       Differential and Integral Calculus

Faculty of Mechanical Engineering

Field of Study: Mechanical Engineering

Lectures 15 h, Practices 15 h

The range of the test no. 1- 29.11.2019 (maximum 12 points):

Task. 1. Calculate the surface area of a region limited by given curves (List 1 Task 3).

Task. 2. Calculate the length of a given curve (List 1 Task 4) or the lateral area of a given solid of revolution (List 1 Task 6).

Task. 3. Calculate the volume of a given solid of revolution (List 1 Task 5). LIST 1 LIST 2 LIST 3 LIST 4

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. Improper Integral and its Applications;

2. Basic Properties of n-dimensional Euclidean Space;

3Limits of Several Variable Functions, Continuity;

4Partial Derivatives, Gradient, Total Differential, Directional Derivative, Tangent Plane;

5.  Higher Order Derivatives, Hessian Matrix;

6.  Differential Calculus for Vector Valued Functions, Jacobian Matrix;

7Extreme of Several Variable Function and Its Applications;

8. Introduction and First Definitions on Ordinary Differential Equations;

9. First Order Differential Equations (Separable Equations, Homogeneous Equations);

10. Linear Nonhomogeneous Equation First Order;

11. Higher Order Linear Equations (Homogeneous Linear Equations with Constant Coefficients);

12. Non-Homogeneous Linear Equations, Method of Undetermined Coefficients, Method of Variation of Parameters, Linear Independence and the Wronskian.

Graphic Software:

GeoGebra

Desmos

Bibligraphy

1.1. 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.