Mathematical Analysis III
Course code
MLM6513.DT
old course code
Course title in Estonian
Matemaatiline analüüs III
Course title in English
Mathematical Analysis III
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
The main objective of the course is to apply methods known from previous mathematical analysis courses and to acquire new methods in the theory of multiple integrals, line integrals, and surface integrals. Students will gain knowledge of the theory, fundamental concepts, and main theorems of multiple integrals, line integrals, and surface integrals, as well as become familiar with the methodologies and applications involved.
Students will also acquire the theoretical foundations, key concepts, and theorems necessary for calculating the flux, divergence, circulation, and curl of vector fields, and will learn about their applications in physics and engineering sciences.
Graduates of this course will develop in-depth knowledge of the theory of number series, including the application of convergence criteria for power series and Fourier series. Special attention is given to integrating this course with previous mathematical analysis courses.
Students will also acquire the theoretical foundations, key concepts, and theorems necessary for calculating the flux, divergence, circulation, and curl of vector fields, and will learn about their applications in physics and engineering sciences.
Graduates of this course will develop in-depth knowledge of the theory of number series, including the application of convergence criteria for power series and Fourier series. Special attention is given to integrating this course with previous mathematical analysis courses.
Brief description of the course
Double and triple integrals, line and surface integrals: existence, properties, calculation methods, and applications. Green's theorem, Gauss's theorem, and Stokes's theorem. Elements of vector field theory.
Convergence and divergence of numerical series. Comparison tests for series, Cauchy's criterion, and D'Alembert's ratio test. Absolutely convergent and conditionally convergent series (Leibniz criterion). Integral test for the convergence of number series. Properties of functional and power series, their convergence and uniform convergence. Power series: radius and interval of convergence, and properties of their sums. Taylor series. Fourier series.
Convergence and divergence of numerical series. Comparison tests for series, Cauchy's criterion, and D'Alembert's ratio test. Absolutely convergent and conditionally convergent series (Leibniz criterion). Integral test for the convergence of number series. Properties of functional and power series, their convergence and uniform convergence. Power series: radius and interval of convergence, and properties of their sums. Taylor series. Fourier series.
Learning outcomes in the course
Upon completing the course the student:
- calculates basic double and triple integrals;
- evaluates line and surface integrals in simple cases;
- applies basic applications of these integrals;
- computes vector field properties such as flux, divergence, circulation, and curl;
- determines the sum of basic number series, analyzes their convergence and absolute convergence;
- identifies the properties and convergence regions of functional and power series;
- calculates the sum of simple power series;
- understands and applies the definition of the trigonometric Fourier series.
- calculates basic double and triple integrals;
- evaluates line and surface integrals in simple cases;
- applies basic applications of these integrals;
- computes vector field properties such as flux, divergence, circulation, and curl;
- determines the sum of basic number series, analyzes their convergence and absolute convergence;
- identifies the properties and convergence regions of functional and power series;
- calculates the sum of simple power series;
- understands and applies the definition of the trigonometric Fourier series.
Teacher
Maria Zeltser
Prerequisite course 1
Study programmes containing that course