Mathematics V - JEB062
Title: Matematika V
Guaranteed by: Institute of Economic Studies (23-IES)
Faculty: Faculty of Social Sciences
Actual: from 2021
Semester: winter
E-Credits: 6
Examination process: winter s.:
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: enabled for web enrollment
Guarantor: RNDr. Václav Vlasák, Ph.D.
Teacher(s): RNDr. Václav Vlasák, Ph.D.
Incompatibility : NMMA705
Pre-requisite : JEB029
Interchangeability : NMMA705
Is interchangeable with: NMMA705
Examination dates   WS schedule   Noticeboard   
Annotation -
Formulation of problems of calculus of variations, Euler equation, analysis of examples,
basic problem of optimal control theory, maximum principle.
Last update: ZELENY (14.09.2006)
Aim of the course -

The lecture deals with an introduction to calculus of variations and optimal control theory with respect to applications in economical sciences.

Last update: Kot Pavel, Ing. (15.04.2021)
Course completion requirements -

Credit is given for active participation in exercises (computing problems at the blackboard) or solving given set of problems at home.

Character of the condition does not allow repetitions. Credit is a neccessary condition for registration for the exam.

The exam examines the knowledge of the subject matter in the scope given by the lectures.

Last update: Vlasák Václav, RNDr., Ph.D. (08.09.2023)
Literature - Czech

M.I.Kamien and N.L.Schwartz, Dynamic Optimization, North-Holland 2000.

Last update: ZELENY (14.09.2006)
Requirements to the exam -

The exam consists of written and oral part. Neccessary condition to take part in the oral part is successful passing the written part. Neccessary condition to take part in the written part is obtaining the credit. If a student does not succeed in the written part, the exam is graded by 'F'. If a student does not succeed in the oral part, both parts of the exam must be repeated at the next attempt. The final grade depends on the points obtained in the written and oral part of the exam

Written part consists of three problems, their topics correspond to the sylabus of the lecture and to the topics of the seminar.

Requirements for the oral part correspond to the sylabus of the course in the extend presented in the lectures.

Last update: Kot Pavel, Ing. (15.04.2021)
Syllabus -

Stability of equilibria of autonomous systems. Problems of calculus of variations, Euler's equation, analysis of examples. Basic problem of optimal control theory, maximum principle.

Last update: Kot Pavel, Ing. (15.04.2021)
Entry requirements -

Xerokopy of the lectures

A.C. Chiang: Elements of dynamic optimization, McGraw-Hill 1992 (ISBN 0-07-112568-X),

Last update: Kot Pavel, Ing. (15.04.2021)