Course: Mathematics 2

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Course title Mathematics 2
Course code KMD/MA2-M
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Knobloch Roman, Mgr. Ph.D.
  • Bittnerová Daniela, RNDr. CSc.
  • Finěk Václav, doc. RNDr. Ph.D.
  • Bittner Václav, Mgr. Ph.D.
  • Břehovský Jiří, Mgr. Ph.D.
Course content
Lectures: 1. Infinite series, tests for convergence, absolute convergence. 2. Introduction to metric spaces, multivariable functions. 3. Continuity and limits of multivariable functions. 4. Partial derivatives, total differentials, the chain rule, directional derivatives. 5. Taylor's formula, implicit functions. 6. Repetition. 7. Relative extrema of multivariable functions. 8. Constrained and absolute extrema of multivariable functions. 9. First-order ordinary differential equations, existence and uniqueness of solutions. 10. Second-order ordinary differential equations with constant coefficients. 11. Introduction to numerical solution methods for first-order ordinary differential equations. 12. Introduction to multiple integrals, Fubini's theorem. 13. Substitutions in multiple integrals. Practice: 1. Repetition of integration. 2. Infinite series, tests for convergence, absolute convergence. 3. Infinite series, metric spaces, multivariable functions. 4. Continuity and limits of multivariable functions. 5. Partial derivatives, total differentials, the chain rule, directional derivatives. 6. Taylor's formula, implicit functions. 7. Repetition. 8. Relative extrema of multivariable functions. 9. Constrained and absolute extrema of multivariable functions. 10. Solution methods for first-order ordinary differential equations. 11. Solution methods for second-order ordinary differential equations. 12. Introduction to multiple integrals, Fubini's theorem. 13. Substitutions in multiple integrals. 14. Repetition.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Class attendance - 70 hours per semester
  • Preparation for credit - 28 hours per semester
  • Preparation for exam - 42 hours per semester
  • Home preparation for classes - 40 hours per semester
Learning outcomes
The subject represents an introduction to differential calculus of function of more (especially two) real variables, infinite series, double integrals, and an essential course of differential equations.
Infinite series, differential calculus of multivariable functions, ordinary differential equations, foundations of computational mathematics, and multiple integrals.
Prerequisites
Knowledge of subject Mathematics 1 (MA1-M).

Assessment methods and criteria
Combined examination

Credit: Active participation on seminars + tests. Exam: writtten.
Recommended literature
  • Brabec, J. - Hrůza, B.:. Matematická analýza II. Praha, 1986.
  • Brabec, J.:. Matematická analýza II. Praha, 1979.
  • Budinský, B. - Charvát, J.:. Matematika II. Praha, 1999.
  • Ivan, J.:. Matematika 1; 2. Bratislava/Praha, 1989.
  • Mezník, I. , Karásek, J., Miklíček, J.:. Matematika I pro strojní fakulty. SNTL, Praha, 1992.
  • Nagy, J.:. Elementární metody řešení obyčejných diferenciálních rovnic. Praha, 1978.
  • Nekvinda, M.:. Matematika II.. Liberec, 2000. ISBN 80-7083-374-2.
  • Nekvinda, M.- Říhová, H. - Vild, J.:. Matematické oříšky II. TU Liberec, 2002.
  • Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Applied Sciences in Engineering (2019) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Informatics and Logistics (2015) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Applied Sciences in Engineering (2016) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Information Technology (2013) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer