# MATHEMATICAL ANALYSIS 1

*Last update 27/07/2020 15:28*

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.

RECOMMENDED READING/BIBLIOGRAPHY

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)

CLAUDIO ESTATICO

ROBERTUS VAN DER PUTTEN (President Substitute)

## 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

## 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.