Strona główna
Do góry
O mnie


Mathematics 2

Faculty of Mechanical Engineering

Field of Study: Mechanical Engineering

Lectures 15 h, Practices 15 h


The range of the exam  (maximum 12 points)

  1. Calculate a given indefinite integral by substitution (List 3 Task 3).

  2. Calculate a given indefinite integral by parts (List 3 Task 2).

  3. Calculate a given indefinite integral of a rational function (List 3 Task 1).

The range of the second written test - maximum 15 points (10.01.2020).

1. Construct the graph of a given function using the algorithm (List 2 Task 5).

The range of the first written test - max. 20 points (08.11.2019)

  1. Calculate the derivative of a given function (List 0 Task 1) - 4 points.

  2. Write the equation of the tangent line and the normal line to the plot of a given function (List 0 Task 2) - 4 points.

  3. Calculate the intersection angles for graphs of given functions (List 0 Task 3) - 4 points.

  4. Using the differential calculate the linear approximation of a given number (List 0 Task 4) - 4 points.

  5. Using the de L'Hospital's rule calculate a given limit (List 1 Task 1 ex. (a) - (h)) - 4 points.

Lists of Tasks:








Useful Formulas:

Tables of sine, cosine, derivatives and integrals

Arguments of some complex numbers

Graphs of the main functions

Fundamental Functions

Greek letters with English pronunciation 

Trigonometric identities

Graph of functions sine and cosine

Hiperbolic identities

Derivatives of the most important functions

Graphing of functions using first and second derivatives


Lecture Topics:


1. Application of the Derivative to Construction Tangent and Normal  Lines and of the Differential to Linear Approximation of Numbers;  

2. Application of the Derivative to Calculation of Limits and Polynomial Approximation;

3. Graphing of Functions Using First and Second Derivatives;

4. Definition of the Indefinite Integral;

5. Integration by Parts;

6. Integration by Substitution;

7. Integration of Rational Functions;  

8. Integration of Trigonometric Functions;

9. Integration of Irrational Functions. 

10. Definition of the Riemann Integral;

11. Applications of the Definite Integral.

12. Improper Integral and its Applications.


Graphic Software:




1. E. Zakon, Mathematical Analysis I, The Trillia Group, 2004
2.2. B. S. Schroder, Mathematical Analysis: A Concise Introduction, JohnWiley&Sons,2008
3. 3.G.M. Fichtenholz, Course in the Differential and Integral Calculus vol. I, II, III, Nauka, Moscow, 1969.
4.4. B. Sikora, E. Łobos, A First Course in Calculus, Wydawnictwo Politechniki ¦l±skiej.