       Mathematics 2

Faculty of Mechanical Engineering

Field of Study: Mechanical Engineering

Lectures 15 h, Practices 15 h

Syllabus

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. LIST 0 LIST 1 LIST 2 LIST 3 LIST 4 LIST 5

Useful Formulas:  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  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:

Desmos

Bibligraphy

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 Śląskiej.