# MATHEMATICAL ANALYSIS 1

*Last update 09/05/2021 11:13*

OVERVIEW

The course is directed to first year students which are familiar with basic notions in elementary Mathematics

## AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide the basic knowledge preparatory to other courses that require mathematical methods and tools.

AIMS AND LEARNING OUTCOMES

The course provides basic notions about Functions of one variable, integration of continuous functions and first order ODE’s in view of applications in Physics and Nautic Engineering.

PREREQUISITES

Basic notions in elementary mathematics.

Teaching methods

90 hours of lectures . Distance lectures until the end of sanitary emergency an subsequently frontal lectures.

SYLLABUS/CONTENT

1) Real numbers and the real line. Cartesian coordinates in the plane. Functions and their graphs. Limits and continuity. Theorems about continuous functions. The derivative. Differentiation rules: product, reciprocal, quotient and chain rule. Monotone functions: the inverse function theorem. Derivatives of some elementary functions. Theorems about differentiable functions: Rolle, Lagrange, Cauchy. Higher order derivatives. Extreme values, convexity and inflection. Sketching the graph of a function.

2) Integration. Sums and sigma notation. Areas as limits of sums. The definite integral. Properties of the definite integral. The fundamental Theorem of Calculus. Changes of variable: the method of substitution. Areas of plane regions. Integration by parts. Integrals of rational functions.

3) L’Hopital’s rule. Taylor’ formula and its applications.

3) Ordinary differential equations. First order equations: separable equations, linear equations. Cauchy problems: existence and uniqueness theorem. Linear ODE’s with constant coefficients.

RECOMMENDED READING/BIBLIOGRAPHY

R.A. Adams, Calcolo Differenziale 1 Casa

Editrice Ambrosiana.

Notes & Exercises in aulaweb ( a.a. 10/11 and the following)

## TEACHERS AND EXAM BOARD

**Ricevimento:**
Until the end of the health emergency, a special Teams channel will be set up and students can post their requests. Periodically the teacher will post the answers on Stream

Exam Board

DANILO PERCIVALE (President)

VALENTINA BERTELLA

MARIA VIRGINIA CATALISANO (President Substitute)

## LESSONS

Teaching methods

90 hours of lectures . Distance lectures until the end of sanitary emergency an subsequently frontal lectures.

LESSONS START

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

## EXAMS

Exam description

A written test is required which could be followed by another confirmation test

Assessment methods

Outcome of written test and its confirmation.

## FURTHER INFORMATION

Professor will receive students by appointment.