SYLLABUS
BUSINESS MATHEMATICS 1.
All courses, full time, year 1,
2013/2014– Autumn Term
SYLLABUS
Business Mathematics 1
All courses, full time, year 1
2013/2014 - Autumn Term
Course unit code: SZFNSGE001A AE
Department: Department for Economic Analysis Methodology
Tiszaliget, Main Building, Room 43. Phone: (56)516-068
e-mail address: [email protected]
Course unit leader: Madaras Lászlóné Dr., college professor
Tiszaliget, Main Building, Room 44. Phone: (56)516-068
e-mail address: [email protected]
Tutor(s): Name, title Madaras Lászlóné Dr., college professor
Office hours: Wednesdays 10.00- 11.00
Status: Methodological Core Module
Contact hours: 1+2
Credits: 4
Prerequisites A fairly good level of English
Venue: Tiszaliget, Main Building,
Time: Lecture: Odd Tuesday 09.45 – 11.15.
Seminar: Wednesdays 08.00 – 09.30 Aims and objectives
The course aims to make an introduction to the tools of Analysis. Topics range through differential and integral calculus of one variable to introductory calculus of two variables. We will show the power and usefulness of the calculus in economics and business applications.
By completing the course, students will be able to
understand the special language, notation, and point of view of Functions read, write, speak, and think in mathematical terms
put into practice the basic mathematical methods that have become indispensable for a proper understanding of the current economic literature
model and solve basic calculus problems in science
Course unit description
The course would like to make an introduction to Analysis and closely related topics such as continuity, differentiability and integration. These topics are studied in the context of real numbers and their functions. We will give students a working knowledge of calculus as well as an awareness of its important applications in today’s business life.
Course schedule
Please give a detailed, week-to-week description of your course unit. This should include the date and the topic of the session. This can be a short title, but you may give a more detailed content as well in two or three lines. You can also add readings and/or student tasks from week to week. If you have a seminar as well, complete the table with the appropriate number of rows and fill in seminar content as well.
Seminar 1.
Set Theory. Set Theory Operations. Some Special Sets of Numbers. Absolute value, Distance, Intervals, Neighbourhood. Countable and Uncountable Sets, the Cardinal Formula.
Chapter 1. Exercises 1.9. Lecture
1.
Introduction. The History of Calculus. What idea had led to its discovery? Why function has served as the principal quantitative language of science for more than four hundred years. Review of Precalculus Concepts. Infinite Sequences and Series.
Chapter 3, Chapter 4. Seminar
2.
Concept and Description of a Function. The Inverse of a Function. Composite Functions. Operations with Functions. Some Types of Functions.
Chapter 2. Exercises 2.9.
Seminar 3.
Some Types and Graphs of Functions. Chapter 2. (2.8)
Exercises 2.9. Lecture
2.
Limits of Functions. Continuity. Chapter 5, Chapter 6.
Seminar 4.
Infinite Sequences. The Concept of Real Number Sequence. The Description of Sequences. The Monotonousness and Limitedness of Sequences.
Chapter 3. (3.1-3.4) Exercises 3.5 Seminar
5.
Limiting Values. Operations with Convergent Sequences. The Concept of Infinite Series. Infinite Geometric Series.
Chapter 3. (3.4) 4. Exercises 4.3 Seminar
6.
Limits of Functions. Properties of Limits. One-Sided Limits. Limits at Infinity.
Chapter 5. Exercises 5.6. Lecture
3.
Differentiation of Functions. Rules for Differentiation. L’Hospital’s Rule. Higher Order Derivatives.
Chapter 6. Exercises 7.6. Seminar
8.
The Derivative. Techniques for Finding Derivatives. Higher Order Derivatives. L’Hospital’s Rule.
Chapter 7 Exercises 7.6.
Lecture 4.
Applications of the Derivative to graphing. Curve Sketching. Functions of Several Variables.
Chapter 8, Chapter 9. Seminar
9.
Increasing and Decreasing Functions. Extreme Points. Chapter 8. (8.1-8.2)
Seminar 10.
Concavity of a Graph. Inflection Points. The Examination of Differentiable Functions.
Chapter 8. (8.3-8.5) Lecture
5.
The Antiderivative. The Definite Integral. Applications of the Definite Integral.
Chapter 10, Chapter 11.. Seminar
11.
Applications of the Derivative to graphing. Chapter 8, 9
Seminar 12.
Functions of Two or More Variables. Partial Derivatives. Second-Order Partial Derivatives. Relative Maximum and Minimum.
Chapter 9. Exercises 9.6
Lecture 6.
The Definite Integral. Applications of the Definite Integral. Chapter 10, Chapter 11..
Seminar 13.
The Antiderivative. Some Integration Techniques. Integration by Parts, Integration by Substitution.
Chapter 10. Exercises 10.6
Lecture: Linear Algebra. Matrices. Matrix Applications. Mathematics for Economic Analysis, Chapter 12.
. Seminar 14. Linear Algebra. Matrices. Mathematics for Economic Analysis, Chapter 12. (12.2, 12.6-12.9)
Seminar 15. Matrix Applications.
Mathematics for Economic Analysis, Chapter 12. (12.2, 12.6-12.9
Methodology
There will be one hour of lecture and two hours of seminars a week. The theory will be delivered and elaborated in interactive lectures. Learning will be facilitated through Power Point presentations. The seminars will be very practice oriented. We will focus on problem-solving in real-life situations. Active seminar participation and regular home work is expected from students.
Assessment and grading
The assessment will be based on points reached from three test-papers or exam-test. Grades will be given according to the following pattern:
First test paper: 40 points
Second test paper: 40 points
Third test paper: 20 points
Total (or exam-test): 100 points 0 - 50 points 1 fail 51 - 66 points 2 pass
67 - 78 points 3 satisfactory 79 - 89 points 4 good 90 - 100 points 5 excellent
Course policies
Sessions will be student-centred and participation of students will be encouraged in solving business problems.
Compulsory readings
Knut Sydsaeter Peter J. Hammond: Mathematics for Economic Analysis. Prentice hall, Upper Saddle River, New Jersey 07458
Study-aid to Business Mathematics I. by Lászlóné Madaras Dr. Szolnok, 2007. Mathematics Problem Book by Ildikó Reisch and László Szigeti, International
Business School Budapest, 2001 Handouts
Recommended readings
Calculus. A Short Course with Application by Gerald Freilich and Frederick P. Greenleaf, 1985, by Harcourt Brace Joanovich, publishing
Business Mathematics I. by Norbert Hegyvári, published by Budapest Business School, Faculty of Commerce, Catering and Tourism, Distributed by Student Kft, Budapest
Calculus by Dennis D. Berkley and Paul Blanchard, 1992, by Saunders College Publishing
Calculus with Applications by Dale Varberg and Walter Fleming, Published by Prentice-Hall, Inc. 1991
16.09.2013. Szolnok
Madaras Lászlóné Dr. College professor
