Course: Mathematics II

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Course title Mathematics II
Course code UMKM/PMT2
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 1
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Šulista Milan, doc. RNDr. CSc.
  • Sekerka Bohuslav, prof. RNDr. CSc.
  • Brebera Jan, RNDr.
  • Koudela Libor, Mgr. Ph.D.
  • Jindrová Pavla, Mgr. Ph.D.
  • Brebera David, Mgr.
Course content
Function series. Power series. Radius, interval and domain of convergence. Taylor series.Linear spaces with a dot product, euclidean space. Functions of several variables - limits and continuity, partial derivatives, differential. Superposition of functions, functions defined implicitly and their derivatives, local extrema. Ordinary differential equations of the first order, the Cauchy problem, separation of variables. Linear differential equations of the first and second order, variation of parameters, method of unknown coefficients. Riemann's multiple integral, Fubini's theorem. Calculation of double integrals, theorem on substitution, improper integrals, applications.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
Learning outcomes
The course is designed to acquaint students with basics of differential and integral calculus of functions of several real variables and theory of ordinary differential equations and to develop their ability to find and use appropriate mathematical methods to solve problems of various economic and technical disciplines.
Students will be able to solve problems of all topics covered by this course and to find and use appropriate methods to solve problems of subsequent mathematically oriented subjects.

Assessment methods and criteria
Written examination

Assignment - attendance at seminars, completion of all given tasks and passing the written test. Examination - a set of problems and a set of theoretical questions to be solved.
Recommended literature
  • Kolda S. - Černá M. Úvod do lineární algebry a analytické geometrie. null. Pardubice, 2007. ISBN null.
  • Kolda S.- Machačová L. Matematika II, skriptum. Pardubice, 2007.
  • Kolda S.-Machačová L.-Prachař O. Cvičebnice z Matematiky II.. Pardubice, 2007.
  • Prachař O. - Jelínková J. Průvodce předmětem MATEMATIKA II (čtvrtá část) -Úlohy z diferenciálního počtu funkcí více reálných proměnných. Pardubice, 2007.
  • Prachař O. - Jelínková J. Průvodce předmětem MATEMATIKA II (pátá část) - Úlohy z obyčejných diferenciálních rovnic.. Pardubice, 2008.
  • Prachař O. - Jelínková J. Průvodce předmětem MATEMATIKA II (šestá část) -Úlohy z vícerozměrného a křivkového integrálu.. Pardubice, 2007.
  • Prachař O.-Cabrnochová R. Průvodce předmětem MATEMATIKA (třetí část)- Úlohy z lineární algebry, analytické geometrie a z nekonečných řad. Pardubice, 2007.

Study plans that include the course