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

approximate amount of contact lessons

56

Teaching semester

spring

Assessment form

Examination

lecturer of 2019/2020 Spring semester

õppejõud on määramata

lecturer of 2020/2021 Autumn semester

lecturer not assigned

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.

Independent work

(approximately 74 academic hours) includes work with the literature and lecture notes, solving the exercises, doing homework

Learning outcomes in the course

After passing this 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.

- 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.

Assessment methods

The course grade is based on the total number of points gained from written tests completed during the semester and a final examination. The maximal number of credit points (100) is equally divided between current semester work and the final examination.

Teacher

lekt Anna Šeletski

The course is a prerequisite

Study literature

Reimers, E. 1988 Matemaatilise analüüsi praktikum I. Tallinn: Valgus;

Kangro, G. 1982 Matemaatiline analüüs I. Tallinn: Valgus. (osaliselt kohustuslik).

Kangro, G. 1982 Matemaatiline analüüs I. Tallinn: Valgus. (osaliselt kohustuslik).

Replacement literature

Kangro, G. 1982 Matemaatiline analüüs I. Tallinn: Valgus;

Fihtengolts, G. M. 2001 Kurs diferentsialnogo i integralnogo istshislenija I (vene keeles) Moskva-Sankt Peterburg: Fizmatlit,

Fihtengolts, G. M. 2001 Kurs diferentsialnogo i integralnogo istshislenija II (vene keeles). Moskva-Sankt Peterburg: Fizmatlit;

Protter, M. H.; Morrey, C. B. 1991 A First Course in Real Analysis. New York-Berlin-Heidelberg: Springer-Verlag;

Tali, A. 2010 Matemaatiline analüüs I (käsikiri);

Tammeraid, I. 2002 Matemaatiline analüüs I. Tallinn: TTÜ.

Fihtengolts, G. M. 2001 Kurs diferentsialnogo i integralnogo istshislenija I (vene keeles) Moskva-Sankt Peterburg: Fizmatlit,

Fihtengolts, G. M. 2001 Kurs diferentsialnogo i integralnogo istshislenija II (vene keeles). Moskva-Sankt Peterburg: Fizmatlit;

Protter, M. H.; Morrey, C. B. 1991 A First Course in Real Analysis. New York-Berlin-Heidelberg: Springer-Verlag;

Tali, A. 2010 Matemaatiline analüüs I (käsikiri);

Tammeraid, I. 2002 Matemaatiline analüüs I. Tallinn: TTÜ.