Basic Differential and Integral Calculus

Course code

MLM6190.DT

old course code

Course title in Estonian

Diferentsiaal- ja integraalarvutuse algkursus

Course title in English

Basic Differential and Integral Calculus

ECTS credits

6.0

Assessment form

Examination

lecturer of 2024/2025 Autumn semester

Maria Zeltser (language of instruction:Estonian)

lecturer of 2024/2025 Spring semester

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

Course aims

To offer to the students an overview of terms and notions of diferential and integral calculus, which are useful for those who choose to teach mathematics at the first and the secondary school level.

Brief description of the course

The set of real numbers. The concept of a function. Sequences. Limit of a sequences. Limit of a function and its properties. Continuous functions and their properties. Functions continuous and their properties. Derivative of a function, its properties, interpretations and conditions for existence. Differentiability and differential of a function. Higher-order derivatives and differentials. Mean value theorems in differential calculus, their applications to the finding of limits and treating of functions. Applications in geometry.

Indefinite integral, its properties, changing the variable of integration. Definite integral, its properties, geometric interpretation. Newton-Leibniz formula. Measurable sets on the plane, their areas. Geometric and physical applications of definite integrals.

Indefinite integral, its properties, changing the variable of integration. Definite integral, its properties, geometric interpretation. Newton-Leibniz formula. Measurable sets on the plane, their areas. Geometric and physical applications of definite integrals.

Learning outcomes in the course

Upon completing the course the student:

- knows main notions of differential and integral calculus;

- is familiar with the main properties, relations, theorems and some simplest proof methods of this course;

- is able to use and apply methods taught in a subject in order to solve exercises.

- knows main notions of differential and integral calculus;

- is familiar with the main properties, relations, theorems and some simplest proof methods of this course;

- is able to use and apply methods taught in a subject in order to solve exercises.

Teacher

lektor Anna Šeletski

The course is a prerequisite

Additional information

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

Abel E., Jõgi, E., Mitt E. (2001). Matemaatika ülesannete kogu keskkoolile. Tallinn: Koolibri.

Kõiv H., Allik I., Jõgi T. (2000). Vastustega matemaatika ülesannete kogu riigieksamiks valmistujale. Tallinn: Tallinna Tehnikaülikool

Asenduskirjandus: Fihtengolts, G. M. 2001 Kurs diferentsialnogo i integralnogo istshislenija I (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;

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

Abel E., Jõgi, E., Mitt E. (2001). Matemaatika ülesannete kogu keskkoolile. Tallinn: Koolibri.

Kõiv H., Allik I., Jõgi T. (2000). Vastustega matemaatika ülesannete kogu riigieksamiks valmistujale. Tallinn: Tallinna Tehnikaülikool

Asenduskirjandus: Fihtengolts, G. M. 2001 Kurs diferentsialnogo i integralnogo istshislenija I (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;

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