Zachodniopomorski Uniwersytet Technologiczny w Szczecinie

Administracja Centralna Uczelni - Wymiana międzynarodowa (S3)

Sylabus przedmiotu MATHEMATICAL MODELING:

Informacje podstawowe

Kierunek studiów Wymiana międzynarodowa
Forma studiów studia stacjonarne Poziom trzeciego stopnia
Stopnień naukowy absolwenta
Obszary studiów studia trzeciego stopnia
Profil
Moduł —
Przedmiot MATHEMATICAL MODELING
Specjalność przedmiot wspólny
Jednostka prowadząca Katedra Bioinżynierii
Nauczyciel odpowiedzialny Arkadiusz Telesiński <Arkadiusz.Telesinski@zut.edu.pl>
Inni nauczyciele
ECTS (planowane) 3,0 ECTS (formy) 3,0
Forma zaliczenia zaliczenie Język angielski
Blok obieralny — Grupa obieralna —

Formy dydaktyczne

Forma dydaktycznaKODSemestrGodzinyECTSWagaZaliczenie
wykładyW1 20 1,50,62zaliczenie
ćwiczenia audytoryjneA1 20 1,50,38zaliczenie

Wymagania wstępne

KODWymaganie wstępne
W-1Basic knowledge of linear algebra, mathematical analysis and theory of probability

Cele przedmiotu

KODCel modułu/przedmiotu
C-1The aim of the course is to provide methods and tools for modeling and analysis of dynamic models described by ordinary differential equations and partial.

Treści programowe z podziałem na formy zajęć

KODTreść programowaGodziny
ćwiczenia audytoryjne
T-A-1Introduction - purpose and scope of modeling, basic definitions.2
T-A-2Stages of modeling. Formal description, assumption, model, scale, algorithm, simulation.2
T-A-3Model verification2
T-A-4Local and global formulation. Scale effect.2
T-A-5Deterministic and random models.3
T-A-6Static and dynamic models.3
T-A-7Analytical and numerical methods of solving.2
T-A-8Modeling with differential equations.2
T-A-9Optimization methods in modeling. Sensitivity analysis.2
20
wykłady
T-W-1Reminder knowledge of differential and integral calculus. The concept of the model. Linear and nonlinear models. Static and dynamic models. Models of deterministic and non-deterministic. Models of continuous and discrete. Basic operators. Transform of Laplace, Fourier and Z. Modeling interference. The concept of stochastic processes. Smoothing, filtering and prediction.4
T-W-2Ordinary differential equations. Uniqueness of solutions. Initial and boundary conditions. Linear equations. Bringing higher-order equations to a system of first order equations. Matrix derivatives.4
T-W-3Compartmental models. Models with fixed parameters. The models of the first, second, third and fourth order. Examples of models of real systems. Properties of compartmental models. Tasks reverse. Traceability parametric models. Regularization. Problems properly defined. Sensitivity and conditioning tasks.4
T-W-4The models in the form of state equations. The structure of the model. Partial differential equations. General solution. Initial and boundary conditions. Uniqueness of the solution. The most important types of partial differential equations of second order. General partial differential equation of second order. Classification of linear equations of second order. Basic methods of solving second-order equations: the method of characteristics, method of separated variables, examples.4
T-W-5Basic numerical methods for solving linear partial differential equations: finite difference method, Galerkin method, finite element method. The use of Fourier transform for solving equations with boundary conditions. Application of the Laplace transform to solve equations with initial conditions.4
20

Obciążenie pracą studenta - formy aktywności

KODForma aktywnościGodziny
ćwiczenia audytoryjne
A-A-1Participation in worhshops20
A-A-2Preparing to pass workshops18
38
wykłady
A-W-1Participation in lectures20
A-W-2Reading the specified literature10
A-W-3Preparing to pass lectures8
38

Metody nauczania / narzędzia dydaktyczne

KODMetoda nauczania / narzędzie dydaktyczne
M-1Lectures
M-2Workshops
M-3Self solving mathematics tasks

Sposoby oceny

KODSposób oceny
S-1Ocena formująca: Evaluation of self solving mathematics tasks
S-2Ocena formująca: Test

Zamierzone efekty uczenia się - wiedza

Zamierzone efekty uczenia sięOdniesienie do efektów kształcenia dla dyscyplinyOdniesienie do efektów zdefiniowanych dla obszaru kształceniaCel przedmiotuTreści programoweMetody nauczaniaSposób oceny
WM-WKSiR_3-_null_W01
Student has basic knowledge of mathematics		——C-1T-A-1, T-A-2, T-A-3, T-A-4, T-A-5, T-A-6, T-A-7, T-A-8, T-A-9, T-W-1, T-W-2, T-W-3, T-W-4, T-W-5M-1, M-2, M-3S-1

Zamierzone efekty uczenia się - umiejętności

Zamierzone efekty uczenia sięOdniesienie do efektów kształcenia dla dyscyplinyOdniesienie do efektów zdefiniowanych dla obszaru kształceniaCel przedmiotuTreści programoweMetody nauczaniaSposób oceny
WM-WKSiR_3-_null_U01
Student can solve mathematical modeling tasks		——C-1T-A-1, T-A-2, T-A-3, T-A-4, T-A-5, T-A-6, T-A-7, T-A-8, T-A-9M-2, M-3S-1

Zamierzone efekty uczenia się - inne kompetencje społeczne i personalne

Zamierzone efekty uczenia sięOdniesienie do efektów kształcenia dla dyscyplinyOdniesienie do efektów zdefiniowanych dla obszaru kształceniaCel przedmiotuTreści programoweMetody nauczaniaSposób oceny
WM-WKSiR_3-_null_K01
Student is aware of the importance of mathematical modeling in life sciences		——C-1T-A-1, T-A-2, T-A-3, T-A-4, T-A-5, T-A-6, T-A-7, T-A-8, T-A-9M-3S-1

Kryterium oceny - wiedza

Efekt uczenia sięOcenaKryterium oceny
WM-WKSiR_3-_null_W01
Student has basic knowledge of mathematics		2,0
3,0Student has basic knowledge about mathematical models
3,5
4,0
4,5
5,0

Kryterium oceny - umiejętności

Efekt uczenia sięOcenaKryterium oceny
WM-WKSiR_3-_null_U01
Student can solve mathematical modeling tasks		2,0
3,0Student can solve basic mathematical models
3,5
4,0
4,5
5,0

Kryterium oceny - inne kompetencje społeczne i personalne

Efekt uczenia sięOcenaKryterium oceny
WM-WKSiR_3-_null_K01
Student is aware of the importance of mathematical modeling in life sciences		2,0
3,0Student knows the meaning of mathematical modeling
3,5
4,0
4,5
5,0

Literatura podstawowa

  1. R. Illner et al., Mathematical Modelling: A Case Studies Approach, AMS, 2005
  2. E. Bender, Introduction to Mathematical Modelling, Dover, 2000
  3. J. Kapur, Maximum-entropy Models in Science and Engineering, Wiley, 1989

Literatura dodatkowa

  1. D. Higham, N.Higham, Matlab Guide, SIAM, 2005
  2. P. Brockwell, R. Davis., Introduction to Time Series and Forecasting, Springer, 2010

Treści programowe - ćwiczenia audytoryjne

KODTreść programowaGodziny
T-A-1Introduction - purpose and scope of modeling, basic definitions.2
T-A-2Stages of modeling. Formal description, assumption, model, scale, algorithm, simulation.2
T-A-3Model verification2
T-A-4Local and global formulation. Scale effect.2
T-A-5Deterministic and random models.3
T-A-6Static and dynamic models.3
T-A-7Analytical and numerical methods of solving.2
T-A-8Modeling with differential equations.2
T-A-9Optimization methods in modeling. Sensitivity analysis.2
20

Treści programowe - wykłady

KODTreść programowaGodziny
T-W-1Reminder knowledge of differential and integral calculus. The concept of the model. Linear and nonlinear models. Static and dynamic models. Models of deterministic and non-deterministic. Models of continuous and discrete. Basic operators. Transform of Laplace, Fourier and Z. Modeling interference. The concept of stochastic processes. Smoothing, filtering and prediction.4
T-W-2Ordinary differential equations. Uniqueness of solutions. Initial and boundary conditions. Linear equations. Bringing higher-order equations to a system of first order equations. Matrix derivatives.4
T-W-3Compartmental models. Models with fixed parameters. The models of the first, second, third and fourth order. Examples of models of real systems. Properties of compartmental models. Tasks reverse. Traceability parametric models. Regularization. Problems properly defined. Sensitivity and conditioning tasks.4
T-W-4The models in the form of state equations. The structure of the model. Partial differential equations. General solution. Initial and boundary conditions. Uniqueness of the solution. The most important types of partial differential equations of second order. General partial differential equation of second order. Classification of linear equations of second order. Basic methods of solving second-order equations: the method of characteristics, method of separated variables, examples.4
T-W-5Basic numerical methods for solving linear partial differential equations: finite difference method, Galerkin method, finite element method. The use of Fourier transform for solving equations with boundary conditions. Application of the Laplace transform to solve equations with initial conditions.4
20

Formy aktywności - ćwiczenia audytoryjne

KODForma aktywnościGodziny
A-A-1Participation in worhshops20
A-A-2Preparing to pass workshops18
38
(*) 1 punkt ECTS, odpowiada około 30 godzinom aktywności studenta

