Zachodniopomorski Uniwersytet Technologiczny w Szczecinie

Wydział Ekonomiczny - Economics (S1)
specjalność: Property Valuation and Real Estate Transactions

Sylabus przedmiotu Mathematics I:

Informacje podstawowe

Kierunek studiów Economics
Forma studiów studia stacjonarne Poziom pierwszego stopnia
Tytuł zawodowy absolwenta licencjat
Obszary studiów charakterystyki PRK
Profil ogólnoakademicki
Moduł
Przedmiot Mathematics I
Specjalność przedmiot wspólny
Jednostka prowadząca Katedra Zastosowań Matematyki w Ekonomii
Nauczyciel odpowiedzialny Joanna Perzyńska <joanna.perzynska@zut.edu.pl>
Inni nauczyciele Maciej Oesterreich <Maciej.Oesterreich@zut.edu.pl>
ECTS (planowane) 4,0 ECTS (formy) 4,0
Forma zaliczenia zaliczenie Język polski
Blok obieralny Grupa obieralna

Formy dydaktyczne

Forma dydaktycznaKODSemestrGodzinyECTSWagaZaliczenie
wykładyW1 20 1,60,50zaliczenie
ćwiczenia audytoryjneA1 30 2,40,50zaliczenie

Wymagania wstępne

KODWymaganie wstępne
W-1Knowledge of the advanced level mathematics from the secondary school

Cele przedmiotu

KODCel modułu/przedmiotu
C-1Students will gain basic knowledge of higher mathematics.
C-2Students will gain basic knowledge necessary to understand subjects using advanced mathematics techniques: statistics, operational research, quantitative methods in economics.
C-3Students will apply mathematical knowledge to the study of economic phenomena.

Treści programowe z podziałem na formy zajęć

KODTreść programowaGodziny
ćwiczenia audytoryjne
T-A-1Limits of numerical sequences and functions, continuity of functions8
T-A-2Test # 12
T-A-3Derivative of the one variable function6
T-A-4Local and global extrema of the one variable function6
T-A-5Course of variability of the one variable function6
T-A-6Test # 22
30
wykłady
T-W-1Limits of numerical sequences and functions4
T-W-2Continuity of functions2
T-W-3Derivative of the one variable function4
T-W-4Local and global extrema of the one variable function4
T-W-5Course of variability of one variable function4
T-W-6Test2
20

Obciążenie pracą studenta - formy aktywności

KODForma aktywnościGodziny
ćwiczenia audytoryjne
A-A-1Participation in classes.30
A-A-2Preparations for classes10
A-A-3Homework10
A-A-4Preparation for tests10
60
wykłady
A-W-1Participation in lectures20
A-W-2Preparation for lectures5
A-W-3Studying the literature5
A-W-4Preparation for the test10
40

Metody nauczania / narzędzia dydaktyczne

KODMetoda nauczania / narzędzie dydaktyczne
M-1Information-problem lecture.
M-2Exercises.

Sposoby oceny

KODSposób oceny
S-1Ocena formująca: Evaluation of activity during classes.
S-2Ocena formująca: Evaluation of individual problem solving during classes.
S-3Ocena formująca: Evaluation of homework solving (individually and in groups).
S-4Ocena podsumowująca: Test.

Zamierzone efekty uczenia się - wiedza

Zamierzone efekty uczenia sięOdniesienie do efektów kształcenia dla kierunku studiówOdniesienie do efektów zdefiniowanych dla obszaru kształceniaCel przedmiotuTreści programoweMetody nauczaniaSposób oceny
Ec_1A_B01_W01
The student knows the theoretical basis of the differential calculus of the one variable function.
Ec_1A_W07C-1, C-3, C-2T-W-1, T-W-3, T-W-4, T-W-5, T-W-2M-1S-4

