# MATHEMATICAL ANALYSIS 1

_
iten
Code
56584
2019/2020
CREDITS
12 credits during the 1st year of 8784 Mechanical Engineering (L-9) LA SPEZIA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/05
LANGUAGE
Italian
TEACHING LOCATION
LA SPEZIA (Mechanical Engineering)
semester
Annual
Teaching materials

OVERVIEW

The aim of this course is to provide a practical working tool for students in Engineering or in any other field where rigorous
Calculus is needed. The basic focus is on functions of one real variable and  basic ordinary differential equations, separation
of variables, linear first-order, and constant coefficients ODE.

## AIMS AND CONTENT

LEARNING OUTCOMES

The aim is to achieve good knowledge of differential and integral calculus for one or two variables functions.

AIMS AND LEARNING OUTCOMES

The student will have to acquire a solid ability in Mathematical Analysis, in particular he must know how to study a function of one or more real variables. Moreover  he will have to know how to apply the various theorems for the resolution  of simple differential equations of the first order and higher order (linear with constant coefficients).

PREREQUISITES

Elementary algebra: equations and inequalities, trigonometry.

Teaching methods

106 hours of  lessons. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course  many exercises will be solved.  During the academic year some guided exercises will be carried out.

SYLLABUS/CONTENT

Real numbers, infimum and supremum, functions of one real variable, elementary functions, limits, infinitesimals and infinities, continuous functions, derivable functions, differentiable functions, Taylor’s formula, expansion of elementary functions, primitives and indefinite integrals, methods of indefinite integration, definite integrals, fundamental theorem of integral calculus, first order differential equations, Cauchy’s problem and theorem, resolution of linear first order differential equations and separable variables equations, linear differential equations with constant coefficients of order n.

F. Parodi, T. Zolezzi, Appunti di Analisi matematica, ECIG, 2007
R. A. Adams, Calcolo differenziale 1 & 2, Casa Editrice Ambrosiana, 2007
A. Bacciotti, F. Ricci, Lezioni di Analisi Matematica 1 e 2, Levrotto & Bella, 1991.
M. Bramanti, C. Pagani, S. Salsa, Analisi matematica 1 e 2 Zannichelli, 2008

M.Baronti-F.De Mari-R.Van Der Putten-I.Venturi: Calculus Problems, Springer

## TEACHERS AND EXAM BOARD

Ricevimento: The teacher is available for explanations one afternoon a week.

Exam Board

MARCO BARONTI (President)

ROBERTUS VAN DER PUTTEN (President)

CLAUDIO ESTATICO

## LESSONS

Teaching methods

106 hours of  lessons. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course  many exercises will be solved.  During the academic year some guided exercises will be carried out.

LESSONS START

Lessons start on September.

ORARI

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

Vedi anche:

MATHEMATICAL ANALYSIS 1

## EXAMS

Exam description

The final exam consists of a written test and an oral exam. The student must obtain an evaluation of at least 12/30 in the written test  to access the oral exam.

Assessment methods

During the written test the student will have to solve some exercises concerning the study of functions and  the differential problem. During the oral examination the student must highlight critical analytical skills and must be able to apply the main theorems for the solution of  easy exercises.

Exam schedule

Date Time Location Type Notes
09/06/2020 09:30 LA SPEZIA Scritto
13/07/2020 09:30 LA SPEZIA Scritto
15/09/2020 09:30 LA SPEZIA Scritto