#### MATHEMATICAL ANALYSIS

###### Domain: Environmental Engineering • Field of study: Environmental Engineering
 Type of course: Compulsory Language of instruction: Romanian Erasmus Language of instruction: English Name of lecturer: Valer Daniel Breaz Seminar tutor: Ioan Lucian Popa Form of education Full-time
 Form of instruction: Class Number of teaching hours per semester: 56 Number of teaching hours per week: 4 Semester: Autumn Form of receiving a credit for a course: Grade Number of ECTS credits allocated 5

#### Course aims:

After browsing the course, the students will gain skills in the use of mathematical analysis for transposition of problems in various programming languages.
So the discipline contributes to the formation of some general skills specific for the study domain.
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#### Course contents:

1.Strings. 1.1 Strings applications, real numbers strings, strings in metric spaces. 1.2 Calculation of string limits 2. Numerical series. 2.1 Applications to numerical series and convergence criteria for series with random terms. 2.2 Applications to absolute convergent series, semiconvergent series, and series with positive terms. 3. Functions between metrical spaces. 3.1 Applications regarding function calculation of the limits in one point. 3.2 Continuity of functions between metric spaces. 4. Integration of real functions. 4.1 Calculation of some integrals out of real functions. 4.2 Applications to calculate defined integrals. 5. Strings and series of functions 5.1 Applications of strings and series of functions. 5.2 Applications of rise series and Taylor series. 6. Functions derivations of more than one variable 6.1 Applications to function derivations of more than one variable, partial derivations. 6.2 Applications to functions differentials of more than one variable and functions extremes of more than one variables. 6.3 Conditioned extremes. 7. Basic knowledge regarding integrals 7.1 Improper integrals applications. 7.2 Applications of integrals with parameters. 7.3 Applications of Eulerian integrals and double integrals

#### Teaching methods:

Lecture, discussion, exemplification.

#### Learning outcomes:

In order to obtain credits for this discipline the student have to know how to work with elementary mathematical analysis notions, which are necessary in the basic theoretical bases of computer science and formal models.

#### Learning outcomes verification and assessment criteria:

Final evaluation – 50%; continuous assessment – 50%.