Course code:  ZVMT 
Course title in language of instruction:  Základy vyšší matematiky 
Course title in Czech:  Základy vyšší matematiky 
Course title in English:  Rudiments of Higher Mathematics 
Mode of completion and number of credits:  Exam (4 credits) (1 ECTS credit = 28 hours of workload) 
Mode of delivery/Timetabled classes:  fulltime, 1/2 (fulltime, hours of lectures per week / hours of seminars per week) 
Language of instruction:  Czech 
Level of course:  bachelor 
Semester:  SS 2018/2019  FA 
Name of lecturer:  Mgr. Petr Liška, Ph.D. (instructor) RNDr. Ludmila Stará (examiner, instructor, lecturer, supervisor) 
Prerequisites:  none 

Aims of the course:  Obtaining basic knowledge of differential and integral calculus of one real variable, linear algebra and some numerical methods.
Achieving the level of mathematical knowledge, strenghtening mathematical skills and development of logical thinking needed for applications in professional courses.
Mastery of mathematical tools necessary to formulate and solve real problems in biotechnological processes. 
Course contents:  1.  Differential calculus (allowance 5/11)   a.  Function  basis concepts and properties  b.  Limit and continuity  c.  Derivative and its application  d.  Minima, maxima, convexity, concavity , points of inflection, asymptotes 
 2.  Integral calculus (allowance 4/8)   a.  Indefinite integral, basic integration methods  b.  Riemann definite integral  c.  Applications of integral calculus 
 3.  Linear algebra (allowance 3/6)   a.  Vectors, linear dependence and independence of vectors  b.  Matrices, determinants  c.  Systems of linear equations 
 4.  Introduction to numerical methods (allowance 2/3)   a.  Solution of algebraic equations  b.  Funkcion approximation 


Learning outcomes and competences:  Generic competences:     ability to analyse and synthesize    ability to solve problems    ability to work independently    basic computing skills    capacity to learn 
 Specific competences:     Ability of logical evaluation and argumentation in solving of mathematical problems    Ability to apply mathematical knowledge and skills to practical problems and use them for study of professional literature    Ability to solve basic problems (student can differentiate and integrate, work with matrices, determinants and solve systems of linear equations)    Basic knowledge of differential and integral calculus and linear algebra    Capacity for abstract thinking 


Type of course unit:  required 
Year of study:  Not applicable  the subject could be chosen at anytime during the course of the programme. 
Work placement:  There is no compulsory work placement in the course unit. 
Recommended study modules:  none 
Assessment methods:  Two 50 minutes written tests will be conducted during the course. There are 8 short math problems on each test. The first test contains problems from differential calculus, the second from integral calculus, linear algebra and numerical method. Maximum points for each test is 8, so maximal amount to receive is 16. For Credit is necessary to have at least 8 points (50%). Tests will be written 7th and 12th week of the semester. Participation on the written tests at aforementioned weeks is mandatory. The course is finished with 90 minutes written exam. Credit is mandatory for final exam participation. The final exam contains 7 problems and 10 theoretical questions. For exam Credit student has to receive minimal 21 points from maximal amount of 50 points. 

Learning activities and study load (hours of study load) 
Type of teaching method  Daily attendance 

Direct teaching  lecture  14 h  practice  28 h  Selfstudy  preparation for exam  42 h  preparation for regular testing  28 h  Total  112 h 

Basic reading list 
 RÁDL, P.  ČERNÁ, B.  STARÁ, L. Základy vyšší matematiky. 3rd ed. Mendelova univerzita v Brně, 2014. 176 p. ISBN 9788075091109.
 NAVRÁTIL, M.  STARÁ, L. Matematika pro AF, ZF a FRRMS (1.část). [online]. 2009. URL: https://is.mendelu.cz/auth/eknihovna/slozky_objekty.pl?slozka=107;zobrazit=1484;typ=opora;lang=cz.
 NAVRÁTIL, M.  STARÁ, L. Matematika pro AF, ZF a FRRMS (2.část). [online]. 2011. URL: http://is.mendelu.cz/eknihovna/slozky_objekty.pl?slozka=107;zobrazit=2327;typ=opora.

Recommended reading list 
