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## MATHEMATICAL ANALYSIS 2

CODE 57048 2019/2020 12 credits during the 2nd year of 8758 PHYSICS (L-30) GENOVA 8 credits during the 2nd year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA MAT/05 Italian GENOVA (PHYSICS) Annual Prerequisites You can take the exam for this unit if you passed the following exam(s): PHYSICS 8758 (coorte 2018/2019) MATHEMATICAL ANALYSIS 1 52474 Prerequisites (for future units) This unit is a prerequisite for: PHYSICS 8758 (coorte 2018/2019) MATHEMATICAL METHODS IN PHYSICS 1 61734 AULAWEB

## OVERVIEW

Basic topics in calculus of severable variables are treated. The course is split into two semesters. The first part is devoted to differential calculus,  integration theory in two (or several) variables and function series. The second part deals with integration along curves and surfaces, Gauss and Stokes' theorems and their consequences, and an introduction to systems of differential equations. SMID students need to take only part I (first semester - 8 credits). Both semesters are mandatory for Physics students.

## AIMS AND CONTENT

### LEARNING OUTCOMES

Students will become acquinted with the most important topics regarding functions of several variables and how they are used in practice.  We  only present proofs that illustrate fundamental principles and are free of technicalities.
Applications to Physics and Probability are emphasised.

### AIMS AND LEARNING OUTCOMES

Students will be able to manipulate functions of several variables and solve basic optimization problems. Moreover they will be at their ease with mean and conditional expectation.

### PREREQUISITES

First year calculus (derivatives and integrals for functions of a single variable). Vector spaces, eigevalues and eigenvectors are frequently used.

### TEACHING METHODS

Both theory and exercises are presented by the teacher in the classroom on the blackboard. The first semester consists of 12 weeks with four hours of theory and two hours of exercises per week. The second semester consists of 12 weeks with three hours of theory and two hours of exercises per week.

### SYLLABUS/CONTENT

This course covers differential, integral and vector calculus for functions of several variables. Topics include:

• Sequences and series (numerical, function series, power series,...)
• Functions of several variables: continuity, partial derivatives, differentiability, local maxima and minima, implicit functions, optimization.
• Parametrized curves, arc length, curvature, torsion.
• Vector fields, gradient, curl, divergence.
• Multiple integrals, change of variables, line integrals, surface integrals.
• Stokes' theorem in one, two, and three dimensions.
• Solutions to systems of constant coefficient linear ordinary differential equations

Serge Lang - Calculus of Several Variables, Third Edition, Undergraduate Texts in Mathematics, Springer, 1987.

## TEACHERS AND EXAM BOARD

### Exam Board

FRANCESCA ASTENGO (President)

MARCO BENINI

## LESSONS

### TEACHING METHODS

Both theory and exercises are presented by the teacher in the classroom on the blackboard. The first semester consists of 12 weeks with four hours of theory and two hours of exercises per week. The second semester consists of 12 weeks with three hours of theory and two hours of exercises per week.

### LESSONS START

Classes will start according to the accademic calendar.

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

Written and oral exam

### ASSESSMENT METHODS

The written examination consists in solving four/five exercises covering the topics of the course. It is approved with grade at least 15/30.

If your written exam is approved with grade at least 18/30, then the oral exam is optional. In case you do not want to take the oral part

• the final mark is the grade of the written exam if less than or equal to 24
• the final mark is 24 if the grade of the written exam is greater than 24

If you take also the oral part, the final mark is a weighted average of the written and oral tests.

### Exam schedule

Date Time Location Type Notes
16/01/2020 09:00 GENOVA Scritto
16/01/2020 09:00 GENOVA Scritto Per gli studenti in Fisica a.a. 2018/2019 e precedenti
16/01/2020 09:00 GENOVA Compitino Compitino per Fisica a.a. 2019/2020
07/02/2020 09:00 GENOVA Scritto esame per CS in Fisica a.a. 2018/2019 e precedenti
10/02/2020 09:00 GENOVA Scritto
10/02/2020 09:00 GENOVA Compitino Compitino per studenti Fisica a.a. 2019/2020
17/06/2020 09:00 GENOVA Scritto
17/06/2020 09:00 GENOVA Scritto
06/07/2020 09:00 GENOVA Scritto
06/07/2020 09:00 GENOVA Scritto
17/09/2020 09:00 GENOVA Scritto
17/09/2020 09:00 GENOVA Scritto

### FURTHER INFORMATION

For further information, please send a message to astengo@dima.unige.it