Mathematical Analysis III
Course code
old course code
Course title in Estonian
Matemaatiline analüüs III
Course title in English
Mathematical Analysis III
ECTS credits
Assessment form
lecturer of 2022/2023 Autumn semester
Maria Zeltser (language of instruction:Estonian)
lecturer of 2022/2023 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.
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.

Maria Zeltser