Differential and Integral Calculus

Faculty of Mechanical Engineering

Field of Study: Mechanical Engineering

Lectures 15 h, Practices 15 h

Lists of Tasks:

	LIST 1
	LIST 2
	LIST 3
	LIST 4

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. Definite Integral and its Applications;

2. Basic Properties of n-dimensional Euclidean Space;

3. Partial Derivatives, Gradient, Total Differential, Directional Derivative, Tangent Plane;

4. Higher Order Derivatives, Hessian Matrix;

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

6. Extreme of Several Variable Function and Its Applications;

7. Introduction and First Definitions on Ordinary Differential Equations;

8. First Order Differential Equations (Separable Equations, Linear Nonhomogeneous Equations);

9. Higher Order Linear Equations (Homogeneous Linear Equations with Constant Coefficients and 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.