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Course info
KMA / MA2
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Course description
Department/Unit / Abbreviation
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KMA
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MA2
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mathematical Analysis 2
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
4
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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154 / -
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9 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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KMA/MA2-A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The aim of this course is an introduction and active understanding of the concepts the advanced mathematical analysis such as: - function sequences and function series; - vector functions of one real variable; - real functions of more variables; - differential and integral calculus in Rn. The subject of this course is equivalent to KMA/M2, but the theoretical parts are more emphasized. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1 or KMA/MA1.
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Requirements on student
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Two tests during the semester, totaling at least 60% of the maximum,
combined exam (written and oral part).
Knowledge of basic notions and statements. The ability to apply theoretical tools when solving practical problems.
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Content
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Week 1: Point-wise and uniform convergence of function sequences;
Week 2: Function series;
Week 3: Power series and their convergence; Fourier series;
Week 4: Vector functions of one real variable and their properties; curves in Rn;
Week 5: Subsets of Rn and their topological properties;
Week 6: Functions of n variables, their limits and continuity;
Week 7: Directional derivative, total differential, tangent manifolds; chain rule;
Week 8: Solvability of functional equations and differentiation of implicit functions;
Week 9: Fundamental notions of min/max theory in Rn;
Week 10: Mapping from Rn to Rm, its continuity and differentiability; regular mappings and transformations of coordinate systems;
Week 11: Double and triple integral, Fubini theorem, basic techniques;
Week 12: Application of double and triple integrals in geometry and physics;
Week 13: Integrals depending on parameters and their differentiation.
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Activities
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Fields of study
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V rámci systému Courseware jsou studentům k dispozici veškeré informace týkající se výuky předmětu a příslušné elektronické studijní opory (studijní materiály, výukové texty, řešené i neřešené příklady, domácí úlohy apod.).
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Guarantors and lecturers
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Guarantors:
Doc. Ing. Gabriela Holubová, Ph.D. (100%),
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Lecturer:
Doc. Ing. Gabriela Holubová, Ph.D. (100%),
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Tutorial lecturer:
Mgr. Jakub Hesoun (100%),
Doc. Ing. Gabriela Holubová, Ph.D. (100%),
Ing. Lukáš Kotrla, Ph.D. (100%),
Ing. Petr Nečesal, Ph.D. (100%),
RNDr. Jonáš Volek, Ph.D. (100%),
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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 comprehensive test (10-40)
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24
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Contact hours
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78
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Preparation for an examination (30-60)
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56
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Total
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158
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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: |
rozumět základním principům z oblasti diferenciálního počtu funkcí jedné proměnné |
rozumět základním principům z oblasti integrálního počtu funkcí jedné proměnné |
rozumět základním principům z oblasti lineární algebry |
rozumět základním principům z oblasti číselných posloupností a řad |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
derivovat a integrovat funkce jedné proměnné |
ovládat aritmetické operace s vektory a maticemi |
pro zadanou matici vypočítat vlastní čísla a vlastní vektory |
rozhodnout o konvergenci či divergenci číselné posloupnosti |
rozhodnout o konvergenci či divergenci číselné řady |
nalézt extrémy funkce jedné proměnné |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
prokázat znalost definic a základních tvrzení týkajících se funkčních posloupností, funkčních řad, vektorových funkcí jedné reálné proměnné a reálných funkcí více proměnných |
rozumět základním principům teorie diferenciálního počtu funkcí více proměnných |
rozumět základním principům teorie integrálního počtu funkcí více proměnných |
rozumět základním principům teorie vektorových funkcí jedné proměnné |
rozumět základním principům teorie funkčních posloupností a řad |
Skills - skills resulting from the course: |
pracovat s funkčními posloupnostmi a řadami |
rozvinout danou funkci v mocninnou nebo Fourierovu řadu |
popsat křivky v Rn a pracovat s nimi |
určit vlastnosti reálných funkcí vice proměnných (spojitost, hladkost apod.) |
počítat derivace ve směru a parciální derivace funkcí více proměnných |
formulovat základní úlohy na maximum, resp. minimum, a tyto úlohy vyřešit s využitím diferenciálního počtu |
počítat dvojné a trojné integrály |
pracovat s integrály závislými na parametru |
Competences - competences resulting from the course: |
N/A |
N/A |
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: |
Combined exam |
Skills demonstration during practicum |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Skills demonstration during practicum |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Skills demonstration during practicum |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Interactive lecture |
Task-based study method |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Interactive lecture |
Task-based study method |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
Interactive lecture |
Task-based study method |
Practicum |
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