Cycle of education: 2022/2023
The name of the faculty organization unit: The faculty Chemistry
The name of the field of study: Chemical and process engineering
The area of study: technical sciences
The profile of studing:
The level of study: first degree study
Type of study: full time
discipline specialities : Hydrogen technologies, Processing of polymer materials , Product design and engineering of pro-ecological processes
The degree after graduating from university: Bachelor of Science (BSc)
The name of the module department : Department of Mathematics
The code of the module: 266
The module status: mandatory for teaching programme Hydrogen technologies, Processing of polymer materials , Product design and engineering of pro-ecological processes
The position in the studies teaching programme: sem: 1, 2, 3 / W75 C75 / 15 ECTS / E,E,Z
The language of the lecture: Polish
The name of the coordinator: Millenia Lecko, PhD
office hours of the coordinator: Według harmonogramu pracy jednostki.
semester 1: Justyna Madej, MSc , office hours According to the work schedule of the unit.
semester 2: Mariola Walczyk, PhD
The main aim of study: Explore the basic messages and methods Linear Algebra and Mathematical Analysis. Development of mathematical knowledge and ability to solve basic mathematical and technical problems with the help of mathematical apparatus.
The general information about the module: The module is implemented in the first and second semester. In the first and second semester there are 30 hours of lectures and 30 hours tutorials. Both in the first and second semester the module ends with an exam.
1 | M. Gewert, Z. Skoczylas | Analiza matematyczna 1, definicje, twierdzenia, wzory | Oficyna Wydawnicza GiS Wrocław . | 2006 |
2 | M. Gewert, Z. Skoczylas | Analiza matematyczna 2, definicje, twierdzenia, wzory | Oficyna Wydawnicza GiS Wrocław . | 2006 |
3 | M. Gewert, Z. Skoczylas | Algebra liniowa 1, definicje, twierdzenia, wzory | Oficyna Wydawnicza GiS, Wrocław. | 2006 |
4 | M. Gewert, Z. Skoczylas | Równania różniczkowe zwyczajne. teoria, przykłady, zadania | Oficyna Wydawnicza GiS, Wrocław. | 2002 |
5 | S. Łanowy, F. Przybylak, B. Szlęk | Równania różniczkowe | Wydawnictwo Politechniki Śląskiej, Gliwice. | 2002 |
1 | W. Krysicki, L. Włodarski | Analiza matematyczna w zadaniach, część I i II | PWN Warszawa. | 2004 |
2 | S. Łanowy, F. Przybylak, B. Szlęk | Równania różniczkowe | Wydawnictwo Politechniki Śląskiej, Gliwice. | 2002 |
3 | J.Niedoba, W. Niedoba ; pod red. Bogdana Choczewskiego | Równania różniczkowe, zwyczajne i cząstkowe : zadania z matematyki | Kraków : AGH Uczelniane Wydawnictwa Naukowo-Dydaktyczne. | 2001 |
4 | praca zbiorowa pod red. L. Siewierskiego | Ćwiczenia z analizy matematycznej z zastosowaniami, Tom II | PWN, Warszawa. | 1981 |
1 | M. Gewert, Z. Skoczylas | Analiza matematyczna 1, przykłady i zadania | Oficyna Wydawnicza GiS, Wrocław. | 2006 |
2 | M. Gewert, Z. Skoczylas | Analiza matematyczna 2, przykłady i zadania | Oficyna Wydawnicza GiS, Wrocław. | 2006 |
3 | M. Gewert, Z. Skoczylas | Algebra liniowa 1, przykłady i zadania | Oficyna Wydawnicza GiS, Wrocław. | 2006 |
4 | M. Gewert, Z. Skoczylas | Równania różniczkowe zwyczajne. teoria, przykłady, zadania | Oficyna Wydawnicza GiS, Wrocław. | 2002 |
5 | S. Łanowy, F. Przybylak, B. Szlęk | Równania różniczkowe | Wydawnictwo Politechniki Śląskiej, Gliwice. | 2002 |
6 | J.Niedoba, W. Niedoba ; pod red. Bogdana Choczewskiego | Równania różniczkowe, zwyczajne i cząstkowe : zadania z matematyki | Kraków : AGH Uczelniane Wydawnictwa Naukowo-Dydaktyczne. | 2001 |
7 | praca zbiorowa pod red. L. Siewierskiego | Ćwiczenia z analizy matematycznej z zastosowaniami, Tom II | PWN, Warszawa. | 1981 |
Formal requirements: According to the regulations of PRz.
Basic requirements in category knowledge: Basic knowledge of mathematics on secondary school level
Basic requirements in category skills: Ability to use the fundamental mathematical tools in the area of the secondary school
Basic requirements in category social competences: The student is prepared to undertake objective and justified actions in order to solve the posed exercise
MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
---|---|---|---|---|---|
01 | Knows the basic properties of functions of one real variable and basic elementary functions | lecture, tutorials | written test |
K_W01+ |
P6S_WG |
02 | Knows how to calculate the basic limits of sequences and functions | lecture, tutorials | written test or written exam |
K_W01++ |
P6S_WG |
03 | Knows how to calculate the derivatives of functions of one real variable and use the theorems and methods of differential calculus of functions of one real variable in tasks | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
04 | Knows how to integrate the functions of one real variable by parts and by substitution, knows how to calculate integrals of basic class of functions | lecture, tutorials | written test or written exam |
K_W01++ |
P6S_WG |
05 | Can perform basic operations on complex numbers | lecture, tutorials | written test or written exam |
K_W01++ |
P6S_WG |
06 | Knows how to calculate the determinants of square matrixes and how to solve Cramer's systems of linear equations | lecture, tutorials | written test or written exam |
K_W01++ |
P6S_WG |
07 | Knows how to solve simple linear first-order differential equations and differential equations with separated variables | lecture, tutorials | written test or written exam |
K_W01++ |
P6S_WG |
08 | Knows the basic concepts of analytic geometry in 3-dimensional space and knows how to use them | lecture, tutorials | written test or written exam |
K_W01+ K_U19+ |
P6S_UU P6S_WG |
09 | Knows how to calculate the derivatives of functions of several variables and knows how to use theorems and methods of differential calculus of functions of several variables to search for local extrema of functions; knows the basic properties of double integrals, and can be applied in simple tasks; an calculate a triple integral over a normal region at a basic level of difficulty | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
10 | Knows theorems about the existence and uniqueness of solutions for systems of equations first order ordinary differential. He can solve some systems of such equations by the elimination method and the method of the first integrals | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
11 | Knows the structure of a set of solutions of the system of linear differential quations, he can solve linear homogeneous systems with constant coefficients and use the fixed constants method for solving non-homogeneous linear systems | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
12 | Is able to solve certain partial linear and quasi-linear differential equations of the first order | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
13 | Knows the theory of the Fourier series | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
14 | Can classify and reduced to canonical form (and in some cases also solve) the partial differential equation of the second order | lecture, tutorials | written test or written exam |
K_W01+ |
P6S_WG |
Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).
Sem. | TK | The content | realized in | MEK |
---|---|---|---|---|
1 | TK01 | W01, W02, W03, W04, C01, C02, C03, C04 | MEK01 | |
1 | TK02 | W05, W06, W07, C05, C06, C07 | MEK02 | |
1 | TK03 | W08, W09, W10, C08, C09, C10, C11, | MEK03 | |
1 | TK04 | W11, W12, W13, W14, W15, C12, C13, C14, C15 | MEK04 | |
2 | TK01 | W01, W02, C01, C02 | MEK05 | |
2 | TK02 | W03, W04, W05, C03, C04, C05, | MEK06 | |
2 | TK03 | W06, W07, W08, C06, C07, C08, | MEK07 | |
2 | TK04 | W09, W10, C09, C10, C11 | MEK08 | |
2 | TK05 | W11, W12, W13, W14, W 15, C12, C13, C14, C15 | MEK09 | |
3 | TK01 | W01, W02, W03, W04, C01, C02, C03, C04 | MEK10 | |
3 | TK02 | W05, W06, C05, C06 | MEK11 | |
3 | TK03 | W07, W08, C07, C08 | MEK12 | |
3 | TK04 | W09, W10, C09, C10 | MEK13 | |
3 | TK05 | W11, W12, W13, W14, W15, C11, C12, C13, C14, C15 | MEK14 |
The type of classes | The work before classes | The participation in classes | The work after classes |
---|---|---|---|
Lecture (sem. 1) | The preparation for a test:
30.00 hours/sem. |
contact hours:
30.00 hours/sem. |
complementing/reading through notes:
15.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem. |
Class (sem. 1) | The preparation for a Class:
15.00 hours/sem. The preparation for a test: 10.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
10.00 hours/sem. |
Advice (sem. 1) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
4.00 hours/sem. |
|
Exam (sem. 1) | The preparation for an Exam:
20.00 hours/sem. |
The written exam:
2.00 hours/sem. The oral exam: 2.00 hours/sem. |
|
Lecture (sem. 2) | The preparation for a test:
20.00 hours/sem. |
contact hours:
30.00 hours/sem. |
complementing/reading through notes:
10.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem. |
Class (sem. 2) | The preparation for a Class:
10.00 hours/sem. The preparation for a test: 10.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
10.00 hours/sem. |
Advice (sem. 2) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
5.00 hours/sem. |
|
Exam (sem. 2) | The preparation for an Exam:
20.00 hours/sem. |
The written exam:
2.00 hours/sem. The oral exam: 2.00 hours/sem. |
|
Lecture (sem. 3) | The preparation for a test:
5.00 hours/sem. |
contact hours:
15.00 hours/sem. |
complementing/reading through notes:
5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem. |
Class (sem. 3) | The preparation for a Class:
10.00 hours/sem. |
contact hours:
15.00 hours/sem. |
Finishing/Studying tasks:
5.00 hours/sem. |
Advice (sem. 3) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
4.00 hours/sem. |
|
Credit (sem. 3) | The preparation for a Credit:
2.00 hours/sem. |
The written credit:
2.00 hours/sem. |
The type of classes | The way of giving the final grade |
---|---|
Lecture | A credit for the lecture is based on the result of the written exam to which only those students who have obtained credit for the exercises are admitted. |
Class | A credit for the classes is based on the attendance, the results of a test and activities in the classes. |
The final grade | Final grade is determined on the basis of the credit from the lecture or on the basis of the credit for the classes and the lectures. |
Lecture | A credit for the lecture is based on the result of the written exam to which only those students who have obtained credit for the exercises are admitted. |
Class | A credit for the classes is based on the attendance, the results of a test and activities in the classes. |
The final grade | Final grade is determined on the basis of the credit from the lecture or on the basis of the credit for the classes and the lectures. |
Lecture | A credit for the lecture is based on the result of the written exam to which only those students who have obtained credit for the exercises are admitted. |
Class | A credit for the classes is based on the attendance and activities in the classes. |
The final grade | The final grade is determined on the basis of grades for passing the classes and the lecture. |
Required during the exam/when receiving the credit
(-)
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : yes
Available materials :