B_AMa Applied Mathematics

University of Finance and Administration
Winter 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
PaedDr. Renata Majovská, PhD. (seminar tutor)
Guaranteed by
PaedDr. Renata Majovská, PhD.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Ivana Plačková
Timetable of Seminar Groups
B_AMa/cEKKV: Thu 12:15–12:59 KV211, Thu 13:00–13:45 KV211, R. Majovská
B_AMa/cEKPH: Wed 17:30–18:14 E230, Wed 18:15–19:00 E230, R. Majovská
B_AMa/pEKKV: Thu 10:30–11:14 KV211, Thu 11:15–12:00 KV211, R. Majovská
B_AMa/pEKPH: Wed 15:45–16:29 E230, Wed 16:30–17:15 E230, R. Majovská
B_AMa/vEKPH: Fri 18. 10. 14:00–15:30 E225, 15:45–17:15 E225, Fri 1. 11. 14:00–15:30 E225, 15:45–17:15 E225, Fri 29. 11. 14:00–15:30 E225, 15:45–17:15 E225, Fri 13. 12. 14:00–15:30 E225, 15:45–17:15 E225, R. Majovská
Prerequisites
The student should have knowledge of high school mathematics - especially basic knowledge of functions, solving systems of equations and mathematical symbols.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course aims is to introduce students to the basic concepts and procedures of linear algebra, sequences, and differential and integral calculus. These are the concepts and procedures necessary for the study of economics.
Learning outcomes
Upon successful completion of the course, students:
1. Will be able to perform operations with matrices, calculate the inverse matrix, solve simple matrix equations, determine the determinant of a matrix, solve systems of linear equations, calculate the limits and derivatives of economic functions, investigate the progress of these functions, use the method of integration per partes and the substitution method for calculating indefinite integrals, use Newton's definition of the definite integral and the definition of the improper integral.
2. Will understand the differences between discrete and continuous models and be able to apply mathematical knowledge in economics.
3. Will use the Wolfram Alpha program and other suitable freely available programs, or calculators.
Syllabus
  • 1. Linear algebra - Matrices, rank of a matrix, operations with matrices, determinants and their use.
  • 2. Inverse matrices, solving matrix equations.
  • 3. Systems of linear equations, Frobein's theorem, structural models.
  • 4. Modeling in economics, discontinuous and continuous models. Sequences, sequence limit.
  • 5. Functions of one variable - overview of elementary functions, domain, graphs, properties, demand functions, supply, production functions, market equilibrium.
  • 6. Limit of a function of one variable.
  • 7. Continuity of a function of one variable, derivative of a function of one variable, derivatives of higher orders, L'Hospital's rule.
  • 8. The equation of the tangent to the graph of the function, the average and the limiting slope of the function.
  • 9. Meaning of the first and second derivatives for the course of a function (monotonic function, local and global extrema, convexity and concavity, inflection points), extrema of a function of one variable, course of a function. Cost function, profit maximization.
  • 10. Functions of two variables - domain, function graph, partial derivatives, bound extrema.
  • 11. Integral calculus - Primitive functions, indefinite integral, per partes, and substitution methods.
  • 12. Definite integral, improper integral. Accumulation of capital.
Literature
    required literature
  • Moučka, Jiří a Rádl, Petr. Matematika pro studenty ekonomie. Praha: Grada Publishing, 2015 ISBN: 978-80-247-5406-2
  • BUDINSKÝ, Petr a Ivan HAVLÍČEK. Sbírka příkladů z matematiky pro vysoké školy ekonomického a technického zaměření. Praha: VŠFS, 2005 (dotisk 2016). 121 s. ISBN 80-86754-52-9
  • BUDINSKÝ, Petr a Ivan HAVLÍČEK. Matematika pro vysoké školy ekonomického a technického zaměření. Praha: VŠFS, 2005 (dotisk 2013). 131 s. ISBN 80-86754-45-6
    recommended literature
  • Delventhal, Katka Maria. Kissner, Alfred. Kulick, Malte. Henzler, Jiří. Kompendium matematiky: vzorce a pravidla, četné příklady včetně řešení: od základních operací po vyšší matematiku. Praha: Knižní klub, 2013 ISBN: 978-80-242-3946-0
  • Kaňka, Miloš. Sbírka řešených příkladů z matematiky pro studenty vysokých škol. Praha: Ekopress, 2009 ISBN: 978-80-86929-53-8
  • Šubrt, Tomáš. Ekonomicko-matematické metody. Plzeň: Vydavatelství a nakladatelství Aleš Čeněk s.r.o., 2015 ISBN: 978-80-7380-563-0
Teaching methods
Teaching takes place in the form of lectures and exercises in the face-to-face form of study and controlled group consultations in the combined form of study.
The minimum mandatory participation is 75 % in exercises in the face-to-face form of study and 50 % in controlled group consultations in the combined form of study.
Instead of attending classes, students with ISP will hand in 5 examples of their own on the relevant topic to the IS drop-in office.
Students will be introduced to the Wolfram Alpha program (https://www.informacnigramotnost.cz/wolframalpha-answer-engine-znalosti/) and other freely available programs, or calculators, to solve problems.
Assessment methods
The subject is completed with credit and an exam. In order to obtain a credit, it is necessary to successfully (at least 60%) pass the credit test and have the mandatory 75% attendance. Obtaining a credit is a necessary condition for access to the exam. The exam consists of a written and an oral part; a necessary condition for proceeding to the oral part is to complete at least 50% of the written part. The oral exam verifies knowledge of basic concepts.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Information on the extent and intensity of the course: 16 hodin KS/semestr.
The course is also listed under the following terms Winter 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/winter2024/B_AMa