Karta przedmiotu - Numerical Methods

Kierunek: Applied Informatics

Wymagania wstępne
  1. Completed courses "Introduction to Mathematics" and "Mathematical analysis and linear algebra" (1st year of 1st degree studies).
  2. Ability of calculating derivatves of real functions, finding the greatest and least values in compacts.
  3. Ability of operating on matrices and basic methods of solving systems of linear equations.
  4. Ability of conducting the arithmetic and algebraic operations (demandings like in secondary school).

Nazwa przedmiotuNumerical Methods
Język prowadzenia przedmiotu angielski
Kod/Specjalność
ZI-IA-XX-X1-22/23Z-NUMMETbrak
Kategoria przedmiotu kierunkowe lub ogólne
Profil studiów Ogólnoakademicki
Poziom PRK Poziom 6 - 1. stopień (studia licencjackie)
Rok studiów/semestr 2/3
Forma zajęć/liczba godzin
stacjonarne: Wykład: 15 Ćwiczenia: 30
niestacjonarne:
Dyscypliny/punkty ECTS
Nauki o zarządzaniu i jakości: 0
Informatyka: 2
Inne dyscypliny: 3
Razem5
Wykładowca odpowiedzialny za przedmiot Kornafel Marta, dr (Katedra Matematyki)
Cele przedmiotu
Kod Opis
C1 Presentation of knowledge in the area of numerical methods and their applications in analysis of mathematical models.
C2 Formation of the skill of exact and approximate solving the problems with use of adequate numerical methods and estimating the error of result.
C3 Formation of the skill of correct analysis of presented solutions, formulation of logic conclusions and practical intepretation of results.
C4 Formation of the ability of abstract thinking and systematic and reliable approach to solving problems.
Realizowane efekty uczenia się
Kod Kat. Opis Kierunkowe efekty uczenia się
E1 W Student has basic knowledge of goals and role of numerical methods in analysis of mathematical models, knows basic problems in this area and methods of solving them. ZI-X1-IA-W01-22/23Z
ZI-X1-IA-W02-22/23Z
ZI-X1-IA-W03-22/23Z
E2 U Student is able to use the basic tools of numerical methods in order to use problems in mathematical modelling of processes, for each method recognizes the possibility of its usage and is able to implement it in form of some program. Student can correctly estimate the error of obtained result, interpret it and indicate a way to receive better result. ZI-X1-IA-U02-22/23Z
ZI-X1-IA-U03-22/23Z
ZI-X1-IA-U08-22/23Z
E3 K Student is dutiful, responsible and represents ethic approach to the subject, shows respect to the teachers and other students. Student understands the necessity of constant self-improvement and is ready to solve the problems of Cracow, Poland, Europe and our galactics with usage of mathematical methods. ZI-X1-IA-K06-22/23Z
ZI-X1-IA-K01-22/23Z
Sposoby weryfikacji efektów uczenia się Egzamin pisemny, Średnia ważona albo arytmetyczna ocen cząstkowych, Aktywność na zajęciach, Ćwiczenie praktyczne, Kolokwium, Projekt indywidualny, Zadania tablicowe.
Treści przedmiotu
Wykład
Kod OpisS (15)N ()
W1 Error theory - sources of computational errors. Absolute and relative errors. Methods of calculating the errors and inverse problem of error theory. Basis of computational complexity, notation O. 2 0
W2 Direct methods of solving the systems of linear equations: LU decomposition and Cholesky methods. Numerical complexity in comparison with Gauss and Gauss-Jordan elimination methods. 2 0
W3 Approximate methods of solving the systems of linear equations: simple iteration and Seidel iteration methods. 1 0
W4 Eigenvalues and eigenvectors - localisation theorems and power method. 1 0
W5 Approximate methods of solving the nonlinear equations: bisection, iteration, falsi and Newton methods. Newton method for systems of nonlinear equations. 3 0
W6 Polynomial interpolation: Lagrange, Newton and Hermit methods. Error of interpolation. Chebyshev polynomials. 4 0
W7 Numerical differentation and integration. Trapezoid, 1/3 Newton and 3/8 Newton methods. 2 0

Ćwiczenia
Kod OpisS (30)N ()
C1 Error theory - sources of computational errors. Absolute and relative errors. Methods of calculating the errors and inverse problem of error theory. Basis of computational complexity, notation O. 3 0
C2 Direct methods of solving the systems of linear equations: LU decomposition and Cholesky methods. Numerical complexity in comparison with Gauss and Gauss-Jordan elimination methods. 5 0
C3 Approximate methods of solving the systems of linear equations: simple iteration and Seidel iteration methods. 2 0
C4 Eigenvalues and eigenvectors - localisation theorems and power method. 2 0
C5 Approximate methods of solving the nonlinear equations: bisection, iteration, falsi and Newton methods. Newton method for systems of nonlinear equations. 9 0
C6 Polynomial interpolation: Lagrange, Newton and Hermit methods. Error of interpolation. Chebyshev polynomials. 5 0
C7 Numerical differentation and integration. Trapezoid, 1/3 Newton and 3/8 Newton methods. 4 0