Zamierzone efekty uczenia się - umiejętności

Zamierzone efekty uczenia sięOdniesienie do efektów kształcenia dla kierunku studiówOdniesienie do efektów zdefiniowanych dla obszaru kształceniaCel przedmiotuTreści programoweMetody nauczaniaSposób oceny
Ec_1A_B01_U01
The student can use the learned definitions and theorems of mathematical analysis to solve practical tasks.
Ec_1A_U01, Ec_1A_U11C-1, C-3, C-2T-A-1, T-A-3, T-A-4, T-A-5M-2S-2, S-1, S-3, S-4

Zamierzone efekty uczenia się - inne kompetencje społeczne i personalne

Zamierzone efekty uczenia sięOdniesienie do efektów kształcenia dla kierunku studiówOdniesienie do efektów zdefiniowanych dla obszaru kształceniaCel przedmiotuTreści programoweMetody nauczaniaSposób oceny
Ec_1A_B01_K01
The student has mastered the principles of self-solving problems
Ec_1A_K01C-1, C-3, C-2T-A-1, T-A-3, T-A-4, T-A-2, T-A-6, T-A-5M-1, M-2S-2, S-1, S-3, S-4

Kryterium oceny - wiedza

Efekt uczenia sięOcenaKryterium oceny
Ec_1A_B01_W01
The student knows the theoretical basis of the differential calculus of the one variable function.
2,0The student does not meet the requirements for a positive grade.
3,0The student explains in his own words the definitions and theorems from the studied areas of higher mathematics.
3,5The student correctly formulates definitions and theorems from the known sections of higher mathematics in mathematical language.
4,0Moreover, the student knows examples illustrating the known definitions and theorems.
4,5The student also knows geometric interpretation of the known definitions and theorems and conclusions resulting from them.
5,0The student also knows the economic interpretation of the definitions and theorems.

Kryterium oceny - umiejętności

Efekt uczenia sięOcenaKryterium oceny
Ec_1A_B01_U01
The student can use the learned definitions and theorems of mathematical analysis to solve practical tasks.
2,0The student does not meet the requirements for a passing grade.
3,0The student can: - calculate the limit of the arithmetic and geometrical sequence, - calculate the limit of a rational function, - calculate the derivative of the function of one variable based on formulas.
3,5The student is also able to: - calculate the limit of any function of one variable, - calculate the derivative of a function of one variable based on definitions, - calculate the derivative of any order based on formulae, - calculate global extrema of a function of one variable, - determine monotonicity intervals of functions of one variable.
4,0In addition, the student can independently: - examine the continuity of a function of one variable, - calculate the limit of a function of one variable based on de L'Hospital's rule, - determine asymptotes of functions of one variable, - determine inflection points and convexity and concavity intervals of functions.
4,5The student is also able to independently: - perform the above tasks using examples familiar from economics (e.g., determine the minimum of the cost function, determine and interpret asymptotes of the Tornquist demand function), - carry out a complete study of the course of variation of a function of one variable.
5,0The student is also able to independently: - perform the above tasks on new examples (different from those presented in class and assigned at home), - to carry out comprehensive checking, analysis and interpretation of obtained results, - suggest alternative methods of solving tasks.

Kryterium oceny - inne kompetencje społeczne i personalne

Efekt uczenia sięOcenaKryterium oceny
Ec_1A_B01_K01
The student has mastered the principles of self-solving problems
2,0The student has not mastered the principles of self-solving research problems
3,0The student solves research problems following the teacher's instructions.
3,5The student solves research problems using the teacher's few tips.
4,0The student is able to identify the methods needed to solve a defined problem, solves the tasks and is able to make a preliminary analysis of the results obtained.
4,5The student is able to identify the methods needed to solve a defined problem, solve problems, can make a preliminary analysis and present the obtained results.
5,0The student is able to identify all the methods needed to solve a defined problem, solves problems, can make a comprehensive analysis and presentation of the results obtained.

