The aim of studying and bibliography

The main aim of study: Supplementing the knowledge of mathematics in application to the chemical engineering.

The general information about the module: The student is getting the knowledge in scope of the operator calculation, advanced methods of integrating, solving of ordinal and partial differential equations. This knowledge is essential to understand theoretical bases of the chemical engineering.

Bibliography required to complete the module

Bibliography used during lectures

1	Steiner E.	Matematyka dla chemików	WNT.	2000
2	Traczyk T., Mączyński M.	Matematyka stosowana w inżynierii chemicznej	WNT.	1970
3	Palczewski A.D.	Równania różniczkowe zwyczajne. Teorie i metody numeryczne z wykorzystaniem komputerowego systemu ob	WNT.	1999
4	Massimo Morbidelli, Arvind Varma	Mathematical Methods in Chemical Engineering	OXFORD UNIV PR.	1997

Bibliography used during classes/laboratories/others

1

PRACA ZBIOROWA

Poradnik Inżyniera matematyka

WNT.

1996

Basic requirements in category knowledge/skills/social competences

Formal requirements: registration for the given semester

Basic requirements in category knowledge: Student has knowledge from the range of mathematics on the level of the basic courses of mathematics at the universities.

Basic requirements in category skills: Student has knowledge from the range of mathematics on the level of the basic courses of mathematics at the Universities

Basic requirements in category social competences: NONE

Module outcomes

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	Student has a knowledge about solving a differential equations, specific for the chemical engineering, He knows methods of calculatingsurface integrals and integrals along curves. He understands the sence of lintroduction of the gradient, divergence, rotation and Laplace operators in orthogonal systems of coordinates.	lecture	Colloquium,	K_W01++ K_W13+	P6S_WG
02	He is able to solve specific to the chemical engineering, ordinal differential equations. He is able to calculate the surface integrals and integrals along curves. He is able to use operators of gradient, divergence, rotation and Laplace in orthogonal systems of coordinates.	exercises for lectures	Colloquium	K_U12+	P6S_UW

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).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
7	TK01	Vector operations, Operator of gradient, divergence rotation. Integration along curves. Surface, volume integrals. Ordinal differential equations, sets of differential equations, method of integration. Partial differential equations, Furrier method of solution, method of Laplace transform.	W15, C15	MEK01 MEK02

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 7)		contact hours: 15.00 hours/sem.	Studying the recommended bibliography: 5.00 hours/sem.
Class (sem. 7)		contact hours: 15.00 hours/sem.
Advice (sem. 7)
Credit (sem. 7)	The preparation for a Credit: 15.00 hours/sem.	The written credit: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture
Class
The final grade	(Arithmetic mean from grades of the lecture and exercises.)*w but not less than 3, w - coefficient taking into account the term when positive final grade was obtained, w = 1,0 first term, w = 0,9 second term, w = 0,8 third term.

Sample problems

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 : no

The contents of the module are associated with the research profile: yes

1	K. Kaczmarski; M. Szukiewicz	Analytical and numerical solutions of linear and nonlinear chromatography column models	2024
2	T. Fornstedt; K. Kaczmarski; M. Leśko; J. Samuelsson	Prediction of overloaded concentration profiles under ultra-high-pressure liquid chromatographic conditions	2024
3	W. Czechtizky; T. Fornstedt; M. Jora; K. Kaczmarski; T. Leek; M. Leśko; J. Samuelsson; K. Stavenhagen	Strategies for predictive modeling of overloaded oligonucleotide elution profiles in ion-pair chromatography	2023
4	K. Kaczmarski; E. Lorenc-Grabowska; M. Przywara	Advanced modelling of adsorption process on activated carbon	2022
5	T. Fornstedt; K. Kaczmarski; M. Leśko; J. Samuelsson	A closer study of overloaded elution bands and their perturbation peaks in ion-pair chromatography	2022
6	K. Kaczmarski; M. Szukiewicz	An efficient and robust method for numerical analysis of a dead zone in catalyst particle and packed bed reactor	2021
7	K. Kaczmarski; M. Szukiewicz	Modeling of a Real-Life Industrial Reactor for Hydrogenation of Benzene Process	2021
8	M. Chutkowski; K. Kaczmarski	Impact of changes in physicochemical parameters of the mobile phase along the column on the retention time in gradient liquid chromatography. Part A – temperature gradient	2021
9	T. Fornstedt; E. Glenne; K. Kaczmarski; M. Leśko; J. Samuelsson	Predictions of overloaded concentration profiles in supercritical fluid chromatography	2021
10	T. Fornstedt; K. Kaczmarski; M. Leśko; J. Samuelsson	Experimental and theoretical investigation of high- concentration elution bands in ion-pair chromatography	2021
11	D. Asberg; T. Fornstedt; K. Kaczmarski; M. Leśko; J. Samuelsson	Evaluating the advantages of higher heat conductivity in a recently developed type of core-shell diamond stationary phase particle in UHPLC	2020
12	M. Chutkowski; K. Kaczmarski	Note of solving Equilibrium Dispersive model with the Craig scheme for gradient chromatography case	2020
13	E. Chmiel-Szukiewicz; K. Kaczmarski; A. Szałek; M. Szukiewicz	Dead zone for hydrogenation of propylene reaction carried out on commercial catalyst pellets	2019