SylabUZ
| Course name | Mathematics |
| Course ID | 06.9-WM-MaPE-P-Mat-23 |
| Faculty | Faculty of Mechanical Engineering |
| Field of study | Management and Production Engineering |
| Education profile | academic |
| Level of studies | First-cycle studies leading to Engineer's degree |
| Beginning semester | winter term 2023/2024 |
| Semester | 1 |
| ECTS credits to win | 6 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Exam |
| Class | 30 | 2 | - | - | Credit with grade |
To equip students with knowledge concerning basic algebraic structures and with basic notions of mathematical analysis.
Secondary school mathematics.
Lecture
1.Elements of mathematical logic and set theory. (1h)
2.Complex numbers. Operations on complex numbers. Fundamental theorem of algebra. (2h)
3. Matrices. Operations on matrices. Determinant of the matrix. Inverse matrix. (2h)
4. Systems of linear equations. Cramer's theorem. Rank of a matrix . Kronecker Capelli's theorem. (3h)
5. System solving methods. Gauss elimination method. (2h)
6. Analytic geometry in space. Vectors. Dot product, Vector product and mixed product of vectors. (2h)
7. Planes and lines in space. (2h)
8. The definition of a number sequence. Limit of sequences. . (2h)
9 .Limit of function. Limit theorems. Asymptotes. (2h)
10. Continuity of function. Theorems about continuous functions. (2h)
11. The derivative of the function. Function differential. Higher order derivatives. (2h)
12. Derivative theorems. The de L'Hospital rule. (2h)
13. Function study. Monotonicity and extrema of functions. Convexity and inflection points of functions. (2h)
14. Integration of functions. (2h)
15. Calculation of definite integrals and its applications in geometry and physics. (2h)
Class
1. Elements of mathematical logic and set theory. (1h)
2. Complex numbers. Operations on complex numbers. Fundamental theorem of algebra. (2h)
3. Matrices. Operations on matrices. Determinant of the matrix. Inverse matrix. (2h)
4. Systems of linear equations. Cramer's theorem. Rank of a matrix . Kronecker Capelli's theorem. (2h)
5. System solving methods. Gauss elimination method. (2h)
6. Analytic geometry in space. Vectors. Dot product. Vector product and mixed product of vectors. (2h)
7. Planes and lines in space. (2h)
8. Class test. (1h)
9. The definition of a number sequence. Limit of sequences. . (2h)
10. Limit of function. Limit theorems. Asymptotes. (2h)
11. Continuity of function. Theorems about continuous functions. (1h)
12.The derivative of the function. Function differential. Higher order derivatives. (2h)
13. Derivative theorems. The de L'Hospital rule. (2h)
14. Function study. Monotonicity and extrema of functions. Convexity and inflection points of functions. (2h)
15. Integration of functions. (2h)
16. Calculation of definite integrals and its applications in geometry and physics. (2h)
17. Class test. (1h)
Lecture: conventional, problematic, presentation.
Classes: work in groups, solving typical tasks illustrating the subject matter of the subject. Exercises on applying the theory, solving problematic tasks.
| Outcome description | Outcome symbols | Methods of verification | The class form |
Classes: Average grades from tests and activity during classes.
Lecture: Exam/colloquium in written/oral form preceded by obtaining a pass from the exercises.
Final grade: The condition for passing the course is to pass all its forms. The final grade for completing the course is the arithmetic average of the grades for individual forms of classes.
Modified by dr Aleksandra Rzepka (last modification: 10-05-2023 21:52)