Literatura podstawowa

  1. Babula E., Czerwonka L., Zastosowanie matematyki w ekonomii i zarządzaniu / Mathematical applications in economics and management, Wydawnictwo Uniwersytetu Gdańskiego, 2015
  2. M.Pemberton, N.Rau, Mathematics for Economists, Manchester University Press, 2012
  3. SC Aggarwal, RK Rana, Basic Mathematics for Economists, FK Publications, 2010

Literatura dodatkowa

  1. Krysicki W., Włodarski L., Analiza matematyczna w zadaniach. cz.1 i 2., PWN, Warszawa, 2021
  2. Winnicki K., Miklewska J., Perzyńska J., Zbiór przykładów i zadań z matematyki dla studentów studiów zaocznych, AR, Szczecin, 2002

Treści programowe - ćwiczenia audytoryjne

KODTreść programowaGodziny
T-A-1Limits of numerical sequences and functions, continuity of functions8
T-A-2Test # 12
T-A-3Derivative of the one variable function6
T-A-4Local and global extrema of the one variable function6
T-A-5Course of variability of the one variable function6
T-A-6Test # 22
30

Treści programowe - wykłady

KODTreść programowaGodziny
T-W-1Limits of numerical sequences and functions4
T-W-2Continuity of functions2
T-W-3Derivative of the one variable function4
T-W-4Local and global extrema of the one variable function4
T-W-5Course of variability of one variable function4
T-W-6Test2
20

Formy aktywności - ćwiczenia audytoryjne

KODForma aktywnościGodziny
A-A-1Participation in classes.30
A-A-2Preparations for classes10
A-A-3Homework10
A-A-4Preparation for tests10
60
(*) 1 punkt ECTS, odpowiada około 30 godzinom aktywności studenta

