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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BI-MA1.21 Mathematical Analysis 1 Extent of teaching: 2P+1R+1C
Instructor: Kalvoda T., Paták P. Completion: Z,ZK
Department: 18105 Credits: 5 Semester: L

Annotation:
We begin the course by introducing students to the set of real numbers and its properties, and we note its differences with the set of machine numbers. Then we study real sequences and real functions of a real variable. We gradually introduce the notions of limits of sequences and functions, continuous functions, and derivatives of functions. This theoretical foundation is then applied to root-finding problems (iterative method of bisection and Newton?s method), construction of cubic interpolation (spline), and formulation and solution of simple optimization problems (i.e., the issue of finding extrema of functions). The course is closed with the Landau?s asymptotic notation and methods of mathematical description of complexity of algorithms.

Lecture syllabus:
1. Extended real number line: rational and irrational numbers, completeness axiom, neighborhood, infinity. Relation to machine numbers.
2. Basic properties of functions and sequences. Elementary functions (polynomials, trigonometric functions, exponential, and logarithm).
3. Limit of a sequence and limit of a function: definition, meaning, and illustrations.
4. Computation of limits: algebraic properties of limits, squeeze theorem, examples.
5. The continuity of a function, continuity of elementary functions, implications for root finding (the bisection method as an example of iterative numerical method).
6. The derivative of a function, geometric meaning, linearity of differentiation, product and quotient rule. Derivative of inverse function. Differentiation of elementary functions.
7. Newton?s method for root finding.
8. Cubic interpolation (splines). L?Hospital?s rule.
9. Lagrange?s mean value theorem, implications for monotony and convexity/concavity of functions.
10. Local extrema of functions. Sufficient conditions for their existence.
11. Analytical graph plotting: examples. The notion of an optimization problem.
12. Landau?s asymptotic notation.
13. Mathematical description of the complexity of algorithms.

Seminar syllabus:
This is an outline of proseminars and subsequent exercises.
1. Functions and sequences, basic properties.
2. Elementary functions (polynomials, trigonometric functions, exponential and logarithm).
3. Limits of sequences and functions.
4. Continuity of functions.
5. Derivative of a function.
6. Analytical graph sketching (monotonicity, local exrtrema, asymptotes, etc.).

Literature:
The course is equipped with a dedicated textbook. Additionaly one can consult the following publications.
1. Oberguggenberger M., Ostermann A. : Analysis for Computer Scientists. Springer, 2018. ISBN 978-0-85729-445-6.
2. Stewart J. : Calculus (8th Edition). Cengage Learning, 2015. ISBN 978-1285740621.
3. Bittinger M.L., Ellenbogen D.J., Surgent S.A. : Calculus and Its Applications (11th Edition). Pearson, 2015. ISBN 978-0321979391.
4. Kopáček J.: Matematická analýza nejen pro fyziky I, Matfyzpress, 2016, ISBN 978-80-7378-353-4

Requirements:
Knowledge of high school mathematics, basics of mathematical logic (BIE-DML.21), and BIE-LA1.21.

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
BI-SPOL.21 Unspecified Branch/Specialisation of Study PP 2
BI-PI.21 Computer Engineering 2021 (in Czech) PP 2
BI-PG.21 Computer Graphics 2021 (in Czech) PP 2
BI-MI.21 Business Informatics 2021 (In Czech) PP 2
BI-IB.21 Information Security 2021 (in Czech) PP 2
BI-PS.21 Computer Networks and Internet 2021 (in Czech) PP 2
BI-PV.21 Computer Systems and Virtualization 2021 (in Czech) PP 2
BI-SI.21 Software Engineering 2021 (in Czech) PP 2
BI-TI.21 Computer Science 2021 (in Czech) PP 2
BI-UI.21 Artificial Intelligence 2021 (in Czech) PP 2
BI-WI.21 Web Engineering 2021 (in Czech) PP 2


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška