| Nazwa przedmiotu | Numerical Methods |
| Język prowadzenia przedmiotu |
angielski |
| Kod/Specjalność | ZI-IA-XX-X1-23/24Z-NUMMET | brak |
|
| 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 | | Razem | 5 |
|
| 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 knows and understands the 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-W03-23/24Z
ZI-X1-IA-W05-23/24Z
|
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-U02-23/24Z
ZI-X1-IA-U03-23/24Z
|
E3 |
K |
Students is ready to perform systematic, consequent, reliable and ethical actions in order to solve the problems. Student is ready to cooperate with teacher and other students. Student is ready to constant self-improvement. |
ZI-X1-IA-K01-23/24Z
ZI-X1-IA-K06-23/24Z
| |
| 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 |
Opis | S (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 |
Opis | S (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 |
E1 | ZI-X1-IA-W03-23/24Z
ZI-X1-IA-W05-23/24Z
| 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 |
E2 | ZI-X1-IA-U02-23/24Z
ZI-X1-IA-U03-23/24Z
| C2 C3 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 |
E3 | ZI-X1-IA-K01-23/24Z
ZI-X1-IA-K06-23/24Z
| C2 C3 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 §28 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 (80%) and tasks in laboratory (20%) plus (extra) activity during classes (max 15% within the semester).
The classes are passed if student gathers at least 50%.
Passing the problem sessions is necessary condition to sit the exam.
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 §28 pkt. 5 Regulaminu studiów) |
Final grade
With the exception on the highest grades (db+, bdb) described above, the final grade is rounded up to 1 decimal place the weighted mean of the grades: on practicals and on exams:
s*(final result on practicals) + s*(sum of grades on exams)
where s=1/2 if exam is passed in 1st attempt or s=1/3 if exam is passed in 2nd attempt.
The grades on practicals and on exams are given according to the scale.
If any of: problem sessions or both exams, is failed, then the final grade is 2.0.
Scale:
91-100% very good (5.0)
81-90% better than good (4.5)
71-80% good (4.0)
61-70% better than satisfactory (3.5)
50-60% satisfactory (3.0)
0-49% failed (2.0)
|
| Dodatkowe informacje o sposobie obliczania oceny końcowej lub egzaminie |
| brak |
|
| Osoby prowadzące przedmiot |
| Lp. |
Nauczyciel |
| 1 |
Kornafel Marta, dr (Katedra Matematyki) |
| 2 |
Bielawski Jakub, dr (Katedra Matematyki) |
|
| Informacje dodatkowe |
6h of problem sessions (3 meetings) take place in computer lab. |
