Mathematical Analysis I 2400-L1PPAM1

calculus of functions of a single variable, taking into account the economic context.
The first part of the course will be devoted to reviewing and organizing the fundamental mathematical tools that students are expected to have acquired in secondary school. This thematic block will cover the basics of logic, set theory (including Venn diagrams), properties of polynomials (including the existence of real and complex solutions), trigonometric functions, and the principle of mathematical induction.
In the next part, the mathematical apparatus will be expanded to include exponential and logarithmic functions, with reference to issues related to investment income calculations and loan repayments. Averages and relationships between them will also be defined.
The following section will focus on sequences, series, and infinite products. The introduced basic concepts, properties, and computational methods will form an important component of the mathematical toolkit used in subsequent parts of Mathematical Analysis I and II. Examples will include applications in the context of the cobweb model and actuarial calculations (e.g., present values of annuity payments).
The previously introduced topics will allow for defining limits of functions, introducing the concept of continuity, discussing the most important properties of continuous functions, particularly regarding attaining minima and maxima.
The penultimate part of the course will be dedicated to differential calculus of functions of a single variable. Methods of calculating derivatives and their applications—such as computing limits and identifying local and global extrema—will be presented. In this context, Lagrange’s Mean Value Theorem and its consequences will also be discussed. The mathematical tools developed will be applied to selected economic problems (e.g., utility maximization, portfolio optimization).
The final part will focus on the basics of integral calculus for functions of a single variable. Indefinite, definite, and improper integrals will be defined. Basic methods of integration will be introduced, such as integration by parts, substitution, and applications of integrals to economic problems—for instance, calculating total production costs or profit maximization.
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Estimated student workload: 6 ECTS x 25h = 150 hours
• Contact hours (K), Independent work (S):
o Seminar (classes): 60h (K), 0h (S)
o Consultations: 14.5h (K), 0h (S)
o Midterms: 3h (K), 0h (S)
o Final exam: 2.5h (K), 0h (S)
o Preparation for midterms: 0h (K), 8h (S)
o Preparation for exam: 0h (K), 12h (S)
o Preparation for seminars: 0h (K), 30h (S)
o Work with additional materials on the Moodle platform: 0h (K), 20h (S)

The course covers the basics of differential and integral calculus of functions of a single variable, taking into account the economic context.
The first part of the course will be devoted to reviewing and organizing the fundamental mathematical tools that students are expected to have acquired in secondary school. This thematic block will cover the basics of logic, set theory (including Venn diagrams), properties of polynomials (including the existence of real and complex solutions), trigonometric functions, and the principle of mathematical induction.
In the next part, the mathematical apparatus will be expanded to include exponential and logarithmic functions, with reference to issues related to investment income calculations and loan repayments. Averages and relationships between them will also be defined.
The following section will focus on sequences, series, and infinite products. The introduced basic concepts, properties, and computational methods will form an important component of the mathematical toolkit used in subsequent parts of Mathematical Analysis I and II. Examples will include applications in the context of the cobweb model and actuarial calculations (e.g., present values of annuity payments).
The previously introduced topics will allow for defining limits of functions, introducing the concept of continuity, discussing the most important properties of continuous functions, particularly regarding attaining minima and maxima.
The penultimate part of the course will be dedicated to differential calculus of functions of a single variable. Methods of calculating derivatives and their applications—such as computing limits and identifying local and global extrema—will be presented. In this context, Lagrange’s Mean Value Theorem and its consequences will also be discussed. The mathematical tools developed will be applied to selected economic problems (e.g., utility maximization, portfolio optimization).
The final part will focus on the basics of integral calculus for functions of a single variable. Indefinite, definite, and improper integrals will be defined. Basic methods of integration will be introduced, such as integration by parts, substitution, and applications of integrals to economic problems—for instance, calculating total production costs or profit maximization.

Estimated student workload: 6 ECTS x 25h = 150 hours
Contact hours (K), Independent work (S):
Seminar (classes): 60h (K), 0h (S)
Consultations: 14.5h (K), 0h (S)
Midterms: 3h (K), 0h (S)
Final exam: 2.5h (K), 0h (S)
Preparation for midterms: 0h (K), 8h (S)
Preparation for exam: 0h (K), 12h (S)
Preparation for seminars: 0h (K), 30h (S)
Work with additional materials on the Moodle platform: 0h (K), 20h (S)

Basic literature:
M. Krych Analiza matematyczna dla ekonomistów, Wydawnictwa Uniwersytetu Warszawskiego, 2009
Supplementary literature:
R. Antoniewicz, A. Misztal, Matematyka dla studentów ekonomii. Wykłady z ćwiczeniami, WN PWN, Warszawa 2009.
J. Banaś, S. Wędrychowicz, Zbiór zadań z analizy matematycznej, WNT, Warszawa 2006.
T. Bażańska, I. Karwacka, M. Nykowska, Zadania z matematyki, podręcznik dla studiów ekonomicznych, PWN, Warszawa 1980.
Alpha C. Chiang, Podstawy ekonomii matematycznej, Państwowe Wydawnictwo Ekonomiczne, Warszawa 1994.
W. Dubnicki, J. Kłopotowski, T. Szapiro, Analiza Matematyczna. Podręcznik dla ekonomistów, WN PWN, Warszawa 2010.
W. J. Kaczor, M. T. Nowak, Zadania za analizy matematycznej, część 1, 2 i 3, WN PWN, Warszawa 2005.
W. Kołodziej, Analiza matematyczna, WN PWN, Warszawa 2009.
W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, część I i II, WN PWN, Warszawa 2008.
K. Kuratowski, Rachunek różniczkowy i całkowy. Funkcje jednej zmiennej, WN PWN, Warszawa 2008.
W. Rudin, Podstawy analizy matematycznej, WN PWN, Warszawa 2009.A. Ostoja-Ostaszewski, Matematyka w ekonomii. Modele i metody, t. 1 i 2, PWN, Warszawa 1996.

Basic literature:
M. Krych Analiza matematyczna dla ekonomistów, Wydawnictwa Uniwersytetu Warszawskiego, 2009
Supplementary literature:
R. Antoniewicz, A. Misztal, Matematyka dla studentów ekonomii. Wykłady z ćwiczeniami, WN PWN, Warszawa 2009.
J. Banaś, S. Wędrychowicz, Zbiór zadań z analizy matematycznej, WNT, Warszawa 2006.
T. Bażańska, I. Karwacka, M. Nykowska, Zadania z matematyki, podręcznik dla studiów ekonomicznych, PWN, Warszawa 1980.
Alpha C. Chiang, Podstawy ekonomii matematycznej, Państwowe Wydawnictwo Ekonomiczne, Warszawa 1994.
W. Dubnicki, J. Kłopotowski, T. Szapiro, Analiza Matematyczna. Podręcznik dla ekonomistów, WN PWN, Warszawa 2010.
W. J. Kaczor, M. T. Nowak, Zadania za analizy matematycznej, część 1, 2 i 3, WN PWN, Warszawa 2005.
W. Kołodziej, Analiza matematyczna, WN PWN, Warszawa 2009.
W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, część I i II, WN PWN, Warszawa 2008.
K. Kuratowski, Rachunek różniczkowy i całkowy. Funkcje jednej zmiennej, WN PWN, Warszawa 2008.
W. Rudin, Podstawy analizy matematycznej, WN PWN, Warszawa 2009.A. Ostoja-Ostaszewski, Matematyka w ekonomii. Modele i metody, t. 1 i 2, PWN, Warszawa 1996.