ZUT - Polska Rama Kwalifikacji / Rok 2024/2025 / Administracja Centralna Uczelni / Wymiana międzynarodowa (S2) / Sylabus przedmiotu

Administracja Centralna Uczelni - Wymiana międzynarodowa (S2)

Sylabus przedmiotu Applied Mathematics in Engineering:

Informacje podstawowe

Kierunek studiów	Wymiana międzynarodowa
Forma studiów	studia stacjonarne	Poziom	drugiego stopnia
Tytuł zawodowy absolwenta
Obszary studiów	—
Profil
Moduł	—
Przedmiot	Applied Mathematics in Engineering
Specjalność	przedmiot wspólny
Jednostka prowadząca	Dziekanat
Nauczyciel odpowiedzialny	Bogdan Ambrożek <Bogdan.Ambrozek@zut.edu.pl>
Inni nauczyciele
ECTS (planowane)	4,0	ECTS (formy)	4,0
Forma zaliczenia	zaliczenie	Język	angielski
Blok obieralny	—	Grupa obieralna	—

Formy dydaktyczne

Forma dydaktyczna	KOD	Semestr	Godziny	ECTS	Waga	Zaliczenie
wykłady	W	1	30	2,0	0,50	zaliczenie
ćwiczenia audytoryjne	A	1	30	2,0	0,50	zaliczenie

Wymagania wstępne

KOD	Wymaganie wstępne
W-1	Fundamentals of mathematics.

Cele przedmiotu

KOD	Cel modułu/przedmiotu
C-1	The student will be able to: 1. Describe engineering problems in mathematical form. 2. Identify analytical solution to the differential equations. 3. Interpret the solution to differential equations.

Treści programowe z podziałem na formy zajęć

KOD	Treść programowa	Godziny
ćwiczenia audytoryjne
T-A-1	Formulation of engineering problems.	4
T-A-2	Solution of ordinary differential equations. Solution of coupled Simultaneous ODE.	8
T-A-3	Numerical solution of ODEs: initial value problems and boundary value problems.	6
T-A-4	Analytical and numerical solution of PDEs.	8
T-A-5	Solution of differential equations using Laplace transforms.	4
		30
wykłady
T-W-1	Formulation of engineering problems.	3
T-W-2	Modelling: model building process. Model hierarchy. Models with many variables. Boundary conditions.	4
T-W-3	Vector spaces. Matrices. Matrix algebra: row operations, direct elimination methods, iterative methods.	4
T-W-4	Ordinary differential equations. First-order equations. Solution methods for second-order nonlinear equations. Linear equations of higher order.	5
T-W-5	Coupled Simultaneous ODE.	3
T-W-6	The calculus of finite differences. Approximate methods for ODE solution. Initial value problems. Boundary value problems.	4
T-W-7	Laplace transforms. Solution techniques for solving PDEs.	2
T-W-8	Solution techniques for solving PDEs.	5
		30

Obciążenie pracą studenta - formy aktywności

KOD	Forma aktywności	Godziny
ćwiczenia audytoryjne
A-A-1	Class participation	30
A-A-2	Solving computational problems	17
A-A-3	Final test and discussion of results.	3
		50
wykłady
A-W-1	Class participation	30
A-W-2	Individual work	17
A-W-3	Final test and discussion of results.	3
		50

Metody nauczania / narzędzia dydaktyczne

KOD	Metoda nauczania / narzędzie dydaktyczne
M-1	Lecture illustrated by Power Point presentation and manual and computer calculations
M-2	Classes illustrated by computer and manual calculations

Sposoby oceny

KOD	Sposób oceny
S-1	Ocena formująca: Periodic assessment of student achievement
S-2	Ocena podsumowująca: Lecture: written test at the end of the semester Classes: written test

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
WM-WBiIS_2-_null_W01 The student will be able to describe engineering problems in mathematical form.	—	—	C-1	T-W-3, T-W-5, T-W-7, T-W-8, T-W-4, T-W-2, T-A-1	M-1, M-2	S-1, S-2

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
WM-WBiIS_2-_null_U01 The student will be able to identify analytical and numerical solution to the differential equations.	—	—	C-1	T-W-7, T-W-8, T-W-4, T-W-6, T-A-4, T-A-5, T-A-3	M-1, M-2	S-1, S-2

