B_MAT_2 Mathematics II

Institute of Technology and Business in České Budějovice
summer 2026
Extent and Intensity
2/4/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jaroslav Krieg (seminar tutor)
Mgr. Daniel Lašan (seminar tutor)
Ing. Květa Papoušková, Ph.D. (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – School of Expertness and Valuation – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – School of Expertness and Valuation – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
B_MAT_2/K11: Sat 28. 2. 9:40–11:10 E1, Sun 15. 3. 8:00–12:30 E1, Sun 22. 3. 13:05–17:35 E1, Sun 29. 3. 13:05–17:35 B1, Sat 16. 5. 13:05–16:05 E1, D. Smetanová
B_MAT_2/P01: Thu 13:05–14:35 E1, D. Smetanová
B_MAT_2/S01: Tue 13:05–14:35 E4, Wed 9:40–11:10 D515, D. Lašan
B_MAT_2/S02: Thu 14:50–16:20 E4, Fri 11:25–12:55 B4, D. Lašan
B_MAT_2/S05: Tue 16:30–18:00 D515, Fri 9:40–11:10 B1, D. Lašan
B_MAT_2/S06: Mon 8:00–9:30 B5, Tue 9:40–11:10 B4, K. Papoušková
B_MAT_2/S07: Wed 8:00–9:30 B5, Thu 8:00–9:30 B4, K. Papoušková
B_MAT_2/S08: Mon 9:40–11:10 B4, Thu 9:40–11:10 B5, K. Papoušková
B_MAT_2/S10: Wed 14:50–16:20 D416, Thu 14:50–16:20 E7, J. Krieg
Prerequisites
B_MAT_1 Mathematics I || MAT_z Mathematics I
The student masters the differential calculus of functions of one variable. In addition, he/she masters the bases of the integral calculus. The student knows: the term of primitive function, the difference between definite and indefinite integrals, methods of calculation.
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 556 student(s).
Current registration and enrolment status: enrolled: 324/556, only registered: 12/556
Course objectives supported by learning outcomes
The aim of the course is to complement and complete the knowledge of the integral calculus of functions of one variable, including applications for the calculation of content of areas, volumes of rotating solids and length of curves. The aim is also understanding and practical ability to solve ordinary differential equations of first order and some special types of equations of higher orders. After the successful completion of the course, the student is able to: individually solve integral roles; solve differential equations, analyze and propose a procedure of solving of practical problems related to the problem of integral calculus.
Learning outcomes
After the successful completion of the course, the student is able to: individually solve integral roles; solve differential equations, analyze and propose a procedure of solving of practical problems related to the problem of integral calculus.
Syllabus
  • 1. Some more complicated indefinite integrals.
  • 2. Decomposition of rational functions into partial fractions.
  • 3. Integration of rational functions.
  • 4. Special substitution.
  • 5. Calculation of the volume of the rotating solid, determination of the length of the curve
  • 6. Ordinary differential equations of the first order, separation of variables.
  • 7. Homogeneous and first order linear equations.
  • 8. Variation of parameters, integrating factor method.
  • 9. Bernoulli´s differential equation.
  • 10. Simple differential equations of the second order.
  • 11. Variation of parameters for higher order equations.
  • 12. Linear differential equations with constant coefficients.
  • 13. Linear differential equations with special right side.
Literature
  • NÝDL, Václav; Radka ŠTĚPÁNKOVÁ and Vivian Lee WHITE. Inquiry-based mathematics education in the course of mathematics for economists. In Aplikované úlohy v modernom vyučování natematiky : zborník vedeckých prác. Nitra: Karedra matematiky, Slovenská polnohospodárská univerzita v Nitre, 2012, p. 21-24. ISBN 978-80-552-0823-7. info
  • CHARVÁT, Jura; Václav KELAR and Zdeněk ŠIBRAVA. Matematika 2 : sbírka příkladů. 2. vyd. V Praze: České vysoké učení technické, 2012, 206 pp. ISBN 978-80-01-04989-1. info
  • KALOVÁ, Jana. Učební opory pro kombinované studium - Matematika 2. 2010. URL info
  • KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
  • CHARVÁT, Jura; Václav KELAR and Zdeněk ŠIBRAVA. Matematika 2 : sbírka příkladů. Vyd. 1. Praha: Nakladatelství ČVUT, 2006, 206 pp. ISBN 80-01-03537-9. Obsah info
Organizační formy výuky
Lecture
Seminar
Tutorial
Consultation
Komplexní výukové metody
Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Partner Teaching
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
E-learning
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test2032
Preparation for Lectures26 
Preparation for Seminars, Exercises, Tutorial2890
Preparation for the Final Test3060
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion52 
Total:182182
Metody hodnocení a jejich poměr
Test – mid-term 30%
Test – final 70%
Podmínky testu
Final written test (max 70 points). Up to 30 points can be obtained for ongoing activities at the seminar.
Overall classification of the course, ie points for the test (70 - 0) + points from the continuous assessment (30 - 0): A 100 - 90, B 89.99 - 84, C 83.99 - 77, D 76.99 - 73, E 72.99 - 70, FX 69.99 - 30, F 29.99 - 0. The teacher has the right in case of unclear and controversial calculations in the test to ask the student for an explanation in the additional oral exam.
Language of instruction
Czech
Follow-Up Courses
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
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