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Course objectives:
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Constrained extrema of a function of several variables. Riemann integral of a function of several variables. Geometric and physical applications.
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Requirements on student
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Students have to pass three written tests. Students have the right to retake one of the tests. If the student gains mark "excellent" up to "very good" from the tests written in the seminar, he/she has the right not to sit at written exam and the grade is recognized as the final grade.
Course completion: written examination.
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Content
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1.-2. Constrained extrema of a function. Extrema of a function on a set.
3.-4. Riemann integral on a rectangular set.
5. Null sets, integrable functions, criteria of integrability.
6. Riemann integral on an open set.
7. Partition of unity, improper integral of the second kind.
8. Fubini theorem.
9.-10. Transformation theorem.
11.-12. Geometric and physical applications.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for test
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20
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Self-tutoring
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60
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Continuous tasks completion (incl. correspondence tasks)
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20
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Being present in classes
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52
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Consultation of work with the teacher/tutor (incl. electronic)
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5
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Unaided e-learning tasks completion
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15
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Preparation for an exam
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40
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Total
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212
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Prerequisites
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Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
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| Student understands differential and integral calculus in one variable and differential calculus in several variables. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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| Student is able to define integral of a bounded function on a bounded set. |
| Student knows properties of integrable functions. |
| Student knows basic methods of integration. |
Skills - skills resulting from the course: |
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| Student is able to apply the methods to integrate functions of two and three variables. |
| Student is able to apply the methods in geometric and physical problems. |
| Student acquires the ability to study relevant technical literature. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
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| Continuous analysis of student´s achievements |
| Written examination |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
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| Computer-based tutoring |
| Dialogic (discussion, dialogue, brainstorming) |
| Monologic (explanation, lecture, briefing) |
| Working with text (coursebook, book) |
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