Course syllabus MA1 - Mathematics I (ŠAVŠ - WS 2019/2020)

     Czech          English          

Course title: Mathematics I
Semester: WS 2019/2020
Course supervisor: Mgr. Radka Picková, Ph.D.
Supervising department: Department of Informatics and Quantitative Methods (ŠAVŠ)
Prerequisites for registration: not Bachelor state examination
Time allowance: full-time, 2/2 (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 (5 credits), Exam (5 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 methods, problem solving method.
 
Course content:
1.Basics of mathematical logic, sets and set operations. Number sets. (allowance 1/1)
 
a.Review of secondary school mathematics.
b.Basics of mathematical logic. Sets and set operations.

2.Basic functions and their transformations. (allowance 1/1)
 
a.Properties and graphs of linear, quadratic, and reciprocal functions.
b.Transformations of functions. Functions with absolute value.

3.Functions of one real variable and their properties. Compound function. Inverse function. (allowance 1/1)
 
a.The domain and the range of a function. Properties of functions
b.Power functions, exponential and logarithmic functions.
c.Definition of compound functions. Definition of the inverse function.

4.Sequences and their limits. Series. (allowance 1/1)
 
a.Basic properties of sequences.
b.Arithmetic and geometric sequences.
c.Limits of sequences.
d.Series. Geometric series. Convergence.

5.Limits of functions. Continuity of a function. (allowance 1/1)
 
a.Definition and properties of limits of functions.
b.Computation of limits of functions.
c.Continuous functions.

6.Derivative of a function. Powers and polynomial functions. (allowance 1/1)
 
a.Definition of derivative, basic properties and rules for computation.
b.Derivatives of powers and polynomial functions.
c.Using the first derivative for plotting graphs of functions.
d.Monotonicity and local extrema.

7.The second derivative of a function. Powers and polynomial functions. (allowance 1/1)
 
a.Using the second derivative for plotting graphs of functions.
b.Intervals of convexity and concavity, points of inflections.
c.Plotting graphs of powers and polynomial functions.

8.Rational functions. Asymptotes. (allowance 1/1)
 
a.The domain and range of rational functions.
b.One-sided limits.
c.Vertical, horizontal and oblique asymptotes.

9.Derivative of a product and a ratio of two functions. Derivative of a compound function. (allowance 1/1)
 
a.Derivative of a product of two functions.
b.Derivative of a ratio of two functions.
c.Plotting graphs of functions that are given as a product, or a ratio, of two functions.
d.Derivative of compound functions.
e.Plotting graphs of compound functions.

10.L'Hopital's rule. Trigonometric and inverse trigonometric functions. (allowance 1/1)
 
a.Computing limits using L'Hospital rule.
b.Trigonometric functions.
c.Inverse trigonometric functions.

11.Economic applications. Global extrema. (allowance 1/1)
 
a.Examples of functions used in economics.
b.Global extrema (on a bounded interval).

12.Reserve. (allowance 1/1)
 
a.Review and preparation for the final exam.

 
Learning outcomes and competences:
After completing the course, student will be able to:
 
-Will apply mathematical software when solving more difficult exercises
-Will define and explain terms and tools used during describing functions of one real variable and will clarify their relation
-Will determine basic properties of functions of one real variable
-Will draw, transform and use graphs of elementary functions
-Will know tools of differential calculus used during describing functions of one real variable and will apply them when solving practical exercises

Teaching methods and workload (hours of workload):
Type of teaching methodDaily attendanceCombined form
Direct teaching
     Attendance of lectures24 h16 h
     Attendance of courses/seminars/tutorials24 h0 h
     Consultations with teacher (part-time form of study)0 h10 h
Self-study
     Course reading and ongoing preparation48 h60 h
     Ongoing evaluation16 h8 h
     Composing of individual (seminar) work6 h6 h
     Preparation for final test22 h40 h
Total140 h140 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.).

EVALUATION:
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:
Basic:
Language of instruction: Czech
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
DAWKINS, P. Paul's Online Math Notes - Calculus I.  [online]. 2003. URL: http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx.
STRANG, G. Calculus.  [online]. 2005. URL: https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/.

