Mathematical Analysis

Course code

MLM7091.DT

old course code

Course title in Estonian

Matemaatiline analüüs

Course title in English

Mathematical Analysis

ECTS credits

5.0

Assessment form

assessment

lecturer of 2024/2025 Autumn semester

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

lecturer of 2024/2025 Spring 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

1. The set of real numbers.

2. The concept of a function.

3. Limit of a function, its properties and conditions for existence.

4. Continuous functions, their properties.

5. Derivative of a function, its properties, interpretations and conditions for existence.

6. Differentiability and differential of a function. Higher-order derivatives and differentials.

7. Mean value theorems in differential calculus, their applications to the finding of limits and treating of functions.

8. Applications in analysis and geometry.

9. Indefinite integral, its properties, technique of integration.

10. Definite integral, its properties, geometric interpretation and conditions for existence.

11. Newton-Leibniz formula.

12. Geometric and physical applications of definite integrals. Improper integrals.

Attending lectures is a prerequisite of the learning process.

2. The concept of a function.

3. Limit of a function, its properties and conditions for existence.

4. Continuous functions, their properties.

5. Derivative of a function, its properties, interpretations and conditions for existence.

6. Differentiability and differential of a function. Higher-order derivatives and differentials.

7. Mean value theorems in differential calculus, their applications to the finding of limits and treating of functions.

8. Applications in analysis and geometry.

9. Indefinite integral, its properties, technique of integration.

10. Definite integral, its properties, geometric interpretation and conditions for existence.

11. Newton-Leibniz formula.

12. Geometric and physical applications of definite integrals. Improper integrals.

Attending lectures is a prerequisite of the learning process.

Learning outcomes in the course

Upon completing the course the student:

- knows main notions of 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.

- knows main notions of 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

Anna Šeletski

Study programmes containing that course