*Conducted in term:*2020Z

*Erasmus code:*11.1

*ECTS credits:*10

*Language:*Polish

# Differential and integral calculus 1100-1ENRACHR1

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.

## Type of course

## Prerequisites (description)

## Course coordinators

## Mode

## 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 criteria

Explained in the subject webpage:

https://www.fuw.edu.pl/~gmoreno/RRiC

## Bibliography

0. G. MORENO, LECTURES NOTES (!DRAFT!), download here: https://drive.google.com/file/d/1R6M9ZAGTEPGWnqLaHTMPXWOQQkq2I73W/view?usp=sharing

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.

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

- Nuclear Power Engineering and Nuclear Chemistry, full time 3 year programme leading to B. Sc. Degree
- Physics, full-time, first cycle programme
- Nanostructure Engineering, first cycle programme

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: