Study programmes / B-EMEN Economics and Management / Mathematics I
Course code:MT1A
Course title in language of instruction:Mathematics I
Course title in Czech:Matematika I v AJ
Course title in English:Mathematics I
Mode of completion and number of credits:Exam (5 credits)
(1 ECTS credit = 28 hours of workload)
Mode of delivery/Timetabled classes:full-time, period A 4/1, period B 2/1
(full-time, hours of lectures per week / hours of seminars per week)
Language of instruction:English
Level of course:bachelor
Semester:WS 2016/2017 - FBE
Name of lecturer:RNDr. Karel Mikulášek, Ph.D. (examiner, instructor, lecturer, supervisor)
Prerequisites:not Aplied Mathematics I
 
Aims of the course:Students should get an understanding of the basic concepta and methods of linear algebra and calculus. Solving suitable problems at workhops, they will prepare to tackle simple mathematical problems they may come across in practice.
Course contents:
1.Linear algebra (allowance 8/8)
 
a.Vector spaces
b.Matrices
c.Determinants
d.Systems of linear equations
e.Matrix algebra

2.Calculus (allowance 14/14)
 
a.Functions, properties of functions, parametric functions
b.Limits of functions, continuous functions
c.Derivatives of functions, methods of differentiating
d.Applications of derivatives, sketching the graph of a function
e.Sequences, power series

3.Integral calculus (allowance 6/6)
 
a.Rieman integral, antiderivative
b.Integration rules
c.Applications of integrals

Learning outcomes and competences:
Generic competences:
 
-ability to apply knowledge
-ability to solve problems
-ability to work independently
-basic computing skills
-general knowledge

Specific competences:
 
-Student is able to describe properties of function and analyze it. Furthermore, from graph derivate their properties.
-Student knows how to use operations with matrices and determinants for solving of systems of linear and matrix equations.
-Student knows to calculate limits and derivatives of one variable functions and interpret it on function graphs.
-Student knows to use derivatives for finding of extreme function values, i.e. its minimums and maximums.
-Student will acquire properties and operations with matrices and determinants. This knowledge is necessary for solving of linear programming problems.

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:At mid-term, in a written test, students are required to submit solutions to several practical problems for them to see the improvement needed. To complete the course a written test consisting of practical and theoretical parts is required. In the practical part, students have to solve 3 to 4 problems and, in the theoretical part, to give correct answers to 3 to 4 questions to see whether they have a good understanding of the background theory. The points obtained in both parts are then added. To pass the examination, a student has to achieve at least 50 percent of the total number of points.
 
Learning activities and study load (hours of study load)
Type of teaching methodDaily attendance
Direct teaching
     lecture28 h
     practice28 h
     seminar0 h
Self-study
     preparation for exam36 h
     preparation for regular assessment12 h
     preparation for regular testing36 h
     elaboration and execution of projects0 h
Total140 h

Basic reading list
  • BENCE, S. -- HOBSON, M. -- RILEY, K. Mathematical Methods For Physics and Engineering. Cambridge: Cambridge University Press, 2006. 1362 p. ISBN 978-0-521-86153-3.
  • LANG, S. A Firtst Course in Calculus. New York: Springer Verlag, 1993. 624 p. ISBN 0-387-96201-8.
  • STROUD, K. Engineering Mathematics. New York: Palgrave acmillan, 2001. 1220 p. ISBN 978-1-4039-4246-3.