Metody i formy prowadzenia zajęć Ćwiczenia laboratoryjne, Ćwiczenia tablicowe, E-learning, Wykład audytoryjny.
Nakład pracy studenta (liczba godzin kontaktowych, pracy on-line i pracy samodzielnej)
Rodzaj aktywności Liczba godzin
stacjonarne niestacjonarne
Udział w zajęciach dydaktycznych 45 0
Udział w konsultacjach 8 0
Udział w kolokwiach/egzaminie 4 0
Praca własna studenta 56 0
E-learning 12 0
Inne (kontaktowe) 0 0
Inne (bezkontaktowe) 0 0
Suma godzin 125 0
Liczba punktów ECTS 5 0
Macierz realizacji przedmiotu
Efekt uczenia się Odniesienie do efektów kierunkowych Cele przedmiotu Treści przedmiotu Metody/narzędzia dydaktyczne Sposoby weryfikacji efektu
E1ZI-X1-IA-W01-22/23Z
ZI-X1-IA-W02-22/23Z
ZI-X1-IA-W03-22/23Z
C2 C4 C1 W2 W1 W3 W4 W5 W6 W7 C1 C2 C3 C4 C5 C6 C7 N1 N9 N11 N13 F1 F2 F6 F8 F9
P2 P4
E2ZI-X1-IA-U02-22/23Z
ZI-X1-IA-U03-22/23Z
ZI-X1-IA-U08-22/23Z
C3 C2 C4 C1 W2 W1 W3 W4 W5 W6 W7 C1 C2 C3 C4 C5 C6 C7 N1 N9 N11 N13 F1 F2 F6 F8 F9
P2 P4
E3ZI-X1-IA-K06-22/23Z
ZI-X1-IA-K01-22/23Z
C3 C2 C4 C1 C1 C2 C3 C4 C5 C6 C7 N1 N9 N11 N13 F1 F2 F6 F8 F9
Literatura podstawowa
Lp. Opis pozycji
1 Gautschi W., Numerical Analysis, 2nd ed., Birkhauser 2012
2 Hoffman J.D., Numerical Methods for Engineers and Scientists, CRC Press 2001
3 Kincaid D., Cheney W., Analiza numeryczna, WNT, Warszawa 2005
Kincaid D., Cheney W., Numerical analysis, AMS Pure and Applied Undergraduate Texts, vol. 2, 2002
Literatura uzupełniająca
Lp. Opis pozycji
1 Fortuna Z., Macukow B., Wąsowski J., Metody numeryczne, WNT 1993
2 Kornafel M. (red.), Baran S., Bielawski J., Kosiorowski G., Szulik G., Metody Numeryczne. Przykłady i zadania, Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków 2020
3 Kosiorowska M., Stanisz T., Metody Numeryczne, Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków 2004
Forma i warunki zaliczenia przedmiotu
Sposób obliczania średniej z ocen bieżących (zgodnie z §18 pkt. 4 Regulaminu studiów)
1. Presence: min. 50% of meetings – condition of being evaluated in the course.

2. The result from the problem sessions is calculated as the sum of points from two middle-semester tests (2x40p) and tasks in laboratory (20p) plus (extra) activity during classes (max 15p=15%*100p within the semester). The classes are passed if student gathers at least 50p.

3. The highest grades (4,5 and 5,0) waive student from the exam. However, they must be confirmed by correct realization of a project, including the practical implementation of some numerical method.
The final grade is the arithmetic mean from the grade from classes and grade form the project (at least 4,0).
In case student resigns from writing the project or the project is rejected, his final grade is 4,0 (with waiver from exam).

4. The grades from classes mentioned in the second and third point are assigned according to the general percentage scheme given below.
Sposób obliczania oceny końcowej (zgodnie z §18 pkt. 5 Regulaminu studiów)
0.5*(result from problem sessions) + 0.5*(result from exam)
Dodatkowe informacje o sposobie obliczania oceny końcowej lub egzaminie
Passing the problem sessions is necessary condition to sit the exam.

1st attempt: The exam contains closed and open questions. The exam is passed if student gathers at least 50% of points.

2nd attempt: The exam contains closed and open questions. The exam is passed if student gathers at least 50% of points.
The grade in the 2nd attempt is the arithmetic mean of grades in 1st and 2nd attempts.

Grades:
91-100% bdb (5,0)
81-90% db+ (4,5)
71-80% db (4,0)
61-70% dst+ (3,5)
50-60% dst (3,0)
0-49% ndst (2,0)
Osoby prowadzące przedmiot
Lp. Nauczyciel
1 Kornafel Marta, dr (Katedra Matematyki)
Informacje dodatkowe

6h of problem sessions (3 meetings) take place in computer lab.


Status karty: ZAAKCEPTOWANY  przez: Jędrzejczyk Marcin, dr hab.