University of West Bohemia
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for academic year 2024/2025
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Course: Mathematical Analysis 1

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Course title Mathematical Analysis 1
Course code KMA/MA1
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 2
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Hesoun Jakub, Mgr.
  • Tomiczek Petr, RNDr. CSc.
  • Stehlík Petr, Doc. RNDr. Ph.D.
  • Cibulka Radek, Doc. Ing. Ph.D.
  • Volek Jonáš, RNDr. Ph.D.
  • Nečesal Petr, Ing. Ph.D.
Course content
Week 1: Sets and elementary operations; subsets of real numbers; absolute value; maximum, minimum, least upper bound, and greatest lower bound of a subset of real numbers; Week 2: Sequences of real numbers; subsequences; bounded and monotone sequences; recursively defined sequences; convergent and divergent sequences; Week 3: Algebra of limits and fundamental theorems concerning the properties of a limit; Week 4: Conditions ensuring the convergence of infinite sequences and series; Week 5: Absolute and relative convergence, alternating series; Week 6: Functions of one real variable; graphical representation; inverse functions; composition of functions; Week 7: Local and global behaviour of a function; limits; one-sided limits; algebra of limits; Week 8: Continuity of a function at a point; points of discontinuity; continuity in a closed interval; Week 9: Derivative and differential of a function - definition and both the geometrical and the physical meaning; differentiability and continuity of a function; Week 10: Differentiation from first principles, product rule and chain rule, Rolle's theorem, Langrange's and Cauchy's mean value theorems; stationary points of a function; l'Hospital's rule; Week 11: Indefinite integral; fundamental theorem of calculus; integration by parts and integration by substitution; Week 12: Definite integral and its applications; mean value theorem inequalities for integrals; Week 13: Improper integrals; higher order derivatives and differentials; Taylor's theorem;

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, Task-based study method
  • Contact hours - 78 hours per semester
  • Preparation for comprehensive test (10-40) - 24 hours per semester
  • Preparation for an examination (30-60) - 56 hours per semester
prerequisite
Knowledge
be familiar with high school mathematics
explain basic methods of solving simple mathematical problems
understand a simple mathematical text
Skills
solve linear and quadratic equations and inequalities as well as their systems
work with absolute values, powers and simplify mathematical expressions
sketch the graphs of elementary functions and their simple modifications
Competences
N/A
N/A
learning outcomes
Knowledge
demonstrate knowledge of the definitions and the elementary properties of sequences, series, and differentiable functions of one real variable
be able to read and understand mathematical text
use logical constructions in formulating basic definitions and theorems
Skills
use the calculus rules to differentiate functions
sketch the graph of a function using critical points, the derivative tests for monotonicity and concavity properties
set up max/min problems and use differentiation techniques to solve them
evaluate integrals using techniques of integration, such as substitution and integration by parts
to work with sequences and series of real numbers
use developed theory in solving problems on physical systems
use l'Hospital's rule
Competences
N/A
N/A
teaching methods
Knowledge
Lecture supplemented with a discussion
Interactive lecture
Task-based study method
Skills
Lecture
Practicum
Competences
Lecture
Practicum
assessment methods
Knowledge
Oral exam
Written exam
Test
Skills
Oral exam
Written exam
Test
Competences
Oral exam
Written exam
Test
Recommended literature
  • Canuto, Claudio. Mathematical analysis I. New York : Springer, 2008. ISBN 978-88-470-0875-5.
  • Děmidovič, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod : Fragment, 2003. ISBN 80-7200-587-1.
  • Drábek, Pavel; Míka, Stanislav. Matematická analýza I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-558-8.
  • Míková, Marta; Kubr, Milan; Čížek, Jiří. Sbírka příkladů z matematické analýzy I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-568-5.
  • Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
  • Pultr, Aleš. Matematická analýza I. Praha : Matfyzpress, 1995. ISBN 80-8586-3-09-X.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (19) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (15) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (17) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (18) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (19) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (18) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (17) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (16) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (16) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (15) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (18) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (19) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (17) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (17) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (16) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (19) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (17) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (17) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (19) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (18) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (19) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Music in Education (19) Category: Art and applied art 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (16) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (15) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (1) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (18) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): English Language in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (14) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (15) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
University of West Bohemia, date of update: 26.07.2024 23:53. Data created for academic year 2024/2025