Course: Mathematical Analysis 2

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Course title Mathematical Analysis 2
Course code KMA/MA2
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 1
Semester Winter and summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Holubová Gabriela, Doc. Ing. Ph.D.
  • Benedikt Jiří, Doc. RNDr. Ph.D.
  • Kotsu Matas Aleš, Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
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. Further information and the lecture notes can be found on the web page http://analyza.kma.zcu.cz.

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, Task-based study method
  • Preparation for comprehensive test (10-40) - 24 hours per semester
  • Preparation for an examination (30-60) - 56 hours per semester
  • Contact hours - 78 hours per semester
prerequisite
professional knowledge
There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1 or KMA/MA1.
learning outcomes
By the end of the course, a successful student should be able to: 1. Demonstrate knowledge of the definitions and fundamental theorems concerning function sequences, function series, vector functions of one real variable and real functions of more variables; 2. Deal with function sequences and function series; 3. Expend a function into a power of Fourier series; 4. Describe curves in Rn and work with them; 5. Determine properties of functions of more variables; 6. Compute directional and partial derivatives of functions of more variables; 7. Formulate basic min/max problems and solve them using differential calculus; 8. Evaluate double and triple integrals; 9. Deal with integrals depending on parameters; 10.Use developed theory in solving problems on physical systems.
teaching methods
Lecture supplemented with a discussion
Interactive lecture
Task-based study method
assessment methods
Combined exam
Skills demonstration during practicum
Recommended literature
  • Brabec, Jiří; Hrůza, Bohuslav. Matematická analýza II. Praha : SNTL, 1986.
  • Drábek, Pavel; Míka, Stanislav. Matematická analýza II. 3. nezm. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-528-6.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 1 Summer
Faculty of Education Studies in Mathematics (1) Mathematics courses 3 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 1 Summer
Faculty of Education Studies in Mathematics (15) Mathematics courses 3 Summer
Faculty of Applied Sciences Computer Modelling (2016) Special and interdisciplinary fields 1 Summer
Faculty of Education Studies in Mathematics (17) Mathematics courses 3 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Computer Modelling (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computations and Design (1) Special and interdisciplinary fields 1 Summer
Faculty of Education Studies in Mathematics (14) Mathematics courses 3 Summer
Faculty of Education Studies in Mathematics (13) Mathematics courses 3 Summer
Faculty of Education Studies in Mathematics (16) Mathematics courses 3 Summer
Faculty of Applied Sciences Computations and Design (2014) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Modelling (2014) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 1 Summer
Faculty of Applied Sciences Computations and Design (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Computations and Design (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 1 Summer