Mathematics 2 (FSI-Z2M)

Academic year 2025/2026
Supervisor: doc. Ing. Jiří Šremr, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Course type: departmental course
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:
 
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

Conditions for awarding the course-unit credit (0-100 points, minimum 50 points):

  • two written tests (each maximum 50 points); students who fail to score 50 points in total will be allowed to resit the test during the first week of the examination period.

Conditions for passing the exam (0-100 points, minimum 50 points):

  • written test (maximum 85 points),
  • discussion about the test and the oral part of the exam (maximum 15 points),
  • maximum 100 points, the overall classification is given by ECTS grade scale.

Lecture: Attendance at lectures is obligatory and checked, only one unexpected absence is allowed, absence may be compensated for based on an agreement with the teacher.

Seminar: Attendance in seminars is obligatory and checked, only one unexpected absence is allowed, absence may be compensated for based on an agreement with the teacher.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. compulsory                  
    Exercise  13 × 3 hrs. compulsory                  
Course curriculum:
    Lecture

  • Improper Riemann integral.

  • First-order ordinary differential equations (basic notions, direction field, initial value problem, solving of some first-order non-linear differential equations).

  • Higher-order ordinary differential equations (basic notions, linear differential equations, solving of higher-order non-homogeneous linear equations with constant coefficients, initial and boundary value problems).

  • Systems of first-order linear differential equations (solving of homogeneous systems of first-order linear equations with constant coefficients).

  • Functions of more real variables (basic notions, graph, level curves, vector function, vector field).

  • Differential calculus of functions of more variables (partial derivatives, directional derivative, gradient, continuity, differential, tangent plane, linear and quadratic approximations, potential vector field, potential, differential operators).

  • Double integrals (double integral, Fubini theorem, change to polar coordinates, applications).

  • Real sequences, introduction to series (series of reals, convergence, sum, geometric serie, convergence tests, reminder).
    Exercise

  • Improper Riemann integral.

  • Solving of selected types of first-order non-linear differential equations, examples of a possible use in geometry and physics.

  • Solving of higher-order non-homogeneous linear equations with constant coefficients, examples of a possible use in dynamics and problems of strength analysis.

  • Solving of homogeneous systems of first-order linear equations with constant coefficients, illustration of solutions in the phase space.

  • Basic properties of functions of more real variables, vector field, examples of a possible use in geometry and evaluation of line integrals.

  • Evaluation of partial derivatives, linear and quadratic approximations, potential vector field, potential function, local extremes, examples of a possible use in physics.

  • Evaluation of double integrals, change of variables, examples of a possible use in geometry and physics.

  • Limit of a sequence, convergence tests for series of reals.
Literature - fundamental:
1. STEWART, James, Daniel CLEGG a Saleem WATSON. Calculus: early transcendentals. 9th Edition. Australia: Cengage, 2021, xxx, 1214 stran, A158 : ilustrace, grafy. ISBN 978-0-357-11351-6.
2. BOYCE, William E., Richard C DIPRIMA a Douglas B MEADE. Boyce's elementary differential equations and boundary value problems. 11th edition; Global edition. Singapore: John Wiley, 2017, xii, 607 stran : ilustrace, grafy, výpočty. ISBN 978-1-119-38287-4.
3. JARNÍK, Vojtěch. Diferenciální počet II. 4. vyd. Praha: Academia, 1984, 669 s.
4. JARNÍK, Vojtěch. Integrální počet II. 3. vyd. Praha: Academia, 1984, 763 s.
Literature - recommended:
1. MUSILOVÁ, Jana a Pavla MUSILOVÁ. Matematika pro porozumění i praxi: netradiční výklad tradičních témat vysokoškolské matematiky. II/1-2. Brno: VUTIUM, 2012, xiv, 341 s. : barev. il. ISBN 978-80-214-4071-5.
2. MUSILOVÁ, Jana a Pavla MUSILOVÁ. Matematika pro porozumění i praxi: netradiční výklad tradičních témat vysokoškolské matematiky. III/1-3. Brno: Vysoké učení technické v Brně, Nakladatelství VUTIUM, 2017, 390 stran v různém stránkování : barevné ilustrace. ISBN 978-80-214-5503-0.
3. KALAS, Josef a Jaromír KUBEN. Integrální počet funkcí více proměnných. Brno: Masarykova univerzita, 2009, vi, 272 s. : il. ISBN 978-80-210-4975-8.
4. KALAS, Josef a Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 80-210-2589-1.
5. STEWART, James, Daniel CLEGG a Saleem WATSON. Calculus: early transcendentals. 9th Edition. Australia: Cengage, 2021, xxx, 1214 stran, A158 : ilustrace, grafy. ISBN 978-0-357-11351-6.
6. BOYCE, William E., Richard C DIPRIMA a Douglas B MEADE. Boyce's elementary differential equations and boundary value problems. 11th edition; Global edition. Singapore: John Wiley, 2017, xii, 607 stran : ilustrace, grafy, výpočty. ISBN 978-1-119-38287-4.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
C-AKR-P full-time study CLS -- Cr,Ex 5 Elective 1 1 S
B-KSI-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 1 1 S