Course syllabus MA2 - Mathematics II (ŠAVŠ - Sklad předmětů)

     Czech          English          

Course title: Mathematics II
Semester: -- item not defined --
Course supervisor: Mgr. Petr Kasal
Supervising department: Department of Quantitative Methods (ŠAVŠ)
Prerequisites for registration: not Bachelor state examination
Time allowance: full-time, 1/2 (hours of lectures per week / hours of seminars per week)
part-time, 0/16 (lectures per period / seminars per period)
Type of study: usual
Form of teaching: lecture, seminar
Mode of completion and credits: Fulfillment of requirements (4 credits), Exam (4 credits)
Course objective:
The goal of this course is to introduce basic notions in mathematics that are important in order to understand and apply exact methods of economics, and to explain mathematical tools which students will use during their studies of technical subjects.
The course builds on and further develops some topics from secondary school mathematics with regard to different levels of knowledge of students who graduated at secondary schools of various types. The course focuses on applications of mathematics in economic subjects as well as practical economic problems.
Course methods: Inductive and deductive method, problem solving method.
Course content:
1.Indefinite integral, antiderivative. (allowance 1/2)
a.Definition, rules and basic properties. Antiderivatives of basic functions.
b.Integration by parts.
d.Integration of reciprocal functions.

2.Definite (Riemann) integral. Improper integral. Applications of definite integrals. (allowance 1/2)
a.Definite integrals. Improper integrals. Examples.
b.Applications: areas of regions and volumes of solids of revolutions. Examples.
c.Applications in economics.

3.Functions of several variables - basic terms. Partial derivatives. Local, constrained and glogal extrema of functions of several variables. (allowance 1/2)
a.Definition and domains of functions of several variables.
b.Partial derivatives.
c.Local, constrained and glogal extrema of functions of several variables.
d.Optimizing examples in economics.

4.Linear algebra: Arithmetic vectors and matrices. (allowance 1/2)
a.Arithmetric vectors and operations. Linear combinations. Linear dependence and independence of vectors.
Arithemtic vector space. Definition, subspace, base, dimension, dot product, modulus of vectors, orthogonal vector
b.Matrices and operations with matrices. Properties of matrix multiplication.
c.Ranks of matrices.

5.Linear algebra: Homogeneous and nonhomogeneous systems of linear equations. Determinants. (allowance 1/2)
a.Homogeneous and nonhomogeneous systems of linear equations.
b.Frobenian theorem. Gaussian elimination.
c.Definition of determinants, basic properties and rules. Laplace theorem. Examples.
d.Cramer's rule

6.Inverse matrix. Matrix equations. (allowance 1/2)
a.Definition of an inverse matrix.
b.Methods of finding of an inverse matrix (elimination, adjung matrix).
c.Matrix equations.

Learning outcomes and competences:
After completing the course, student:
-Will apply mathematical software when solving more difficult exercises
-Will define and explain terms and tools used in all mentioned areas
-Will know tools of integral calculus and will apply them when solving general as well as practical exercises
-Will know tools of linear algebra used mainly when solving systems of linear equations
-Will know tools used during describing functions of several variables and will apply them when finding extrema of such functions

Teaching methods and workload (hours of workload):
Type of teaching methodDaily attendanceCombined form
Direct teaching
     Attendance of lectures12 h16 h
     Attendance of courses/seminars/tutorials24 h0 h
     Consultations with teacher (part-time form of study)0 h10 h
     Course reading and ongoing preparation36 h46 h
     Ongoing evaluation14 h14 h
     Composing of individual (seminar) work6 h6 h
     Preparation for final test20 h20 h
Total112 h112 h
Assessment methods:
Requirement typeDaily attendanceCombined form
Active lecture/seminar/workshop/tutorial participation5 %4 %
Term paper5 %5 %
Mid-term test(s)30 %31 %
Final test60 %60 %
Total100 %100 %
Course completion:
Attendance study:
attendance - when missing at most 2 classes 5 p. (missing 3 and more classes 0 p.)
activity during classes - 6 p.
term paper - 5 p.
1st test - 12 p.
2nd test - 12 p.

Combined study:
attendance - 4 p.
homework (4x4 tests) - 16 p.
term paper - 5 p.
test - 15 p.

Total points ............. 40 p. (required minimum 24 p.)

Final Exam - Test:

5 examples per 8 p. ...40 p.
4 theoretical questions per 5 p.... 20 p.

Total points .................... 60 p.

Points will be summed together (i.e. max. 100 p.).

less than 60 points unsatisfactory (failed, unsuccessful)
at least 60 points 3
at least 75 points 2
at least 90 points 1
Support for combined/distance forms of study:
-- item not defined --
Reading list:
Language of instruction: Czech
OTAVOVÁ, M. -- SÝKOROVÁ, I. Matematika k bakalářským zkouškám na VŠE . Praha: Ekopress, 2014. 180 p. ISBN 978-80-87865-15-6.
KLŮFA, J. Učebnice matematiky pro studenty VŠE. Praha: Ekopress, s.r.o., 2013. 188 p. ISBN 978-80-86929-97-2.
Language of instruction: English
STRANG, G. Calculus.  [online]. 2005. URL:
COLORADO, U. Linear Algebra: Vectors.  [online]. 2008. URL:
COLORADO, U. Linear Algebra: Matrices.  [online]. 2008. URL:

Language of instruction: Czech
KLŮFA, J. -- COUFAL, J. Matematika pro ekonomické fakulty 1. PRAHA: EKOPRESS, 2000.
HENZLER, J. -- KAŇKA, M. Matematika pro ekonomické fakulty 2. Praha: EKOPRESS, 2000. ISBN 80-86119-31-9.
BURDA, P. Matematika 1 - online.  [online]. 2008. URL:
HAMŘÍKOVÁ, R. Neřešené příklady z matematiky 1 - 3.  [online]. 2008. URL:
KREML, P. Matematika 2 - online.  [online]. 2008. URL:
KLŮFA, J. Matematika pro studenty VŠE. 1st ed. Praha: EKOPRESS, 2011. ISBN 978-80-86929-74-3.
BITTNEROVÁ, D. -- PLAČKOVÁ, G. Bittnerová, D. - Plačková, G.: Louskáček 2 - Integrální počet funkcí jedné reálné proměnné (sbírka úloh). TUL, Liberec 2009. Liberec: TUL, 2009. 154 p. ISBN 978-80-7372-531-0.

Study plans:
B-EM-BAL Business Administration and Operations, Logistics and Quality Management, full-time form, initial academic year WS 2013/2014
B-EM-BAL Business Administration and Operations, Logistics and Quality Management, part-time form, initial academic year WS 2013/2014
Track MBOE Marketing and Sales Management full-time form, initial academic year WS 2019/2020
Track BFRE Financial Management full-time form, initial academic year WS 2019/2020
B-PM Průmyslový management, full-time form, initial academic year WS 2019/2020
Run in the period of: SS 2019/2020, WS 2019/2020, SS 2018/2019, WS 2018/2019, SS 2017/2018, WS 2017/2018   (and older)
Course tutor: Mgr. Pavel Brom, Ph.D. (examiner, instructor)
Mgr. Radka Hakl Picková, Ph.D. (examiner, instructor, lecturer)
Mgr. Petr Kasal (examiner, instructor, supervisor)
Mgr. Petr Šulc (examiner, instructor)
Teaching language: Czech, English
Room: Mladá Boleslav

Last modification made by Ing. Aleš Kutín on 09/02/2019.

Type of output: