|
|
|
| Algebra List of tasks:
Useful formulas:
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: 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 ¦l±skiej
Mathematics I (Calculus I) Lists of tasks:
Useful formulas:
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; 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: 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 ¦l±skiej.
Mathematics II (Calculus II) List of tasks:
Useful formulas:
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: 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 ¦l±skiej
5.Mathematics III (Calculus III) List of tasks:
Useful formulas:
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: 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 ¦l±skiej
5.
Differential Equations List of tasks:
Useful formulas:
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:
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
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,
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: |
