some interesting physic problems.

In particular,series and Fourier transform will be treated in great detail.with applications to wave and heat equations.

Final part of the course will be devoted to Riemann hypotesys,the most deep and interesting open problem of the mathematics,with its not yet explained links with quantum mechanics.In this perspective,there will be an optional overview about the deviation of the prime counting function pi(x) from logarithmic integral Li(x). #### Prerequisites

- Basic algebra,analytic geometry,differential and integral calculus.

Analisi I,examination passed #### Course programme

- basic topological properties of the euclidean space R^n

(2 hours)

functions of several variables (5 hours)

partial derivatives (5 hours)

curves and surfaces (8 hours)

curvilinear integrals,multiple integrals (10 hours)

series ando Fourier series (8 hours)

Lebesgue integral(6 hours)

partial differential operators,applications to relevant physical problems (8 hours)

Riemann hypothesis (2 hours) #### Didactic methods

- Theoretical/practical lessons.
#### Learning assessment procedures

- Written/oral examination.

The final mark is the mean value between written test and oral exam.

About written exam,the student can be choose wether to sit a final test,or three intermediate tests,during period lesson.

Written exams are devoted to solutions of basic exercises,in order to test the knowledge of technicalities.

The oral exam mainly concern in the proof of a list of theorems.

In order to improve final score,non standard can be proposed. #### Reference texts

- R.Adams,CALCOLO DIFFERENZIALE II,CEA,MILANO

https://en.wikipedia.org/wiki/Lebesgue_integration

see.stanford.edu/Course/EE261

J.Derbyshire,l'ossessione dei numeri primi.

Bollati Boringhieri,2015