Mathematics 5 - NMMA705
Title: Matematika 5
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Tomáš Bárta, Ph.D.
Classification: Mathematics > Differential Equations, Potential Theory, Optimization
Pre-requisite : NMMA704
Interchangeability : JEB062
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Annotation -
Last update: G_M (07.05.2014)
The lecture deals with an introduction to calculus of variations and optimal control theory with respect to applications in economical sciences.
Course completion requirements -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (28.10.2019)

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 consists of a written computative part (90 minutes, three problems, 10 points each) and a following theoretical oral part (30 points). It is neccessary to gain 50% of points in each of the two parts. The exam examines the knowledge of the subject matter in the scope given by the lectures.

Literature -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (28.10.2019)

Xerokopy of the lectures

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

Requirements to the exam -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (28.10.2019)

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.

Syllabus -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (28.10.2019)

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.