Strona główna
Do góry
Publikacje
O mnie
Kontakt
Konsultacje

 

Algebra 

List of tasks:

LIST 1

LIST 2

LIST 3

LIST 4

LIST 5

LIST 6

LIST 7

LIST 8

LIST 9

LIST 10

Useful formulas:

Tables of sine, cosine, derivatives and integrals

Arguments of some complex numbers

Graph of functions sine i cosine

Greek letters with English pronunciation 

Lecture Topics:

1. Foundations of Logic, Types of Proofs, Mathematical Induction;
2. Algebra of Sets and Subsets;
3. Algebraic Structures: Group, Ring, Algebraic Field;
4. Complex Numbers;
5. Polynomials and Rational Functions;
6. Matrices, Matrix Algebra
7. Square Matrices, Determinants, Laplace's Formula;
8. Adjugate Matrix, Inverse Matrix;
9. Systems of Linear Equations, Cramer's Rule;
10. Rouché–Capelli Theorem, Gauss–Jordan Elimination;
11. Vector Spaces, Subspaces;
12. Linear Independence; Bases of Vector Spaces; Changing of Bases;
13. Eigenvalues, Eigenvectors and Diagonalization;
14. Three-dimensional Analytic Geometry.

Graphic software:

GeoGebra

Desmos

Bibligraphy:

1.1. T. Jankowski, Linear algebra, Gdańsk: Politechnika Gdańska, 1997
2.2. Robert A. Beezer, A First Course in Linear Algebra, Waldron Edition, 2008
3.3. W. L. Perry, Elementary Linear Algebra, MacGraw-Hill, 1988
4.4. V.A. Ilyin, E.G. Poznyak, Linear Algebra, Mir Publishers, 1986
5.5. V.V. Konev. Linear Algebra, Vector Algebra and Analytical Geometry, Textbook. Tomsk: TPU Press, 2009
6.6. B. Sikora, E. Łobos, A First Course in Calculus, Wydawnictwo Politechniki Śląskiej

 

Mathematics I (Calculus I)

Lists of tasks:

LIST 0

LIST 1

LIST 2

LIST 3

LIST 4

LIST 5

Useful formulas:

Tables of sine, cosine, derivatives and integrals

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

Integrals of the most important functions

Formulas for the length of a curve, the lateral surface area and the volume of a solid of revolution

Lecture Topics  

1. Differentiation of One Variable Functions;

2. Applications of the Derivative to Geometry and Physics;

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. Definition of the Improper Integral.

 

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.

 

Mathematics II (Calculus II)

List of tasks:

LIST 1

LIST 2

LIST 3

LIST 4

Useful formulas:

Tables of sine, cosine, derivatives and integrals

Fundamental Functions

Integrals of the most important functions

Formulas for length of curve, the lateral surface area and the volume of a solid of revolution

Lecture Topics  

1. Repetition of Definite Integral and Its Applications, Lateral Area and Volume of Surface of Revolution;  

2.  Basic Properties of n-dimensional Euclidean Space;

3.  Limits of Several Variable Functions, Continuity;

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

5.  Higher Order Derivatives, Hessian Matrix;

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

7.  Extreme of Several Variable Function and Its Applications;  

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

9. Linear Nonhomogeneous Equation of First Order.

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

11. 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

 

5.Mathematics III (Calculus III)

List of tasks:

LIST 1

LIST 2

LIST 3

LIST 4

LIST 5

LIST 6

Useful formulas:

Tables of sine, cosine, derivatives and integrals

Triple Integral - Applications 

Lecture Topics

1. Definition and Main Properties of a Double Integral;

2. Change of a Double Integral to an Iterate Integral;

3. Change of Variables in a Double Integral;

4. Applications of a Double Integral to Geometry and Physics;

5. Definition and Main Properties of a Triple Integral;

6. Change of a Triple Integral to an Iterate Integral;

7. Change of Variables in a Triple Integral;

8. Applications of a Triple Integral to Geometry and Physics;

9. Parametric Form of Curves in 3-D Space;

10. Line Integral of a Scalar Fields, Definition, Properties and Change to Definite Integral;

11. Line Integral of a Vector Fields, Definition, Properties and Change to Definite Integral;

12. Potential of Vector Field, Path Independence;

13. Line Integral of a Vector Field in 2-D Space, Green’s Theorem;

14. Parametric Form of Surfaces;

15. Surface Integral of a Scalar Fields, Definition, Properties and Change to Double Integral;

16. Surface Integral of a Vector Fields, Definition, Properties and Change to Double Integral;

17. Rotation and Divergence, Gauss-Ostrogradsky’s and Stokes’ Theorems and Their Applications.

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
5.

 

Differential Equations 

List of tasks:

LIST 1

LIST 2

LIST 3

LIST 4

 

Useful formulas:

Tables of sine, cosine, derivatives and integrals

Lecture Topics

1. Introduction and First Definitions;

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

3. Linear Nonhomogeneous Equation First Order.

4. Exact and Non-Exact Equations, Integrating Factor technique;

5. Bernoulli and Riccati Equations.

6. Second Order Differential Equations (Reduction of Order, Euler-Cauchy Equations);

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

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

9. Systems of Differential Equations (Second Order Equations and Systems);

10. Euler's Method for Systems, Linear Homogenous and Nonhomogenous Systems Second Order;

11. Linear Homogenous and Nonhomogenous Systems Third Order;

12. Qualitative Analysis of Linear Systems.

 

Graphic software:

GeoGebra

Desmos

 

Bibligraphy

1. P. Blanchard, R. L. Devaney, G. R. Hall, Differential equations,  Cengage Learning, 2006;

2. J. C. Robinson, An introduction to ordinary differential equations, Cambridge University Press, 2004;

3. R. Bronson, E. J. Bredensteiner, Differential equations, McGraw-Hill Professional, 2003.

 

Statistics 

PROJECT

List of tasks:

LIST 1

LIST 2

LIST 3

LIST 4

LIST 5

Lecture Topics

 

1. Design of Statistical Experiments and Their Graphical Presentations;

2. Sampling;

3. Distributive Series;

4. Descriptive Statistics;

5. Random Variables and Characteristics;

6. Main Discrete and Continuous Distributions;

7. Point and Interval Estimation;

8. Hypothesis Testing, Significence and Power of Tests;

9. Parametric Statistical Hypothesis;

10. Non-parametric Statistical Hypothesis;

11. Correlation, Linear and Non-linear Regression;

12. Time Series.

 

 

Bibligraphy

1. D. C. Montgomery, G. C. Runger, Applied Statistics and Probability for Engineers,  John Wiley & Sons, 2003;

2. D.Wackerly, W.Mendenhall, R.L.Scheaffer, Mathematical Statistics with Applications, 2007;

3. L . Wasserman, All of Statistics: A Concise Course in Statistical Inference, Springer, Sciences + Business Media, 2004;

4. A. Aron, E. N. Aron, E. J. Coups, Statistics for the Behavioral and Social Sciences: A Brief Course, Pearson International Edition, 2008;

5. A. Franklin, Statistics: The Art and Science of Learning from Data, Pearson International Edition, 2009.

 

STATISTICA Electronic Textbook

Online Statistics: An Interactive Multimedia Course of Study

Graphic software:

GeoGebra

Desmos