Formy aktywności - wykłady

KODForma aktywnościGodziny
A-W-1Participation in lectures20
A-W-2Preparation for lectures5
A-W-3Studying the literature5
A-W-4Preparation for the test10
40
(*) 1 punkt ECTS, odpowiada około 30 godzinom aktywności studenta
PoleKODZnaczenie kodu
Zamierzone efekty uczenia sięEc_1A_B01_W01The student knows the theoretical basis of the differential calculus of the one variable function.
Odniesienie do efektów kształcenia dla kierunku studiówEc_1A_W07He / she knows and understands at an advanced level the issues in the field of quantitative methods (including mathematics, statistics, econometrics and decision-making theory) and examples of their applications in economic practice
Cel przedmiotuC-1Students will gain basic knowledge of higher mathematics.
C-3Students will apply mathematical knowledge to the study of economic phenomena.
C-2Students will gain basic knowledge necessary to understand subjects using advanced mathematics techniques: statistics, operational research, quantitative methods in economics.
Treści programoweT-W-1Limits of numerical sequences and functions
T-W-3Derivative of the one variable function
T-W-4Local and global extrema of the one variable function
T-W-5Course of variability of one variable function
T-W-2Continuity of functions
Metody nauczaniaM-1Information-problem lecture.
Sposób ocenyS-4Ocena podsumowująca: Test.
Kryteria ocenyOcenaKryterium oceny
2,0The student does not meet the requirements for a positive grade.
3,0The student explains in his own words the definitions and theorems from the studied areas of higher mathematics.
3,5The student correctly formulates definitions and theorems from the known sections of higher mathematics in mathematical language.
4,0Moreover, the student knows examples illustrating the known definitions and theorems.
4,5The student also knows geometric interpretation of the known definitions and theorems and conclusions resulting from them.
5,0The student also knows the economic interpretation of the definitions and theorems.
PoleKODZnaczenie kodu
Zamierzone efekty uczenia sięEc_1A_B01_U01The student can use the learned definitions and theorems of mathematical analysis to solve practical tasks.
Odniesienie do efektów kształcenia dla kierunku studiówEc_1A_U01He / she can use the possessed scientific knowledge to interpret socio-economic phenomena
Ec_1A_U11He / she can analyse the indicated solutions to specific problems and propose appropriate solutions in this regard
Cel przedmiotuC-1Students will gain basic knowledge of higher mathematics.
C-3Students will apply mathematical knowledge to the study of economic phenomena.
C-2Students will gain basic knowledge necessary to understand subjects using advanced mathematics techniques: statistics, operational research, quantitative methods in economics.
Treści programoweT-A-1Limits of numerical sequences and functions, continuity of functions
T-A-3Derivative of the one variable function
T-A-4Local and global extrema of the one variable function
T-A-5Course of variability of the one variable function
Metody nauczaniaM-2Exercises.
Sposób ocenyS-2Ocena formująca: Evaluation of individual problem solving during classes.
S-1Ocena formująca: Evaluation of activity during classes.
S-3Ocena formująca: Evaluation of homework solving (individually and in groups).
S-4Ocena podsumowująca: Test.
Kryteria ocenyOcenaKryterium oceny
2,0The student does not meet the requirements for a passing grade.
3,0The student can: - calculate the limit of the arithmetic and geometrical sequence, - calculate the limit of a rational function, - calculate the derivative of the function of one variable based on formulas.
3,5The student is also able to: - calculate the limit of any function of one variable, - calculate the derivative of a function of one variable based on definitions, - calculate the derivative of any order based on formulae, - calculate global extrema of a function of one variable, - determine monotonicity intervals of functions of one variable.
4,0In addition, the student can independently: - examine the continuity of a function of one variable, - calculate the limit of a function of one variable based on de L'Hospital's rule, - determine asymptotes of functions of one variable, - determine inflection points and convexity and concavity intervals of functions.
4,5The student is also able to independently: - perform the above tasks using examples familiar from economics (e.g., determine the minimum of the cost function, determine and interpret asymptotes of the Tornquist demand function), - carry out a complete study of the course of variation of a function of one variable.
5,0The student is also able to independently: - perform the above tasks on new examples (different from those presented in class and assigned at home), - to carry out comprehensive checking, analysis and interpretation of obtained results, - suggest alternative methods of solving tasks.
PoleKODZnaczenie kodu
Zamierzone efekty uczenia sięEc_1A_B01_K01The student has mastered the principles of self-solving problems
Odniesienie do efektów kształcenia dla kierunku studiówEc_1A_K01He / she is ready to define priorities for the implementation of tasks set by himself / herself or others
Cel przedmiotuC-1Students will gain basic knowledge of higher mathematics.
C-3Students will apply mathematical knowledge to the study of economic phenomena.
C-2Students will gain basic knowledge necessary to understand subjects using advanced mathematics techniques: statistics, operational research, quantitative methods in economics.
Treści programoweT-A-1Limits of numerical sequences and functions, continuity of functions
T-A-3Derivative of the one variable function
T-A-4Local and global extrema of the one variable function
T-A-2Test # 1
T-A-6Test # 2
T-A-5Course of variability of the one variable function
Metody nauczaniaM-1Information-problem lecture.
M-2Exercises.
Sposób ocenyS-2Ocena formująca: Evaluation of individual problem solving during classes.
S-1Ocena formująca: Evaluation of activity during classes.
S-3Ocena formująca: Evaluation of homework solving (individually and in groups).
S-4Ocena podsumowująca: Test.
Kryteria ocenyOcenaKryterium oceny
2,0The student has not mastered the principles of self-solving research problems
3,0The student solves research problems following the teacher's instructions.
3,5The student solves research problems using the teacher's few tips.
4,0The student is able to identify the methods needed to solve a defined problem, solves the tasks and is able to make a preliminary analysis of the results obtained.
4,5The student is able to identify the methods needed to solve a defined problem, solve problems, can make a preliminary analysis and present the obtained results.
5,0The student is able to identify all the methods needed to solve a defined problem, solves problems, can make a comprehensive analysis and presentation of the results obtained.