University of Warsaw - Central Authentication System
Strona główna

Differential and integral calculus

General data

Course ID: 1100-1INZ12
Erasmus code / ISCED: 11.101 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (unknown)
Course title: Differential and integral calculus
Name in Polish: Rachunek różniczkowy i całkowy
Organizational unit: Faculty of Physics
Course groups:
Course homepage:
ECTS credit allocation (and other scores): (not available) Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.

view allocation of credits
Language: Polish
Type of course:

obligatory courses

Prerequisites (description):

The aim of this lecture is to familiarize students with the basics of differential and integral calculus of one and two real variables.



Short description:

Nanostructure engineering: Differential and integral calculus

Full description:

The topics of the program of the course, more or less corresponding to each week, are:

1. Mathematical logic and set theory. Mathematical induction.

2. Functions, their properties and graphs.

3. Sequences, their (convergence) and limits.

4. Differentializability of functions, derivatives and their properties, and some computation methods.

5. Study of the graph of a function. Taylor series expansion.

6. The concept of primitive function, integration by parts and a list of basic examples. The definite integrals and their geometric interpretation.

7. Integration of rational and trigonometric functions.

8. Integration by substitution (especially Euler). The concept of Riemman's integral.

9. Improper integrals. The length of curves and the area of ​ figures.

10. Numerical and functional series, their (convergence) and limits.

11. Functions of several variables, their boundaries, partial and directional derivatives and gradient.

12. Free and constrained extrema of functions of several variables. Implicit unctions.

13. First order differential equations.

14. Higher order linear differential equations. Systems of ordinary differential equations. Multiple integrals. The integral of the Gauss function.

15. Several (optional) advanced topics. Recollection of the entire program. Simulations of the oral exam.

The structure of the entire course (lectured since 2018/19 by Dr. Giovanni Moreno) mimics the structure of previous years, lectured by Professor Kaminski.


0. G. MORENO, LECTURES NOTES (!DRAFT!), download here:

1. F. Leja, Rachunek różniczkowy i całkowy, PWN.

2. G. M. Fichtenholtz, Rachunek różniczkowy i całkowy, PWN (3 tomy).

3. D. A. McQuarrie, Matematyka dla przyrodników i inżynierów, PWN (3 tomy).

4. H. Rasiowa, Wstęp do matematyki współczesnej, PWN.

5. W. Krysicki i L. Włodarski, Analiza matematyczna w zadaniach, PWN (2 tomy).

A. Birkholc, Analiza matematyczna. Funkcje wielu zmiennych, PWN.

6. W. W. Jordan i P. Smith, Mathematical Techniques, Oxford.

7. K. F. Riley, M. P. Hobson I S. J. Bence, Mathematical Methods for Physics and Engineering, Cambridge.

8. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons.

9. G. B. Arfken i H. J. Weber, Mathematical Methods for Physicists, Elsevier.

Learning outcomes:

The aim of this lecture is:

- to educate students with mathematical intuition;

- to familiarize students with the basic mathematical methods used in science;

- to teach the use of mathematical formalisms.

After successful completion of the course, students:

- has the accounting expertise;

- determine the appropriate method of analysis of a mathematical problem.

Assessment methods and assessment criteria:

Explained in the subject webpage:

This course is not currently offered.
Course descriptions are protected by copyright.
Copyright by University of Warsaw.
Krakowskie Przedmieście 26/28
00-927 Warszawa
tel: +48 22 55 20 000
contact accessibility statement mapa serwisu USOSweb (2024-06-10)