Mathematical Analysis II

Course code

MLM6003.DT

old course code

MLM6003

Course title in Estonian

Matemaatiline analüüs II

Course title in English

Mathematical Analysis II

ECTS credits

4.0

approximate amount of contact lessons

56

Teaching semester

autumn

Assessment form

Examination

lecturer of 2019/2020 Autumn semester

õppejõud on määramata

lecturer of 2019/2020 Spring semester

lecturer not assigned

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 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. Number series, their properties and conditions for convergence.

Independent work

Homeworks based on lecture materials, literature and problem solving. Preparations for classroom tests and final examination.

Learning outcomes in the course

Knows mathematical truths and is able to use methods in volume of a subject, is able to prove and apply them.

Assessment methods

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

Teacher

lekt Anna Šeletski

Prerequisite course 1

The course is a prerequisite

Differential Geometry (MLM6407.DT)

Functions of Complex Variable (MLM6207.DT)

Functions of Complex Variable (MLM6010.DT)

Functions of Complex Variable (MLM7007.DT)

Functions of a Complex Variable (MLM6312.DT)

Mathematical Analysis III (MLM6009.DT)

Seminar in Mathematical Analysis and its Applications (MLM6049.DT)

Seminar in Mathematical Analysis and its Applications I (MLM6051.DT)

Work Placement in Mathematics I (MLM6404.DT)

Functions of Complex Variable (MLM6207.DT)

Functions of Complex Variable (MLM6010.DT)

Functions of Complex Variable (MLM7007.DT)

Functions of a Complex Variable (MLM6312.DT)

Mathematical Analysis III (MLM6009.DT)

Seminar in Mathematical Analysis and its Applications (MLM6049.DT)

Seminar in Mathematical Analysis and its Applications I (MLM6051.DT)

Work Placement in Mathematics I (MLM6404.DT)

Study literature

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

Kangro, G. 1968 Matemaatiline analüüs II. Tallinn: Valgus.

Kangro, G. 1968 Matemaatiline analüüs II. Tallinn: Valgus.

Replacement literature

Kangro, G. 1968 Matemaatiline analüüs II. Tallinn: Valgus;

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

Tali, A. 2009 Matemaatiline analüüs II (käsikiri);

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. 2009 Matemaatiline analüüs II (käsikiri);

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.