13D081MI - Measure and Integration
Course specification | ||||
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Course title | Measure and Integration | |||
Acronym | 13D081MI | |||
Study programme | Electrical Engineering and Computing | |||
Module | Applied Mathematics | |||
Type of study | doctoral studies | |||
Lecturer (for classes) | ||||
Lecturer/Associate (for practice) | ||||
Lecturer/Associate (for OTC) | ||||
ESPB | 9.0 | Status | elective | |
Condition | Mathematics on the level of compulsory courses at ETF as well as familiarity with elements of probability theory. | |||
The goal | The course presents a generalization of methods of calculus in one and more variables which are based on concepts of length, area and volume. The goal of the course is learnig this classical theory and its applications and gaining knowledge of properties and techniques related to abstract measure theory and integration theory, Laplace and Fourier transform etc. | |||
The outcome | Student will be able to read and understand literature where the concepts of measure and integrations are used and applied in mathematical models. Student will be able to use these concepts and acquired knowledge in his/her own research and to use it in the process of solving applied problems. | |||
Contents | ||||
Contents of lectures | Jordan measure. Lebesgue measure and integral. Lebesgue-Stieltjes integral and its properties. Abstract measure spaces. Types of convergence. Differentiation theorems. Lp spaces. Product measures. Infinite product spaces and Kolmogorov's extension theorem. Fourier and Laplace transform of measures, inversion and applications. | |||
Contents of exercises | ||||
Literature | ||||
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Number of hours per week during the semester/trimester/year | ||||
Lectures | Exercises | OTC | Study and Research | Other classes |
6 | ||||
Methods of teaching | Mentoring, consultations,seminar. Individual programs for each student, depending on his/her background and the area of doctorate. Textbooks are used in selected parts, depending on individual needs. If there is a sufficient number of students, classical lectures will be held, with the main textbook cited first in the list. | |||
Knowledge score (maximum points 100) | ||||
Pre obligations | Points | Final exam | Points | |
Activites during lectures | Test paper | 70 | ||
Practical lessons | Oral examination | |||
Projects | ||||
Colloquia | ||||
Seminars | 30 |