Course: Mathematics II

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Course title Mathematics II
Course code KMD/MA2-E
Organizational form of instruction Lecture + Seminary
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 7
Language of instruction Czech
Status of course Compulsory, Optional
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)
  • Mlýnek Jaroslav, doc. RNDr. CSc.
  • Bittnerová Daniela, RNDr. CSc.
Course content
A. Linear algebra 1. Arithmetic vectors, linear (in)dependence of vectors. Vector space, dimension and basis of a space. 2. Norm of a vector, inner product of vectors. Matrix, operations with matrixes. Rank of a matrix. Gaussian elimination. 3. System of linear algebraic equations, solutions a system of linear algebraic equations. 4. Inverse matrix, properties, calculation of a inverse matrix. Matrix equations, use inverse matrixes to solution matrix equations. 5. Determinant, properties, calculation of determinant. Use: Cramer's rule, calculation of inverse matrix. 6. Eigenvalues and eigenvectors of a matrix. B. Combinatorics 7. Combinatorial rules, permutations, variations and combinations with repetition and without repetition. C. Functions of more variables 8. Euclidean n-space, properties of sets of En. Functions of more variables, domain of definition. 9. Partial derivatives, extremes of functions of more real variables. 10. Constrained and global extremes of functions of two variables. C. Differential and difference equations 11. Differential equations of order 1, basic terms. Separation of variable method. 12. Linear differential equations of order 1, variation of constant method. Homogeneous linear equation of order n with constant coefficients (characteristic equation, fundamental system). 13. Difference equations, solution of linear difference equations.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Preparation for credit - 26 hours per semester
  • Home preparation for classes - 28 hours per semester
  • Preparation for exam - 30 hours per semester
  • Class attendance - 56 hours per semester
  • Semestral paper - 10 hours per semester
Learning outcomes
Basis of the linear algebra. Solving of systems of linear algebraic equations. Inverse matrix and their usage, calculation of determinant. Basis of differential calculus for functions of more variables, especially the investigation of extremes of functions of two variables. Differential equations, basic methods for their solving. All items regarding to economic applications.
Basic knowledge of higher mathematics.
Prerequisites
Credit from MA1*H
KMD/MA1-E
----- or -----
KMD/MA1-H

Assessment methods and criteria
Combined examination

Credit: Regular attendance, passing of two tests, working-out of a semestrial work. Exam: written + oral part
Recommended literature
  • Jirásek F., Čipera S., Vacek M. Sbírka řešených příkladů z matematiky II. SNTL Praha, 1989.
  • Kaňka, M. - Henzler J.:. Matematika 2, Ekopress.. Praha, 2003. ISBN 80-86119-77-7.
  • Klůfa, J. - Coufal, J.:. Matematika 1, Ekopress.. Praha, 2003. ISBN 80-86119-76-9.
  • Nekvinda, M. - Říhová, H. - Vild, J.:. Matematické oříšky II. Liberec 1997..
  • Nekvinda M., Vild J. Matematické oříšky 1.. Liberec : Technická univerzita v Liberc, 2006. ISBN 80-7372-017-5.
  • Nekvinda, M.:. Matematika II.. Liberec, 2000. ISBN 80-7083-374-2.
  • Polák, J. Přehled středoškolské matematiky.. Praha, 1991.
  • Polák, J. Přehled středoškolské matematiky.. Praha, 1991.
  • Rektorys, K. a kol. Přehled užité matematiky. Praha, Prometheus, 1996.
  • Vild, J. - Golka, P. Lineární algebra. Liberec, TU, 2002.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science, Humanities and Education Study plan (Version): Recreology (20) Category: Physical education and sport - Recommended year of study:-, Recommended semester: Summer