Formy aktywności - wykłady

KODForma aktywnościGodziny
A-W-1Participation in lectures20
A-W-2Reading the specified literature10
A-W-3Preparing to pass lectures8
38
(*) 1 punkt ECTS, odpowiada około 30 godzinom aktywności studenta
PoleKODZnaczenie kodu
Zamierzone efekty uczenia sięWM-WKSiR_3-_null_W01Student has basic knowledge of mathematics
Cel przedmiotuC-1The aim of the course is to provide methods and tools for modeling and analysis of dynamic models described by ordinary differential equations and partial.
Treści programoweT-A-1Introduction - purpose and scope of modeling, basic definitions.
T-A-2Stages of modeling. Formal description, assumption, model, scale, algorithm, simulation.
T-A-3Model verification
T-A-4Local and global formulation. Scale effect.
T-A-5Deterministic and random models.
T-A-6Static and dynamic models.
T-A-7Analytical and numerical methods of solving.
T-A-8Modeling with differential equations.
T-A-9Optimization methods in modeling. Sensitivity analysis.
T-W-1Reminder knowledge of differential and integral calculus. The concept of the model. Linear and nonlinear models. Static and dynamic models. Models of deterministic and non-deterministic. Models of continuous and discrete. Basic operators. Transform of Laplace, Fourier and Z. Modeling interference. The concept of stochastic processes. Smoothing, filtering and prediction.
T-W-2Ordinary differential equations. Uniqueness of solutions. Initial and boundary conditions. Linear equations. Bringing higher-order equations to a system of first order equations. Matrix derivatives.
T-W-3Compartmental models. Models with fixed parameters. The models of the first, second, third and fourth order. Examples of models of real systems. Properties of compartmental models. Tasks reverse. Traceability parametric models. Regularization. Problems properly defined. Sensitivity and conditioning tasks.
T-W-4The models in the form of state equations. The structure of the model. Partial differential equations. General solution. Initial and boundary conditions. Uniqueness of the solution. The most important types of partial differential equations of second order. General partial differential equation of second order. Classification of linear equations of second order. Basic methods of solving second-order equations: the method of characteristics, method of separated variables, examples.
T-W-5Basic numerical methods for solving linear partial differential equations: finite difference method, Galerkin method, finite element method. The use of Fourier transform for solving equations with boundary conditions. Application of the Laplace transform to solve equations with initial conditions.
Metody nauczaniaM-1Lectures
M-2Workshops
M-3Self solving mathematics tasks
Sposób ocenyS-1Ocena formująca: Evaluation of self solving mathematics tasks
Kryteria ocenyOcenaKryterium oceny
2,0
3,0Student has basic knowledge about mathematical models
3,5
4,0
4,5
5,0
PoleKODZnaczenie kodu
Zamierzone efekty uczenia sięWM-WKSiR_3-_null_U01Student can solve mathematical modeling tasks
Cel przedmiotuC-1The aim of the course is to provide methods and tools for modeling and analysis of dynamic models described by ordinary differential equations and partial.
Treści programoweT-A-1Introduction - purpose and scope of modeling, basic definitions.
T-A-2Stages of modeling. Formal description, assumption, model, scale, algorithm, simulation.
T-A-3Model verification
T-A-4Local and global formulation. Scale effect.
T-A-5Deterministic and random models.
T-A-6Static and dynamic models.
T-A-7Analytical and numerical methods of solving.
T-A-8Modeling with differential equations.
T-A-9Optimization methods in modeling. Sensitivity analysis.
Metody nauczaniaM-2Workshops
M-3Self solving mathematics tasks
Sposób ocenyS-1Ocena formująca: Evaluation of self solving mathematics tasks
Kryteria ocenyOcenaKryterium oceny
2,0
3,0Student can solve basic mathematical models
3,5
4,0
4,5
5,0
PoleKODZnaczenie kodu
Zamierzone efekty uczenia sięWM-WKSiR_3-_null_K01Student is aware of the importance of mathematical modeling in life sciences
Cel przedmiotuC-1The aim of the course is to provide methods and tools for modeling and analysis of dynamic models described by ordinary differential equations and partial.
Treści programoweT-A-1Introduction - purpose and scope of modeling, basic definitions.
T-A-2Stages of modeling. Formal description, assumption, model, scale, algorithm, simulation.
T-A-3Model verification
T-A-4Local and global formulation. Scale effect.
T-A-5Deterministic and random models.
T-A-6Static and dynamic models.
T-A-7Analytical and numerical methods of solving.
T-A-8Modeling with differential equations.
T-A-9Optimization methods in modeling. Sensitivity analysis.
Metody nauczaniaM-3Self solving mathematics tasks
Sposób ocenyS-1Ocena formująca: Evaluation of self solving mathematics tasks
Kryteria ocenyOcenaKryterium oceny
2,0
3,0Student knows the meaning of mathematical modeling
3,5
4,0
4,5
5,0