Mathematical Analysis II
Course code
MLM6512.DT
old course code
Course title in Estonian
Matemaatiline analüüs II
Course title in English
Mathematical Analysis II
ECTS credits
6.0
Assessment form
Examination
lecturer of 2024/2025 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2025/2026 Autumn 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 integral calculus functions of one (real) variable and differential calculus of functions of several variables. The main attention is focused on theoretical foundations and classical methods of mathematical analysis.
Brief description of the course
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. Improper integrals. Functions of several variables, their limits, partial derivatives, differentiability and differential. Local, global and constrained extremum of a function of several variables. Gradient of a function. Tangent plane to a surface.
Learning outcomes in the course
Upon completing the course the student:
- knows the main integration techniques and is able to apply them;
- is familiar with the fundamental concepts and theorems of the theory of improper integrals and differential calculus of functions of multiple variables;
- understands the proof methods used in the theory of improper integrals and differential calculus of functions of multiple variables and is able to apply them in reasoning;
- is able to compute partial derivatives, extrema, gradients, and the tangent plane of a function of multiple variables, as well as analyze the convergence of improper integrals.
- knows the main integration techniques and is able to apply them;
- is familiar with the fundamental concepts and theorems of the theory of improper integrals and differential calculus of functions of multiple variables;
- understands the proof methods used in the theory of improper integrals and differential calculus of functions of multiple variables and is able to apply them in reasoning;
- is able to compute partial derivatives, extrema, gradients, and the tangent plane of a function of multiple variables, as well as analyze the convergence of improper integrals.
Teacher
Alar Leibak
Prerequisite course 1
The course is a prerequisite
Study programmes containing that course