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CODE 98340
ACADEMIC YEAR 2021/2022
CREDITS
SCIENTIFIC DISCIPLINARY SECTOR MAT/05
LANGUAGE Italian
TEACHING LOCATION
  • LA SPEZIA
SEMESTER Annual
MODULES Questo insegnamento è un modulo di:
TEACHING MATERIALS AULAWEB

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

Exam Board

DANILO PERCIVALE (President)

VALENTINA BERTELLA

SERGIO DE MICHELI

MARIA VIRGINIA CATALISANO (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale 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.

Exam schedule

Data appello Orario Luogo Degree type Note
10/01/2022 09:00 LA SPEZIA Scritto
24/01/2022 09:15 GENOVA Scritto
07/02/2022 14:30 LA SPEZIA Scritto
08/06/2022 09:00 LA SPEZIA Scritto
08/07/2022 09:00 LA SPEZIA Scritto
07/09/2022 09:00 LA SPEZIA Scritto

FURTHER INFORMATION

Professor will receive students by appointment.