Course objectives:
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The main aim of this course is to give students a good insight into the following areas : Differential calculus in Rn, optimalization in R2 and R3. Integral calculus in R2 and R3. Vector differential calculus. Surfaces. Line and surface integrals. Gradient of a scalar field, divergence and curl of a vector field. Divergence theorem of Gauss. Stokes theorem. Greens theorems.
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Requirements on student
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It is necessary to obtain at least 75% points from the assignments given lecturer.
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Content
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gradient, directional derivative, higher order partial derivatives.
Week 2: Fundamental notions of min/max theory in Rn;
Week 3: Double integral, Fubini's theorem.
Week 4: Change of variables in a double integrals, polar coordinates.
Week 5: Triple integral, methods to computation. change of variables.
Week 6: Vector fields, divergence and curl. Hamilton operator, potential.
Week 7: Laplace operator, curves.
Week 8: Path integrals of scalar fields.
Week 9: Path integrals of vector fields,
Week 10: Surfaces and parametrization
Week 11: Surface integral of scalar fields.
Week 12: Surface integral of vector fields.
Week 13: Integration theorems of vector calculus
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Activities
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Fields of study
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Studentům je k dispozici kurz v Google Classroom se všemi materiály a informacemi.
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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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Contact hours
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26
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Preparation for comprehensive test (10-40)
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18
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Preparation for formative assessments (2-20)
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10
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Total
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54
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1E and KMA/M2E. |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
To differentiate and integrate the functions of one real variable. |
To draw basic curves. |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
Students will be able to understand the basic problems of differential calculus in Rn, they will be able to work with scalar and vector functions of one and more variables, to understand basic tasks of integral calculus for scalar and vector functions and integral theorems. |
Skills - skills resulting from the course: |
Students will be able to solve basic problems from differential calculus in Rn, will be able to work with scalar and vector functions of one and more variables, compute simple double and triple integrals including substitutional method, simple curve and surface integrals, including use of integral sentences. |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar |
Seminar classes |
Skills - the following training methods are used to achieve the required skills: |
Seminar |
Seminar classes |
Competences - the following training methods are used to achieve the required competences: |
Seminar |
Seminar classes |
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