# MATHEMATICAL ANALYSIS I

12 credits during the 1st year of 9273 Electronic Engineering and Information Technology (L-8) GENOVA

12 credits during the 1st year of 10375 CHEMICAL AND PROCESSES ENGINEERING (L-9) GENOVA

**Chemical Engineering 8714 (coorte 2019/2020)**- MATHEMATICAL ANALYSIS II 60241
- THEORY OF DEVELOPMENT OF CHEMICAL PROCESSES 66364
- ELECTRICAL ENGINEERING 66016
- SCIENCE AND TECHNOLOGIES OF MATERIALS 84498
- TRAINING AND ORIENTATION 66376

**Electrical Engineering 8716 (coorte 2019/2020)**- CIRCUIT THEORY 60336
- APPLIED PHYSICS 60359
- MATHEMATICAL ANALYSIS II 60241
- ELECTRONICS FOR ELECTRICAL ENGINEERING 84372
- STRUCTURAL MECHANICS 66283
- MECHANICS OF MACHINES 86899
- ELECTRIC AND MAGNETIC FIELDS 60335
- POWER GENERATION 60221
- MATHEMATICAL PHYSICS 1 60352

**Electronic Engineering and Information Technology 9273 (coorte 2019/2020)**- MATHEMATICAL METHODS FOR ENGINEERING 72440

**CHEMICAL AND PROCESSES ENGINEERING 10375 (coorte 2019/2020)**- CHEMICAL REACTORS 90669
- CHEMICAL ENGINEERING LABORATORIES 90664
- SCIENCE AND TECHNOLOGIES OF MATERIALS 84498
- THEORY OF DEVELOPMENT OF CHEMICAL PROCESSES 66364
- STRUCTURAL MECHANICS 90682
- MATHEMATICAL ANALYSIS II AND PHYSICS 90657
- CHEMICAL AND PROCESS PLANTS 90660

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 course provides the fundamentals of integral calculus - differential for functions of one and more variables and the first elements of the study of ordinary differential equations.

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

72 hours of theoretical lessons, 48 hours of classroom practices. 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

P. Marcellini – C. Sbordone: Calcolo, Liguori Editore, Napoli, or any other good text of mathematical analysis.

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

MICHELA LAVAGGI (President)

MARCO BARONTI (President)

FRANCO PARODI

MANUEL MONTEVERDE

MAURIZIO CHICCO

LAURA BURLANDO

## LESSONS

Teaching methods

72 hours of theoretical lessons, 48 hours of classroom practices. 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.

## 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.