# MATHEMATICAL ANALYSIS I

**Academic Year 2018/2019**- 1° Year

**Teaching Staff**

- MODULO 1:
**Ornella NASELLI** - MODULO 2:
**Raffaela Giovanna CILIA**

**Credit Value:**18

**Scientific field:**MAT/05 - Mathematical analysis

**Taught classes:**105 hours

**Exercise:**36 hours

**Term / Semester:**1° and 2°

## Learning Objectives

**MODULO 1**The student will study the principal concepts and technics of Mathematical Analysis. In particular, the course

**objectives**are:**Knowledge and understanding**: the students will get used to the properties of**R**, the limits and the continuity of the functions of one real variable and they will be able to move on to the concept of numerical sequences and series. Some tasks will be entrusted to the most willing students who, thanks to group work or individual work, will be able to present them in short seminars.

**Ability to apply knowledge and understanding****:**the students will be led not only to learn pure concepts, but also to link them and to reflect on the structure properties (e.g. topological) that are the basis of the various topics studied. They can also improve their ability to use the acquired knowledge in other settings: for instance, the students will be invited to independently demonstrate results similar to those studied, and to carry out numerous exercises of application of the theories they have studied. This aspect**will be assessed through**exercises - both manipulative and demonstrative - that will be suggested for their individual study.

**Making judgements**: The students are invited to study some contents individually and to improve their own knowledge comparing different books. They can also proof the solutions of the problems they have studied, during the tutoring class, by sharing the results with the other students in order to find the right solutions.

**Communication skills:**By listening to the lessons and reading the recommended books, the students**will improve**their ability to use mathematical language to express properly and elegantly sophisticated mathematically math concepts.

**Learning skills:**Students will be guided to acquire a method that will allow them to approach a new topic, recognizing immediately the prerequisites needed.**The course aims also at developing students' skills**of computing and manipulating the mathematical objects studied.**MODULO 2**The student will study the principal concepts and technics of Mathematical Analysis. In particular, the course

**objectives**are:**Knowledge and understanding**: he student will acquire the main concepts of Mathematical Analysis and will be guided to link them to the concepts learned in Algebra, in General Topology or the concepts that he will study in Physics.He will learn the main techniques of Mathematical Analysis. In particular, he will study the differential calculus for functions of one variable and its important applications, the theory of integration of a single variable function, the solving methods of ordinary differential equations, the theory of sequences and series of functions. Some tasks will be entrusted to the most willing students who, thanks to group work or individual work, will be able to present them in short seminars.

**Ability to apply knowledge and understanding****:**the students will be led not only to learn pure concepts, but also to link them and to reflect on the structure properties (e.g. topological) that are the basis of the various topics studied. They can also improve their ability to use the acquired knowledge in other settings: for instance, the students will be invited to independently demonstrate results similar to those studied, and to carry out numerous exercises of application of the theories they have studied. This aspect**will be assessed through**exercises - both manipulative and demonstrative - that will be suggested for their individual study.

**Making judgements**: The students are invited to study some contents individually and to improve their own knowledge comparing different books. They can also proof the solutions of the problems they have studied, during the tutoring class, by sharing the results with the other students in order to find the right solutions.

**Communication skills:**By listening to the lessons and reading the recommended books, the students**will improve**their ability to use mathematical language to express properly and elegantly sophisticated mathematically math concepts.

**Learning skills:**Students will be guided to acquire a method that will allow them to approach a new topic, recognizing immediately the prerequisites needed.**The course aims also at developing students' skills**of computing and manipulating the mathematical objects studied

## Course Structure

**MODULO 1**The course is organized by lectures. There will be some team practices.

Periodical meetings will be organized in teamwork with the professor of Algebra and Geometry, in order to give students useful suggestions on how to use and apply the acquired knowledge to the other disciplines.

**MODULO 2**The course is organized by lectures. There will be some team practices.

Periodical meetings will be organized in teamwork with the professor of Algebra and Geometry, in order to give students useful suggestions on how to use and apply the acquired knowledge to the other disciplines.

## Detailed Course Content

**MODULO 1**1. Real and complex numbers

2. Sequences and series

3. Continuous functions

**MODULO 2**Differential Calcul for Functions of one variable

Integral calcul.

Improper integration.

Sequences and series of Functions

Solving methods of differential equations

## Textbook Information

**MODULO 1**1. G. Emmanuele, Analisi Matematica 1, Pitagora (nuova edizione)

2. C.D. Pagani, S. Salsa, Analisi Matematica 1, Zanichelli

3. J.P. Cecconi, G. Stampacchia, Analisi Matematica vol. 1, Liguori

4. G. De Marco, Analisi uno, Zanichelli

**MODULO 2**1) G. Emmanuele Analisi Matematica I Pitagora

2) G. Emmanuele Analisi Matematica II Foxwell Davies

Other books that the student is invited to use

3) Pagani Salsa Analisi Matematica 1, Zanichelli

4) Cecconi Stampacchia, Analisi Matematica , Liguori

5) DeMarco Analisi uno, Zanichelli