Course code

MLM6511.DT

old course code

Course title in Estonian

Matemaatiline analüüs I

Course title in English

Mathematical Analysis I

ECTS credits

6.0

Assessment form

Examination

lecturer of 2024/2025 Spring semester

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

lecturer of 2025/2026 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. The concept of a function. 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. Applications in geometry. Taylor formula. Definite and indefinite integrals.

Learning outcomes in the course

Upon completing the course the student:
- knows the fundamental concepts and key theorems of differential and integral calculus;
- is familiar with the proof methods used in mathematical analysis and is able to apply them in reasoning;
- is able to solve problems related to differential and integral calculus and its applications.

Teacher

Alar Leibak

The course is a prerequisite

Study programmes containing that course

Mathematics, Mathematical Economics and Data Analysis (MLMB/25.DT)
Integrated Natural Sciences (MLLB/25.LT)