(in Polish) Elementy metod matematycznych w zadaniach (kurs internetowy) 2400-ZEWW971
Classes are conducted remotely via the Zoom platform and consist of solving simple computational tasks illustrating theoretical elements. Classes may be recorded and shared on Google Drive.
The course covers key concepts of linear algebra and mathematical analysis, including functions, derivatives (one and many variables), optimization, integration methods, matrices, and systems of linear equations.
Assessment: the final grade is the higher score from two activities: homework (100%) or a summary test (100%), both conducted on the e-learning platform.
Detailed program:
1. Functions: limits of sequences and functions, continuity.
2. Differential calculus (one variable): derivatives of elementary functions, interpretation, higher-order derivatives, Schwarz theorem.
3. Function properties: monotonicity, roots, inverse functions, local/global extrema, optimization, convexity/concavity.
4. Multivariate calculus: partial derivatives, higher-order derivatives, extrema, objective functions, Lagrange theorem.
5. Integral calculus: indefinite and definite integrals, integration by substitution and by parts.
6. Matrices: operations (addition, multiplication, transposition, inversion).
7. Vectors: linear combinations, independence, basis.
8. Determinants: calculation and properties.
9. Inverse matrices and rank: Gauss and Gauss-Jordan elimination methods.
10. Applications: solving systems of linear equations, quadratic forms.
Szacunkowy nakład pracy studenta: 3ECTS x 25h = 75h
(K) - godziny kontaktowe (S) - godziny pracy samodzielnej
wykład (zajęcia): 15h (K) 0h (S)
ćwiczenia (zajęcia): 15h (K) 0h (S)
egzamin: 3h (K) 0h (S)
konsultacje: 7h (K) 0h (S)
przygotowanie do ćwiczeń: 0h (K) 15h (S)
przygotowanie do wykładów: 0h (K) 10h (S)
przygotowanie do kolokwium: 0h (K) 5h (S)
przygotowanie do egzaminu: 0h (K) 5h (S)
…: 0h (K) 0h (S)
Razem: 40h (K) + 35h (S) = 75h
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Term 2025Z:
None |
Course coordinators
Type of course
Prerequisites (description)
Learning outcomes
KNOWLEDGE:
The student knows and understands basic techniques of linear algebra and mathematical analysis; knows how to solve systems of linear equations, calculate determinants and inverse matrices; understands differential and integral calculus and their applications in economics, finance, and statistics.
SKILLS:
The student can use mathematical techniques to analyze socio-economic models; solve linear equations; calculate derivatives and integrals; determine function extrema.
SOCIAL COMPETENCES:
The student is aware of the importance of mathematics in social and economic analysis; understands that mathematical tools are essential for research, analytical, and expert work.
Assessment criteria
Based on the higher result of: homework (100%) or a summary test (100%) via https://elearning.wne.uw.edu.pl/
Grading scale:
[50, 60) - 3;
[60, 70) - 3.5;
[70, 80) - 4;
[80, 90] - 4.5;
(90, 100] - 5.
Bibliography
1. W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach;
2. G.M. Fichtenholz, Rachunek różniczkowy i całkowy;
3. A.C. Chiang, Podstawy ekonomii matematycznej;
4. W. Dubnicki, J. Kłopotowski, Analiza matematyczna;
5. A. Birkholc, Analiza matematyczna;
6. R. Rudnicki, Wykłady z analizy matematycznej;
7. G. Banaszak, W. Gajda, Elementy algebry liniowej;
Supporting materials for classes published on the e-learning platform https://elearning.wne.uw.edu.pl/
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Term 2025Z:
None |