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
WM-WBiIS_2-_null_K01 The student will be able to interpret the solution to differential equations.	—	—	C-1	T-W-5, T-W-7, T-W-4, T-W-2, T-W-6, T-A-1	M-1, M-2	S-1, S-2

Kryterium oceny - wiedza

Efekt uczenia się	Ocena	Kryterium oceny
WM-WBiIS_2-_null_W01 The student will be able to describe engineering problems in mathematical form.	2,0
	3,0	The student is able to describe engineering problems in mathematical form.
	3,5
	4,0
	4,5
	5,0

Kryterium oceny - umiejętności

Efekt uczenia się	Ocena	Kryterium oceny
WM-WBiIS_2-_null_U01 The student will be able to identify analytical and numerical solution to the differential equations.	2,0
	3,0	The student is able to identify analytical solution to the differential equations.
	3,5
	4,0
	4,5
	5,0

Kryterium oceny - inne kompetencje społeczne i personalne

Efekt uczenia się	Ocena	Kryterium oceny
WM-WBiIS_2-_null_K01 The student will be able to interpret the solution to differential equations.	2,0
	3,0	The student is able to interpret the solution to differential equations.
	3,5
	4,0
	4,5
	5,0

Literatura podstawowa

Dasgupta B., Applied Mathematical Methods, Pearson Education India, 2006
Riley K.F., M.P. Hobson M.P., Bence S.J., Mathematical methods for physics and engineering, Cambridge University Press, 2006
Hayek S. I., Advanced Mathematical Methods in Science and Engineering, CRC Press, 2010
Bayin S.S., Mathematical Methods in Science and Engineering, Wiley, 2006
Rice R.G., Do D.D., Applied mathematics and modeling for chemical engineers, Wiley, New York, 2012
Finlayson B.A., Introduction to chemical engineering computing, Wiley, New York, 2005
Loney N.W., Applied Mathematical Methods for Chemical Engineers, CRC, Boca Raton, 2015

Literatura dodatkowa

Basmadjian D., The art of modeling in science and engineering, CRC, Boca Raton, 2000
Tas K., Mathematical Methods in Engineering, Springer, 2006

Treści programowe - ćwiczenia audytoryjne

KOD	Treść programowa	Godziny
T-A-1	Formulation of engineering problems.	4
T-A-2	Solution of ordinary differential equations. Solution of coupled Simultaneous ODE.	8
T-A-3	Numerical solution of ODEs: initial value problems and boundary value problems.	6
T-A-4	Analytical and numerical solution of PDEs.	8
T-A-5	Solution of differential equations using Laplace transforms.	4
		30

Treści programowe - wykłady

KOD	Treść programowa	Godziny
T-W-1	Formulation of engineering problems.	3
T-W-2	Modelling: model building process. Model hierarchy. Models with many variables. Boundary conditions.	4
T-W-3	Vector spaces. Matrices. Matrix algebra: row operations, direct elimination methods, iterative methods.	4
T-W-4	Ordinary differential equations. First-order equations. Solution methods for second-order nonlinear equations. Linear equations of higher order.	5
T-W-5	Coupled Simultaneous ODE.	3
T-W-6	The calculus of finite differences. Approximate methods for ODE solution. Initial value problems. Boundary value problems.	4
T-W-7	Laplace transforms. Solution techniques for solving PDEs.	2
T-W-8	Solution techniques for solving PDEs.	5
		30

Formy aktywności - ćwiczenia audytoryjne

KOD	Forma aktywności	Godziny
A-A-1	Class participation	30
A-A-2	Solving computational problems	17
A-A-3	Final test and discussion of results.	3
		50

(*) 1 punkt ECTS, odpowiada około 30 godzinom aktywności studenta

Formy aktywności - wykłady

KOD	Forma aktywności	Godziny
A-W-1	Class participation	30
A-W-2	Individual work	17
A-W-3	Final test and discussion of results.	3
		50

