### Course: Mathematics 2

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 Course title Mathematics 2 KAP/MV2 Lecture + Lesson Bachelor not specified Summer 6 Czech Compulsory Face-to-face Course does not contain work placement None The course is available to visiting students
Lecturer(s)
• Cvrček Milan, PhDr. Ph.D.
• Šimková Tereza, Mgr. Ph.D.
• Bittner Václav, Mgr. Ph.D.
Course content
I. Integral Calculus 1. Primitive function and indefinite integral. Basic rules, method per partes, substitution method. 2. Integration by partial fractions. 3. Riemann definite integral. Newton-Leibniz's theorem. II. Linear Algebra 4. Real coordinate space. Linear (in)dependece. 5. Norm of vector. Inner product. 6. Matrices, basic operations. Rank of matrix. Gaussian elimination method. 7. Inverse matrix, its properties and calculation. Matrix equations. 8. Systems of linear algebraic equations. Solution. Solvability. 9. Determinant, definition, properties, calculation. Laplaces formula. Cramers rule. Inverse matrix. 10. Eigenvalues and eigen vectors. III. Ordinary Differential Equations 11. Elemental methods for solving the first order ODE. Separation of variable method. 12. Linear ODE of first order. Separation of variable method. Variation of constant. 13. Homogeneous linear ODE of order n with constant coefficients. Fundamental system. Characteristic polynomial. Heterogeneous linear ODE with constant coefficients. Method of guess for special right side.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
• Class attendance - 56 hours per semester
• Preparation for exam - 125 hours per semester
Learning outcomes
Integral Calculus. Linear Algebra. Ordinary Differential Equations.
Basic knowledge of integral calculus, linear algebra and ordinary differential equations.
Prerequisites
Differential calculus - Mathematics 1 (MV1)

Assessment methods and criteria
Combined examination

Requirements on credit: two tests of the subject matter. The date of each test will be announced in advance by teacher. It is necessary to get score at least 50% for each test. Requirements on exam: Knowledge of problem solving, concepts and basic ideas.
Recommended literature
• Bittnerová, D. - Plačková, G.:. Louskáček 2 - integrální počet funkce jedné proměnné.. TUL, liberec, 2008.
• Brzezina M., Veselý J. Obyčejné (lineární) diferenciální rovnice a jejich systémy. Liberec, 2012. ISBN 978-80-7372-909-7.
• Hrubý D., Kubát J. Matematika pro gymnázia : diferenciální a integrální počet. Praha : Prometheus, 2004. ISBN 80-7196-210-4.
• Mezník, I. - Karásek, J. - Miklíček, J. Matematika 1 pro strojní fakulty. Praha, SNTL, 1992.
• Nekvinda, M. Matematika. Část 1.. Liberec : Technická univerzita v Liberci, 2001. ISBN 80-7083-447-1.

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