Intézmény neve
Cím: 1148 Budapest,
Nagy Lajos király útja 1-9.
Tel.:
06-1-2733090
Fax:
06-1-2733099
E-mail: [email protected]
Course-unit Programme
(Regular Full-time Course Syllabus)
1.
Course-unit details:
Name of course-unit (subject): Calculus for Business and Economics I.
Language of instruction (from sample unit): English
Name of course-unit in Hungarian (from sample unit): Gazdasagi matematika I.
ETR (USRS) course-unit code (subject unit):
Validity of course-unit (from subject):
o
date of launch of course-unit: autumn/spring term of academic year 2009/2010
o
Date of termination of course-unit:
Credit value of course unit (from course-unit element) :
……… credits
Institute offering the course-unit (from subject):
Instructor responsible for course-unit (from subject):
o
name: Kovacs Tamas
o
Ministry of Education Registry number*:
o
SIN code*:
Course-unit group (subject DTL):
Course-unit type (subject unit):
o
lecture and practical class to be completed together
Course-unit term requirements (subject unit):





o
examination
o
practical grade based on a scale from 1 to 5
o
mid-term classroom test at practical class + exam (pre-condition of applying
for the exam is at least a 50% performance at the practical class)
These data are generated by ETR (USRS).
These data are generated by ETR (USRS).
These data are generated by ETR (USRS).
These data are generated by ETR (USRS).
These data are generated by ETR (USRS).
Intézmény neve
Cím: 1148 Budapest,
Nagy Lajos király útja 1-9.
Tel.:
06-1-2733090
Fax:
06-1-2733099
E-mail: [email protected]
o
practical grade based on a three-grade scale
Number of contact hours attached to the course-unit (subject unit):
Number of theoretical classes (lectures): 2 classes/week
Number of practical classes (seminars):
2 classes/week
Number of training classes:
0 classes/term
Content features of course-unit:

Teaching objectives of course-unit (description of 2-3 lines) (sample unit): The
objective of the course is to equip students with the mathematical tools necessary for
following core economic and business subjects and solving analytical problems in
Economics.

The topics and detailed syllabus of the factual content of the course-unit in a weekly
breakdown (sample unit):
Detailed curriculum:
1. week Sequences in economics, financial computations
Lecture: Geometric progression. Economic application of finite
sequences: compounded interest, chasing power, inflation, etc.
Seminar: Determining compound interests, comparison at price offers,
calculation of rents.
2. week Limits of functions
Lecture: Limit of a function at finite arguments and at the infinity.
Continuity. Link between the limit and the graph of a function.
Seminar: Limit of functions at finite arguments and at the infinity. Left and
right limits.
3. week Differential calculus
Lecture: Derivative of a function at a given argument. Intuitive
understanding of the concept of derivative. Differentiability and continuity.
Derivatives of elementary functions. Differentiation rules. The L'Hopital
formula.
Seminar: Abstract derivatives. Differentiation of sum, products, quotients,
and compositions of functions.
4. week Applied differential calculus
Lecture: Elasticity. Analysis of single variable functions (domain, range,
limit, derivative, monotonicity, stationary points, etc.)
Seminar: Exercises for the L'Hopital formula. Determining the elasticity of
a function. Monotonicity and extrema of single variable real functions.
Intézmény neve
Cím: 1148 Budapest,
Nagy Lajos király útja 1-9.
Tel.:
06-1-2733090
Fax:
06-1-2733099
E-mail: [email protected]
5. week Function analysis
Lecture: Analysis of single variable real functions. Second derivative and
convexity. Inflection points. Function analysis on computer – WinPlot.
Seminar: Complete analysis of functions using derivatives. Monotonicity,
extrema, convexity, inflection points. Plotting graphs of a function.
6. week Function analysis
Lecture: Analysis of single variable real functions. Function analysis on
computer – GeoGebra.
Seminar: First part of the seminar: 1st mid-term exam (30 min.) Second
part: Complete analysis of functions using derivatives. Monotonicity,
extrema, convexity, inflection points. Plotting graphs of a function.
7. week Economic applications for differentiation
Lecture: Analysis of distinguished functions used in economics. Total
profit and marginal profit. Partial production function, average and
marginal products. Cost functions. Total revenue and marginal revenue.
Function analysis on computer – GeoGebra.
Seminar: Solving maximization and minimization problems in economics.
8. week Multivariable functions
Lecture: Bivariable functions. Graphical representation through level
curves and contour sets. Bivariate differential calculus. Interpretation of
partial derivatives. Checking of the global and local extrema of bivariate
functions. Plotting bivariate functions on computer. Production functions.
Seminar: Partial differentiation. Extrema of bivariate functions.
9. week Integral calculus
Lecture: Concept of the primitive function. Indefinite integrals. Indefinite
integrals of elementary functions. Integration rules. Definite integrals.
Properties of definite integrals. The Newton-Leibnitz rule. Geometrical
interpretation of definite integral. Determining the area – GeoGebra.
Seminar: Determining definite integrals. Exercises for area calculation.
10. week An introduction to model building
Lecture: Model construction (mathematical models of replacement and
maintaince, queuing transportation), graphical solutions of bivariate linear
programming problems.
Seminar: First half of the seminar: 2nd mid-term exam (40 min.)
Second half: simulation, graphical solutions
11. week Linear programming – Graphical solutions
Lecture: Mathematical modeling, graphical solutions using GeoGebra.
Seminar: simulation, graphical solutions
12. week SUMMARY
Lecture: Systematic overview and summary of the course material.
Function analysis on computer. Solving exercises for the end-term exam.
Seminar: RETAKE EXAM (30-40 minutes)
Intézmény neve
Cím: 1148 Budapest,
Nagy Lajos király útja 1-9.
Tel.:
06-1-2733090
Fax:
06-1-2733099
E-mail: [email protected]
For those who do not need to retake any mid-term exam: practising
exercises. Second half: discussion of exercises.
List of practical tasks required to fulfil the term requirements of the practical class:
o
Classroom test
Mid-term exams (50 points)
 Students are required to take the mid-term exams. The firs one (for 20
points) will take place on week 6, the second one (for 30 points) on week
10. The total score obtained at the two mid-term exams counts as the final
(end-term) score. The criteria being admitted to the end-term exam are: 1)
participation at seminars; 2) achieving a minimal total score 25 at the two
mid-term exams; 3) completing the assigned work.
 Those who have obtained a total score of less than 25 points are allowed to
do an exam retake on week 12. The retake exam is also for 20 or 30 points,
respectively, depending on which mid-term exam will be replaced. In this
case the original score of mid-term exam is canceled. Only those who have
taken at least one of the two mid-term exams are admitted to the exam
retake.
Students are not allowed to miss (without a legitimate and officially proven reason)
more than three seminars; otherwise their automatically fail the course and must retake
it.
o
Presentation
o
Essay to be submitted
Detailed description of the methods applied to evaluate and grade student performance at
a lecture:
o
Option to take a preliminary exam the last week of term-time
o
Written exam
end-term exam (40 points)
 Admittance to the end-term exam is conditional on 1) regular participation
on seminars; 2) a minimal total score of 25 points obtained at mid-term
exams; 3) completion of the assigned work until the given date.
At the end-term exam students are examined for their knowledge of the mathematical
theory covered at lectures and their ability to solve related exercises. The end-term
exam is successful when the sum of the obtained score and the score of the assigned
work is not less than 50%.
Assigned work (10 points)

Competition of the assigned work is required to admittance for the end-term
exam. The assigned work will be published on CooSpace and also told
about at lectures. The deadline for submitting the completed assigned work
is the last day of the pre-exam study period. The maximal score one can
Intézmény neve
Cím: 1148 Budapest,
Nagy Lajos király útja 1-9.
Tel.:
06-1-2733090
Fax:
06-1-2733099
E-mail: [email protected]
obtain with assigned work is 10 points depending on the development of
the work. The total score of the end-term exam also contains the result of
the assigned work.
Grading: The final score (total score obtaining for the mid-exams + assigned work + end-term
exam) is converted to a 5 scale grade on the following basis:
0 – 49 points
50 – 62 points
63 – 75 points
76 – 88 points
89 – 100 points
fail (1)
pass (2)
satisfactory (3)
good (4)
excellent (5)
Reading material necessary to complete the course-unit:
List of mandatory readings:
Textbook:
Title: Mathematics for Economists [Chapters: 1--9,14,19,20]
Authors: Pemberton, M. and Rau, N.
Publisher: Manchester Univ. Press
Place of publishing: Manchester, UK
Year: 2001
Number of pages: 615
ISBN: 0-7190-3341-1
Textbook:Title:
Author: W.L. Winston
Year: 2004
Operations research [Chapters: 1,3,4]
Publisher:Thomson Brooks
Number of pages:1348
Exercises:
Title: Thomas' Calculus [Chapters: 2,3,4,5,8,11,14]
Authors: Thomas, G.B.; Weir, M.; Hass, J.R.; Giordano, F.
Publisher: Pearson Education
Place of publishing: Canada
Year: 2004
Number of pages: 984
ISBN: 0-3212-2642-9