Mathematical Analysis III

Course code

MLM6503.DT

old course code

Course title in Estonian

Matemaatiline analüüs III

Course title in English

Mathematical Analysis III

ECTS credits

4.0

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

Core subject of the bachelor level mathematics programme. Extension of Mathematical Analysis I. Knowledge of theoretical foundations, methods and practical applications of differential calculus of functions of several variables. Basics of the theory of functional series.

Brief description of the course

n-dimensional Euclidean space. Functions of several variables, limits and continuity. Partial derivatives, differentiability and differential of a function of several variables. The tangent plane of a surface. Taylor formula. Implicit functions. Extrema of functions: relative, absolute and conditional extrema. Measurable sets on the plane, their areas. Geometric and physical applications of definite integrals. Improper integrals. Gamma function. Number series, their properties and conditions for convergence. Functional series and their properties, convergence and uniform convergence. Power series, their interval and domain of convergence. The properties of the sum of power series. The Taylor series. The Fourier series.

Attending lectures is a prerequisite of the learning process.

Attending lectures is a prerequisite of the learning process.

Learning outcomes in the course

Upon completing the course the student:

- knows mathematical truths and is able to use methods in volume of a subject;

- is able to prove and apply them.

- knows mathematical truths and is able to use methods in volume of a subject;

- is able to prove and apply them.

Teacher

Maria Zeltser

Prerequisite course 1

The course is a prerequisite

Study programmes containing that course

Mathematics, Mathematical Economics and Data Analysis (MLMB/24.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/23.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/22.DT)

Integrated Natural Sciences (MLLB/22.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/21.DT)

Integrated Natural Sciences (MLLB/21.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/20.DT)

Integrated Natural Sciences (MLLB/20.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/19.DT)

Integrated Natural Sciences (MLLB/19.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/18.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/23.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/22.DT)

Integrated Natural Sciences (MLLB/22.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/21.DT)

Integrated Natural Sciences (MLLB/21.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/20.DT)

Integrated Natural Sciences (MLLB/20.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/19.DT)

Integrated Natural Sciences (MLLB/19.LT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/18.DT)