Study programmes / B-PPR Plant Protection / Rudiments of Higher Mathematics
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:full-time, 1/2
(full-time, 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)
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 methodDaily attendance
Direct teaching
     lecture14 h
     practice28 h
     preparation for exam42 h
     preparation for regular testing28 h
Total112 h

Basic reading list
Recommended reading list
  • MAŘÍK, R. Robert Mařík's eReadings on Mathematics.  [online]. 2006. URL:
  • Calculus with analytic geometry. 2nd ed. New York: McGraw-Hill, 1996. 887 p. ISBN 0-07-057642-4.