Mathematical analysis I.2
General data
Course ID:  1000112bAM2a  Erasmus code / ISCED:  11.1 / (0541) Mathematics 
Course title:  Mathematical analysis I.2  Name in Polish:  Analiza matematyczna I.2 (potok I) 
Organizational unit:  Faculty of Mathematics, Informatics, and Mechanics  
Course groups: 
Obligatory courses for 1st grade JSEM Obligatory courses for 1st grade JSIM Obligatory courses for 1st grade Mathematics 

ECTS credit allocation (and other scores): 
10.00 view allocation of credits 

Language:  Polish  
Main fields of studies for MISMaP:  mathematics 

Type of course:  obligatory courses 

Short description: 
The course is a continuation of Analiza matematyczna I.1. It covers the differential and integral calculus of one variable, starting from the notion of a derivative and its applications (de l'Hospital's rule, Taylor polynomials), through sequences and series of functions and their convergence (Weierstrass' test for absolute convergence, ArzelaAscoli theorem), properties of power series, to the theory of the Riemann integral, improper integrals and their applications (length of C^{1} curves, Euler's Γ function, Wallis' formula). 

Full description: 


Bibliography: 
1. A. Birkholc, Analiza matematyczna dla nauczycieli. PWN, Warszawa 1977. 2. B. P. Demidowicz, Zbiór zadań z analizy matematycznej, Naukowa Książka, Lublin 1992 (t. I) i 1993 (t. II i III). Baranenkov, G. S.; Demidovich, B.; Efimenko, V. A.; Kogan, S. M.; Lunts, G.; Porshneva, E.; Sycheva, E.; Frolov, S. V.; Shostak, R.; Yanpolsky, A., Problems in mathematical analysis. (Under the editorship of B. Demidovich). Mir Publishers, Moscow, 1976. 3. G. M. Fichtenholz, Rachunek różniczkowy i całkowy. Tom 12, PWN, Warszawa 2007. 4. W. Kaczor, M. Nowak, Zadania z Analizy Matematycznej 1. Liczby rzeczywiste, ciągi i szeregi liczbowe, PWN, Warszawa 2005. W. Kaczor, M. Nowak, Problems in Mathematical Analysis I, AMS Student Mathematical Library (Book 12), 2001. 5. K. Kuratowski, Rachunek różniczkowy i całkowy, PWN, Warszawa 1979. K. Kuratowski, Introduction to calculus. International Series of Monographs in Pure and Applied Mathematics, Vol. 17. Pergamon Press, OxfordEdinburghNew York; PWN—Polish Scientific Publishers, Warsaw, 1969 6. W. Pusz, A. Strasburger, Zbiór zadań z analizy matematycznej Wydział Fizyki UW, Warszawa 1982. 7. W. Rudin, Podstawy analizy matematycznej, PWN, Warszawa 2000. W. Rudin, Principles of mathematical analysis. International Series in Pure and Applied Mathematics. McGrawHill Book Co., New YorkAucklandDüsseldorf, 1976. 8. P. Strzelecki, Analiza Matematyczna I (lecture notes in Polish), http://dydmat.mimuw.edu.pl/sites/default/files/wyklady/analizamatematycznai.pdf Addition to the lecture notes (auth. M. Jóźwikowski, S. Kolasiński), http://dydmat.mimuw.edu.pl/sites/default/files/wyklady/analizamatematycznaizadania.pdf 

Learning outcomes: 
Student: 1. Can justify the correctness of his reasoning. He operates with examples. 2. Knows methods of calculating derivatives and the most important theorems of differential calculus of functions of one real variable, including Lagrange's theorem on mean value, Taylor formula and de l'Hospital rule. Uses typical tools of differential calculus of functions of one variable, incl. determines local extremes, intervals of monotonicity and convexity as well as limits of real variable functions, and also solves optimization tasks based on the study of extremes. Uses the Taylor formula to calculate limits. 3. Knows the concept of point and uniform convergence of a sequence and a functional series, Weierstrass's criterion of uniform convergence, theorem on the continuity of the limit of a uniformly convergent sequence / series of continuous functions and the theorem on differentiation of functional sequences. He can investigate uniform convergence of functional sequences and prove the continuity or differentiability of the limits of such sequences. 4. Knows the concept of a power series and the most important functional properties of the sum of such a series. He knows the CauchyHadamard formula. Specifies the radius of convergence of the power series; is able to use the theorem on the differentiability of functional series to sum up specific series. 5. knows the concept of a primary function and an indefinite integral; can integrate by parts and by substitution. 6. Knows the concept of definite integral, the definition of the Riemann integral and its geometric interpretation. He knows the relationship between the definite and indefinite integral. Uses the tools of integral calculus in tasks of a geometrical nature. Calculates the area under the graph and the curve length. 7. Knows the concept of indefinite integral and examples of functions defined by such integrals. Using various methods, he/she studies the convergence of indefinite integrals. 

Assessment methods and assessment criteria: 
Final mark based on the sum of points from exercises, the two tests and exam. 
Classes in period "Summer semester 2021/22" (in progress)
Time span:  20220221  20220615 
see course schedule 
Type of class: 
Class, 60 hours more information Lecture, 60 hours more information 

Coordinators:  Marta Szumańska  
Group instructors:  Marcin Bobieński, Daniel Hoffmann, Tomasz Kochanek, Leszek Kołodziejczyk, Katarzyna Mazowiecka, Waldemar Pompe, Mikołaj Rotkiewicz, Marta Szumańska  
Students list:  (inaccessible to you)  
Examination: 
Course 
Examination
Lecture  Examination 
Classes in period "Summer semester 2022/23" (future)
Time span:  20230220  20230618 
see course schedule 
Type of class: 
Class, 60 hours more information Lecture, 60 hours more information 

Coordinators:  Anna ZatorskaGoldstein  
Group instructors:  Marcin Bobieński, Sławomir Kolasiński, Leszek Kołodziejczyk, Michał Miśkiewicz, Marcin Moszyński, Przemysław Ohrysko, Waldemar Pompe, Marta Szumańska, Anna ZatorskaGoldstein  
Students list:  (inaccessible to you)  
Examination: 
Course 
Examination
Lecture  Examination 
Copyright by University of Warsaw.