(*) 1 punkt ECTS, odpowiada około 30 godzinom aktywności studenta

Pole	KOD	Znaczenie kodu
Zamierzone efekty uczenia się	WM-WBiIS_2-_null_W01	The student will be able to describe engineering problems in mathematical form.
Cel przedmiotu	C-1	The student will be able to: 1. Describe engineering problems in mathematical form. 2. Identify analytical solution to the differential equations. 3. Interpret the solution to differential equations.
Treści programowe	T-W-3	Vector spaces. Matrices. Matrix algebra: row operations, direct elimination methods, iterative methods.
	T-W-5	Coupled Simultaneous ODE.
	T-W-7	Laplace transforms. Solution techniques for solving PDEs.
	T-W-8	Solution techniques for solving PDEs.
	T-W-4	Ordinary differential equations. First-order equations. Solution methods for second-order nonlinear equations. Linear equations of higher order.
	T-W-2	Modelling: model building process. Model hierarchy. Models with many variables. Boundary conditions.
	T-A-1	Formulation of engineering problems.
Metody nauczania	M-1	Lecture illustrated by Power Point presentation and manual and computer calculations
Metody nauczania	M-2	Classes illustrated by computer and manual calculations
Sposób oceny	S-1	Ocena formująca: Periodic assessment of student achievement
Sposób oceny	S-2	Ocena podsumowująca: Lecture: written test at the end of the semester Classes: written test
Kryteria oceny	Ocena	Kryterium oceny
	2,0
	3,0	The student is able to describe engineering problems in mathematical form.
	3,5
	4,0
	4,5
	5,0

Pole	KOD	Znaczenie kodu
Zamierzone efekty uczenia się	WM-WBiIS_2-_null_U01	The student will be able to identify analytical and numerical solution to the differential equations.
Cel przedmiotu	C-1	The student will be able to: 1. Describe engineering problems in mathematical form. 2. Identify analytical solution to the differential equations. 3. Interpret the solution to differential equations.
Treści programowe	T-W-7	Laplace transforms. Solution techniques for solving PDEs.
	T-W-8	Solution techniques for solving PDEs.
	T-W-4	Ordinary differential equations. First-order equations. Solution methods for second-order nonlinear equations. Linear equations of higher order.
	T-W-6	The calculus of finite differences. Approximate methods for ODE solution. Initial value problems. Boundary value problems.
	T-A-4	Analytical and numerical solution of PDEs.
	T-A-5	Solution of differential equations using Laplace transforms.
	T-A-3	Numerical solution of ODEs: initial value problems and boundary value problems.
Metody nauczania	M-1	Lecture illustrated by Power Point presentation and manual and computer calculations
Metody nauczania	M-2	Classes illustrated by computer and manual calculations
Sposób oceny	S-1	Ocena formująca: Periodic assessment of student achievement
Sposób oceny	S-2	Ocena podsumowująca: Lecture: written test at the end of the semester Classes: written test
Kryteria oceny	Ocena	Kryterium oceny
	2,0
	3,0	The student is able to identify analytical solution to the differential equations.
	3,5
	4,0
	4,5
	5,0

Pole	KOD	Znaczenie kodu
Zamierzone efekty uczenia się	WM-WBiIS_2-_null_K01	The student will be able to interpret the solution to differential equations.
Cel przedmiotu	C-1	The student will be able to: 1. Describe engineering problems in mathematical form. 2. Identify analytical solution to the differential equations. 3. Interpret the solution to differential equations.
Treści programowe	T-W-5	Coupled Simultaneous ODE.
	T-W-7	Laplace transforms. Solution techniques for solving PDEs.
	T-W-4	Ordinary differential equations. First-order equations. Solution methods for second-order nonlinear equations. Linear equations of higher order.
	T-W-2	Modelling: model building process. Model hierarchy. Models with many variables. Boundary conditions.
	T-W-6	The calculus of finite differences. Approximate methods for ODE solution. Initial value problems. Boundary value problems.
	T-A-1	Formulation of engineering problems.
Metody nauczania	M-1	Lecture illustrated by Power Point presentation and manual and computer calculations
Metody nauczania	M-2	Classes illustrated by computer and manual calculations
Sposób oceny	S-1	Ocena formująca: Periodic assessment of student achievement
Sposób oceny	S-2	Ocena podsumowująca: Lecture: written test at the end of the semester Classes: written test
Kryteria oceny	Ocena	Kryterium oceny
	2,0
	3,0	The student is able to interpret the solution to differential equations.
	3,5
	4,0
	4,5
	5,0