TLÜ ÕIS

Mathematical Analysis I

Course code

MLM6002.DT

old course code

MLM6002

Course title in Estonian

Matemaatiline analüüs I

Course title in English

Mathematical Analysis I

ECTS credits

5.0

Assessment form

Examination

lecturer of 2023/2024 Spring semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

lecturer of 2024/2025 Autumn semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

Course aims

Core subject of the bachelor level mathematics programme. The idea of the course is to deepen students knowledge of differential and integral calculus functions of one (real) variable. The main attention is focused on theoretical foundations and classical methods of mathematical analysis.

Brief description of the course

The set of real numbers, its continuity. Limit of a function, its properties and conditions for existence. Continuous functions, their properties. Functions continuous on a closed interval. Derivative of a function, its properties, interpretations and conditions for existence. Differentiability and differential of a function. Higher-order derivatives and differentials. Parametric functions, their existence and differentiation. Mean value theorems in differential calculus, their applications to the finding of limits and treating of functions. Indefinite integral, its properties, technique of integration. Definite integral, its properties, geometric interpretation and conditions for existence. Definite integral as a function of its upper limit. Newton-Leibniz formula. Measurable sets on the plane, their areas. Geometric and physical applications of definite integrals. Improper integrals.

Learning outcomes in the course

Upon completing the course the student:
- knows main notions of integral and differential calculus;
- is familiar with the main properties, relations and theorems of this course;
- is familiar with some proof methods and is able to use them for some theorems of this course;
- is able to use and apply methods taught in a subject in order to solve exercises.

Teacher

lekt Anna Šeletski

The course is a prerequisite

Mathematical Analysis II (MLM6003.DT)

Study programmes containing that course