Wydział Ekonomiczny - Economics (S1)
Sylabus przedmiotu Mathematics II:
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 II | ||
| 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) | 5,0 | ECTS (formy) | 5,0 |
| Forma zaliczenia | egzamin | Język | polski |
| Blok obieralny | — | Grupa obieralna | — |
Formy dydaktyczne
Wymagania wstępne
| KOD | Wymaganie wstępne |
|---|---|
| W-1 | Knowledge of the advanced level mathematics from the secondary school |
Cele przedmiotu
| KOD | Cel modułu/przedmiotu |
|---|---|
| C-1 | Students will gain basic knowledge of higher mathematics. |
| C-2 | Students will gain basic knowledge necessary to understand subjects using advanced mathematics techniques: statistics, operational research, quantitative methods in economics. |
| C-3 | Students will apply mathematical knowledge to the study of economic phenomena. |
Treści programowe z podziałem na formy zajęć
| KOD | Treść programowa | Godziny |
|---|---|---|
| ćwiczenia audytoryjne | ||
| T-A-1 | Partial derivatives of the functions. | 4 |
| T-A-2 | Local and global extrema of two variable function. | 7 |
| T-A-3 | The integral of the one variable function. | 10 |
| T-A-4 | Differential equations. | 4 |
| T-A-5 | Test # 1. | 2 |
| T-A-6 | Matrices and determinants. Matrix equations. Systems of linear equations.. | 10 |
| T-A-7 | Test # 2. | 1 |
| 38 | ||
| wykłady | ||
| T-W-1 | Partial derivatives of the functions. | 2 |
| T-W-2 | Local and global extrema of two variable function. | 4 |
| T-W-3 | The integral of the one variable function. | 6 |
| T-W-4 | Differential equations. | 2 |
| T-W-5 | Matrices and determinants. | 4 |
| T-W-6 | Matrix equations | 4 |
| T-W-7 | Systems of linear equations | 3 |
| 25 | ||
Obciążenie pracą studenta - formy aktywności
| KOD | Forma aktywności | Godziny |
|---|---|---|
| ćwiczenia audytoryjne | ||
| A-A-1 | Participations in classes. | 38 |
| A-A-2 | Preparation for classes. | 10 |
| A-A-3 | Homework. | 7 |
| A-A-4 | Preparation for tests. | 20 |
| 75 | ||
| wykłady | ||
| A-W-1 | Participation in lectures. | 25 |
| A-W-2 | Preparation for lectures. | 6 |
| A-W-3 | Studying the literature. | 5 |
| A-W-4 | Preparation for exam. | 12 |
| A-W-5 | Exam | 2 |
| 50 | ||
Metody nauczania / narzędzia dydaktyczne
| KOD | Metoda nauczania / narzędzie dydaktyczne |
|---|---|
| M-1 | Information-problem lecture. |
| M-2 | Exercises. |
Sposoby oceny
| KOD | Sposób oceny |
|---|---|
| S-1 | Ocena formująca: Evaluation of activity during classes. |
| S-2 | Ocena formująca: Evaluation of individual problem solving during classes. |
| S-3 | Ocena formująca: Evaluation of homework solving (individually and in groups). |
| S-4 | Ocena podsumowująca: Test. |
| S-5 | Ocena podsumowująca: Exam. |
Zamierzone efekty uczenia się - wiedza
| Zamierzone efekty uczenia się | Odniesienie do efektów kształcenia dla kierunku studiów | Odniesienie do efektów zdefiniowanych dla obszaru kształcenia | Cel przedmiotu | Treści programowe | Metody nauczania | Sposób oceny |
|---|---|---|---|---|---|---|
| Ec_1A_B04_W01 The student knows the theoretical basis of the differential calculus of several variables functions, the integral calculus of the one variable function and linear algebra. | Ec_1A_W07 | — | C-3, C-1, C-2 | T-W-4, T-W-5, T-W-2, T-W-1, T-W-3, T-W-6, T-W-7 | M-1 | S-5 |
Zamierzone efekty uczenia się - umiejętności
| Zamierzone efekty uczenia się | Odniesienie do efektów kształcenia dla kierunku studiów | Odniesienie do efektów zdefiniowanych dla obszaru kształcenia | Cel przedmiotu | Treści programowe | Metody nauczania | Sposób oceny |
|---|---|---|---|---|---|---|
| Ec_1A_B04_U01 The student can use the learned definitions and theorems of mathematical analysis and linear algebra to solve practical tasks. | Ec_1A_U01, Ec_1A_U03, Ec_1A_U11 | — | C-3, C-1, C-2 | T-A-4, T-A-6, T-A-2, T-A-1, T-A-3 | M-2 | S-3, S-4, S-2, S-1, S-5 |
Zamierzone efekty uczenia się - inne kompetencje społeczne i personalne
| Zamierzone efekty uczenia się | Odniesienie do efektów kształcenia dla kierunku studiów | Odniesienie do efektów zdefiniowanych dla obszaru kształcenia | Cel przedmiotu | Treści programowe | Metody nauczania | Sposób oceny |
|---|---|---|---|---|---|---|
| Ec_1A_B04_K01 The student has mastered the principles of self-solving problems | Ec_1A_K01 | — | C-3, C-1, C-2 | T-A-4, T-A-6, T-A-2, T-A-1, T-A-5, T-A-7, T-A-3 | M-1, M-2 | S-3, S-4, S-2, S-1, S-5 |
Kryterium oceny - wiedza
| Efekt uczenia się | Ocena | Kryterium oceny |
|---|---|---|
| Ec_1A_B04_W01 The student knows the theoretical basis of the differential calculus of several variables functions, the integral calculus of the one variable function and linear algebra. | 2,0 | The student does not meet the requirements for a positive grade. |
| 3,0 | The student explains in his own words the definitions and theorems from the studied areas of higher mathematics. | |
| 3,5 | The student correctly formulates definitions and theorems from the known sections of higher mathematics in mathematical language. | |
| 4,0 | Moreover, the student knows examples illustrating the known definitions and theorems. | |
| 4,5 | The student also knows geometric interpretation of the known definitions and theorems and conclusions resulting from them. | |
| 5,0 | The student also knows the economic interpretation of the definitions and theorems. |
Kryterium oceny - umiejętności
| Efekt uczenia się | Ocena | Kryterium oceny |
|---|---|---|
| Ec_1A_B04_U01 The student can use the learned definitions and theorems of mathematical analysis and linear algebra to solve practical tasks. | 2,0 | The student does not meet the requirements for a passing grade |
| 3,0 | The student can: - calculate partial derivatives of two variables functions - calculate the indefinite integral of the elementary functions, - perform basic arithmetic operations on matrices, - calculate the second and third degree determinant. | |
| 3,5 | The student is furthermore able to independently: - calculate partial derivatives of any order of functions of many variables - calculate the indeterminate integral of a function of one variable by substitution and by parts, - calculate the signed integral, - solve a differential equation using the method of separation of variables, - calculate the determinant of any degree using Laplace's theorem, - calculate inverse matrix, - solve a system of linear equations using Cramer's theorem. | |
| 4,0 | The student is additionally able to: - determine local extremes of functions of two variables, - apply the integral to calculate the area, - solve a differential equation with separated variables under an initial condition, - solve a matrix equation, - determine the order of a matrix. | |
| 4,5 | The student is additionally able to: - determine global extrema of functions of two variables, - calculate the improper integral, - solve a linear non-homogeneous differential equation, - solve a system of linear equations based on Kronecker-Capelli theorem. | |
| 5,0 | The student is able to: - perform the above tasks on new examples (different from those presented in class and assigned to homework), - apply the partial derivative to determine selected economic quantities (e.g., marginal cost, elasticity of the production function), - apply the integral to determine the average of economic quantities, - perform a comprehensive check, analysis and interpretation of the results obtained, - propose alternative methods of solving tasks. |
Kryterium oceny - inne kompetencje społeczne i personalne
| Efekt uczenia się | Ocena | Kryterium oceny |
|---|---|---|
| Ec_1A_B04_K01 The student has mastered the principles of self-solving problems | 2,0 | The student has not mastered the principles of self-solving research problems |
| 3,0 | The student solves research problems following the teacher's instructions. | |
| 3,5 | The student solves research problems using the teacher's few tips. | |
| 4,0 | The 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. | |
| 4,5 | The 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. | |
| 5,0 | The 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
- Babula E., Czerwonka L., Zastosowanie matematyki w ekonomii i zarządzaniu / Mathematical applications in economics and management, Wydawnictwo Uniwersytetu Gdańskiego, 2015
- M.Pemberton, N.Rau, Mathematics for Economists, Manchester University Press, 2012
- SC Aggarwal, RK Rana, Basic Mathematics for Economists, FK Publications, 2010
Literatura dodatkowa
- Krysicki W., Włodarski L., Analiza matematyczna w zadaniach. cz.1 i 2., PWN, Warszawa, 2021
- Winnicki K., Miklewska J., Perzyńska J., Zbiór przykładów i zadań z matematyki dla studentów studiów zaocznych, AR, Szczecin, 2002