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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).

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. 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:




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 ¦l±skiej.