Recommended:
Language of instruction: Czech
COUFAL, J. -- KLŮFA, J. Matematika pro ekonomické fakulty 1. 1st ed. Praha: EKOPRESS, 2000. 405 p. ISBN 80-86119-30-0.
KAŇKA, A M. -- HENZLER, J. Matematika pro ekonomy 2. EKOPRESS, 1997.
BURDA, P. Matematika 1 - online.  [online]. 2008. URL: http://www.studopory.vsb.cz/studijnimaterialy/MatematikaI/MI.html.
HAMŘÍKOVÁ, R. Neřešené příklady z matematiky 1 - 3.  [online]. 2008. URL: http://www.studopory.vsb.cz/studijnimaterialy/Sbirka_uloh/index.html.
BITTNEROVÁ, D. -- PLAČKOVÁ, G. Louskáček 1.: Diferenciální počet funkcí jedné reálné proměnné. 2nd ed. Liberec: TU Liberec, 2006. 140 p. ISBN 978-80-7372-158-9.
KLŮFA, J. Matematika pro studenty VŠE. 1st ed. Praha: EKOPRESS, 2011. ISBN 978-80-86929-74-3.

Study plans:
B-FRE Business Administration - Major in Financial Management, full-time form, initial academic year WS 2019/2020
Track BMO Marketing and Sales Management part-time form, initial academic year WS 2019/2020
Track BLMK Logistics and Quality Management part-time form, initial academic year WS 2019/2020
Track BMO Marketing and Sales Management full-time form, initial academic year WS 2019/2020
Track BFR Financial Management full-time form, initial academic year WS 2019/2020
B-LMK Business Administration - Major in Logistics and Quality Management, part-time form, initial academic year WS 2019/2020
Track BFR Financial Management full-time form, initial academic year WS 2019/2020
B-FR Business Administration - Major in Financial Management, full-time form, initial academic year WS 2019/2020
Track MBOE Marketing and Sales Management full-time form, initial academic year WS 2019/2020
Track BLMKE Logistics and Quality Management full-time form, initial academic year WS 2019/2020
Track BFRE Financial Management full-time form, initial academic year WS 2019/2020
B-MOE Business Administration - Major in Marketing and Sales Management, full-time form, initial academic year WS 2019/2020
B-LMKE Business Administration - Major in Logistics and Quality Management, full-time form, initial academic year WS 2019/2020
Track BFR Financial Management part-time form, initial academic year WS 2019/2020
Track BLMK Logistics and Quality Management full-time form, initial academic year WS 2019/2020
B-MO Business Administration - Major in Marketing and Sales Management, part-time form, initial academic year WS 2019/2020
B-FR Business Administration - Major in Financial Management, part-time form, initial academic year WS 2019/2020
B-MO Business Administration - Major in Marketing and Sales Management, full-time form, initial academic year WS 2019/2020
B-FR Business Administration - Major in Financial Management, full-time form, initial academic year WS 2019/2020
B-PM Průmyslový management, full-time form, initial academic year WS 2019/2020
B-PEMI Podniková ekonomika a manažerská informatika, full-time form, initial academic year WS 2019/2020
B-LMK Business Administration - Major in Logistics and Quality Management, full-time form, initial academic year WS 2019/2020
 
Run in the period of: SS 2018/2019, WS 2018/2019, SS 2017/2018, WS 2017/2018, SS 2016/2017, WS 2016/2017   (and older)
Course tutor: Mgr. Iva Bímová (examiner, instructor)
Mgr. Pavel Brom, Ph.D. (examiner, instructor, lecturer)
Mgr. Radomír Holan (examiner, instructor)
Mgr. Petr Kasal (examiner, instructor, lecturer, tutor)
Mgr. Radka Picková, Ph.D. (examiner, instructor, supervisor)
Mgr. Petr Šulc (examiner, instructor)
Teaching language: Czech, English
Room: Mladá Boleslav, Praha


Last modification made by Mgr. Luděk Švejdar on 05/10/2019.

Type of output: