Course outline
Course unit title
Business Mathematics
Name(s), surname(s) and title
of lecturer(s)
Level of course
Prof. dr. Linas Čekanavičius
Semester
ECTS credits
Student working hours
Prerequisites
Language of instruction
Objectives of the course
2
5
Contact hours
Lectures
Seminars
Practical hours
Laboratory hours
Consultations
Independent work
Total
Microeconomics
English, Lithuanian
Learning outcomes
Should match study program
objectives
A student’s knowledge,
comprehension and skills
The objective of the course is
to introduce students to the key
concepts of Higher Mathematics
and develop their skills to apply
the knowledge of mathematics
for the analysis and solution of
various business and economic
problems.
Knowledge and
comprehension:

 Mastering of the main
concepts and techniques of
higher mathematics
(matrix algebra and
calculus),
 Comprehension of the

significance and essence of
application of the learned
techniques of matrix
algebra and calculus to
economic analysis,
business planning and
decision making.
Application skills:
 Have skills to conduct
operations with matrices
and sets, to identify the
analytic expression of the
linear function, to find
Cycle 1
48
16
16
16
82
130
A student’s assessments
methods
In which activity study results
are demonstrated and proved
Group and individual
class work, as well as three
auditorials, that will foster
student skills to perfom
operations with matrices,
sets and functions
Mid-term and final exams,
that will require application
of learned mathematical
techniques to given business
and economics problems:
students are expected to
select an appropriate
mathematical model for the
solution of a given business
or economic problem,
effectively convert initial
data into a mathematical
form, apply a relevant
computation sequence and
Teaching methods
Course unit content
List of Topics
derivatives of functions
evaluate the economic
with single and several
substance of the obtained
variables, to perform
result.
unconstrained and
constrained optimisation
of functions;
 Ability to convert the
unstructured real-world
situation into numerical
problem and to employ
relevant mathematical
methods for its analysis
and decision making
 Ability to translate the
results of mathematical
analysis and computations
back to the real world.
Study methods: problem teaching; combination of theoretical
insight with the modelling of practical (simulated) cases;
collective and individual analysis and solution of the simulated
economic and business problems.
In-class performance is based on the principle of combination of
lectures and tutorials: theoretical insights are immediately
followed by the analysis and solution of simulated business and
economic problems. In order to encourage active participation in
learning, at the end of every topic students should be ready to
the concise check in writing of acquired knowledge and skills.
The aim of the course is to equip undergraduate students
with foundation in mathematical methods that can be useful
–and, in some cases, indispensable- for economic analysis,
business planning and decision making. Course is designed
specifically to meet the demand for a compact and relevant
training in mathematical techniques that are applicable for
business and economic problems. An underlying approach
of the course is that mathematics should provide a set of
techniques which can be usefully employed for (a) better
understanding of various business-related disciplines, and
(b) analysis and decision making. Therefore the “style” of
the course is rather informal and application oriented:
mathematical concepts are presented by as-brief-as-possible
theoretical explanations, relaying on a minimum of proofs
and derivations. Economic or business related examples are
introduced at the early stages of each topic.
Topic title
Introductory lecture: course
objectives, study and assessment
forms and requirements.
Contact
hours
Assignments
and
independent
study hours
2
-
Matrices: basic concepts;
transposition, addition,
subtraction, scalar multiplication
and multiplication of matrices,
inverse matrix.
Application of matrix algebra to
the economic/business problems:
equilibrium models. Cramer’s
rule.
4
Leontjev “input-output” model.
Leontjev matrix.
6
Set theory. The algebra of sets and
its applications
2
Mathematical functions: an
introduction. Linear functions.
Determination of the linear
function. “Break-Even” analysis.
4
Differential calculus: derivatives,
rules of differentiation, higherorder derivatives
2
Applications of differential
calculus: unconstrained
optimization of functions with one
independent variable,.
Functions with several
independent variables. Partial
derivatives.
6
Applications of differential
calculus: unconstrained
optimization of functions with
more than one independent
variable.
Applications of differential
calculus: constrained
optimization. Method of
Lagrangian multipliers
Total:
6
6
Tasks on
operations
with matrices
6
10
Solution of
economic
equilibrium
tasks
10
Solution
„Input-output“
tasks
4
Set theory
application
tasks
6
Identification
of demand
function and
other linear
functions
6
Finding
derivatives of
a singlevariable
function
12
Unconstrained
optimisation
tasks
4
6
Finding
derivatives of
a function
with two
independent
variables
12
Unconstrained
optimisation
tasks
6
48
10
Constrained
optimisation
tasks
82
Reading list
Year of
publishing
2009
Authors and title of the publication
Publishing house
Jacques I. Mathematics for Economics and
Prentice Hall
Business, 6th ed.
2002
Bradley, T. and Patton, P. (eds.) Essential
John Wiley and Sons Ltd
Mathematics for Economics and Business (2nd
ed.)
McGraw-Hill Higher Education
2008
Taylor, R., Hawkins, S. Mathematics for
Economics and Business
Assessment form: mid-term (written), auditorial (written) and the
Assessment requirements
final examination (written). During them students will have to
solve several practical tasks, i e. to apply the learned
mathematical techniques to the simulated economics and
business problems. Students’ active performance in the in-class
solution of assignments is also rewarded. To earn pass, the
weighted sum of the points for the subject, collected during the
semester, has to exceed 40% of the total. There are no additional
'threshold' score requirements for the separate assessment form.
Ability to „diagnose“ economic or business decision problem and
Assessment criteria
converse it into the relevant mathematical form, to perform
mathematical computations and interpret obtained results. Student
performance is assessed on a 0-100 point scale.
The final grade will be determined by the weighted sum of points
The composition of final
earned by the student during the course. The weight of mid-term
accumulative mark
is 30%, end-term exam – 50%, and 20% weight will be assigned
to the points earned during auditorial that will take place during
lectures/tutorials. Furthermore, extra points can be earned by the
active participation in the class work, e.g. solving given
numerical examples. The value of final grade will depend on the
particular decile (in the scale 1…100) to which the weighted sum
of points belongs.
Linas Čekanavičius
Course outline arranged by
Approved by the Study Program 2014-08-20
Committee